diff --git a/crates/trios-phd/src/main.rs b/crates/trios-phd/src/main.rs index a4eb0aa6c5..510ced009c 100644 --- a/crates/trios-phd/src/main.rs +++ b/crates/trios-phd/src/main.rs @@ -810,6 +810,61 @@ fn mechanical_latex_fixes(s: &str) -> String { at_line_start = c == '\n'; i += 1; } + // 4. Wrap every standalone `\begin{tabular}...\end{tabular}` in + // `\resizebox{\linewidth}{!}{...}` so wide tables never overflow + // the text width. Idempotent: skips tables already inside + // `\resizebox{\linewidth}{!}{` or `\adjustbox{`. Does NOT touch + // `tabular*`, `tabularx`, or `longtable` — those have their own + // width discipline. + out = wrap_wide_tabulars(&out); + out +} + +/// Wrap each `\begin{tabular}{...}` ... `\end{tabular}` block in +/// `\resizebox{\linewidth}{!}{ ... }`. Idempotent. +fn wrap_wide_tabulars(s: &str) -> String { + let begin_tag = "\\begin{tabular}"; + let end_tag = "\\end{tabular}"; + let wrap_open = "\\resizebox{\\linewidth}{!}{%\n"; + let wrap_close = "\n}"; + let mut out = String::with_capacity(s.len() + 256); + let mut cursor = 0usize; + let bytes = s.as_bytes(); + while let Some(rel) = s[cursor..].find(begin_tag) { + let abs = cursor + rel; + // Reject `\begin{tabular*}` and `\begin{tabularx}` — different envs. + let after = abs + begin_tag.len(); + if after < bytes.len() && (bytes[after] == b'*' || bytes[after] == b'x') { + out.push_str(&s[cursor..after]); + cursor = after; + continue; + } + // Find matching `\end{tabular}`. + let Some(end_rel) = s[after..].find(end_tag) else { + out.push_str(&s[cursor..]); + return out; + }; + let end_abs = after + end_rel + end_tag.len(); + // Idempotency: if the ~80 chars before `\begin{tabular}` already + // contain `\resizebox{\linewidth}{!}{` with an open brace count > + // close brace count, this tabular is already wrapped. + let look_back_start = abs.saturating_sub(120); + let head = &s[look_back_start..abs]; + let already_resized = head.contains("\\resizebox{\\linewidth}{!}{") + && head.matches('{').count() > head.matches('}').count(); + let already_adjust = head.contains("\\adjustbox{") + && head.matches('{').count() > head.matches('}').count(); + out.push_str(&s[cursor..abs]); + if already_resized || already_adjust { + out.push_str(&s[abs..end_abs]); + } else { + out.push_str(wrap_open); + out.push_str(&s[abs..end_abs]); + out.push_str(wrap_close); + } + cursor = end_abs; + } + out.push_str(&s[cursor..]); out } diff --git a/docs/phd/appendix/A-catalogue.tex b/docs/phd/appendix/A-catalogue.tex index adcc3378ec..f365546661 100644 --- a/docs/phd/appendix/A-catalogue.tex +++ b/docs/phd/appendix/A-catalogue.tex @@ -32,7 +32,7 @@ \begin{figure}[H] \centering -\includegraphics[width=0.92\textwidth,keepaspectratio]{app-a-cover-abstract.png} +\includegraphics[width=0.92\textwidth,keepaspectratio]{A-catalogue.jpg} \caption{Abstract cover art for Appendix A.} \label{fig:appA-cover} \end{figure} @@ -2286,7 +2286,7 @@ \section{42-Formula Summary (Original Catalogue)} \begin{figure}[H] \centering -\includegraphics[width=0.92\textwidth,keepaspectratio]{app-a-cover-abstract.png} +\includegraphics[width=0.92\textwidth,keepaspectratio]{A-catalogue.jpg} \caption{Trinity Identity $\varphi^{2}+\varphi^{-2}=3$ --- algebraic anchor for all 42 formulae.} \label{fig:appA-42} diff --git a/docs/phd/appendix/B-falsification.tex b/docs/phd/appendix/B-falsification.tex index c8cd86d9b7..89d7c923bd 100644 --- a/docs/phd/appendix/B-falsification.tex +++ b/docs/phd/appendix/B-falsification.tex @@ -9,7 +9,7 @@ \chapter*{Appendix B: Falsification Ledger — Popperian Audit Across 33 Chapter \begin{figure}[H] \centering -\includegraphics[width=0.92\textwidth,keepaspectratio]{app-b-golden-ledger.png} +\includegraphics[width=0.92\textwidth,keepaspectratio]{B-falsification.jpg} \end{figure} \addcontentsline{toc}{chapter}{Appendix B: Falsification Ledger} @@ -153,6 +153,7 @@ \section*{B.3 — Bayesian Model Evidence Cross-Checks} the monograph. Under Jeffreys' scale: \begin{center} +\resizebox{\linewidth}{!}{% \begin{tabular}{ll} \hline $\mathrm{BF}_{10}$ & Evidence for $H_1$ \\ @@ -164,6 +165,7 @@ \section*{B.3 — Bayesian Model Evidence Cross-Checks} $>100$ & Decisive \\ \hline \end{tabular} +} \end{center} \begin{description} @@ -210,6 +212,7 @@ \subsection*{B.4.1 — Bonferroni Correction Across IGLA Seed Canon} \noindent\textbf{Seed audit table:} \begin{center} +\resizebox{\linewidth}{!}{% \begin{tabular}{cccc} \hline Seed & Champion BPB & Baseline BPB & $p$-value (one-tailed) \\ @@ -220,6 +223,7 @@ \subsection*{B.4.1 — Bonferroni Correction Across IGLA Seed Canon} 123 & 2.2598 & 2.31 & $0.0093$ \\ \hline \end{tabular} +} \end{center} \noindent All four per-seed $p$-values are $< 0.0125$. The Bonferroni-corrected @@ -256,6 +260,7 @@ \section*{B.5 — Pre-Registration Manifest} canonical URL for each chapter's pre-registered protocol. \begin{center} +\resizebox{\linewidth}{!}{% \begin{tabular}{clp{6cm}} \hline Chapter & Slug & Pre-registration URL \\ @@ -286,6 +291,7 @@ \section*{B.5 — Pre-Registration Manifest} \texttt{https://osf.io/preprints/trinity-ch29} \\ \hline \end{tabular} +} \end{center} \noindent The master pre-registration manifest (including version hashes of @@ -853,6 +859,7 @@ \section*{B.10 — R5 Honesty Audit: Every Admitted Theorem} referenced in the monograph. \begin{center} +\resizebox{\linewidth}{!}{% \begin{tabular}{p{3.5cm}p{4cm}p{4cm}c} \hline \textbf{Theorem / Lemma} & \textbf{Coq File} & \textbf{Reason Admitted} & @@ -872,6 +879,7 @@ \section*{B.10 — R5 Honesty Audit: Every Admitted Theorem} $\ln(9)/\ln(2)$ requires \texttt{Coq.Interval} & Partial \\ \hline \end{tabular} +} \end{center} \noindent \textbf{``Blocks Claim?'' legend:} @@ -1166,6 +1174,7 @@ \section*{B.15 — Summary Table: All Predictions} % ============================================================ \begin{center} +\resizebox{\linewidth}{!}{% \begin{tabular}{p{1.2cm}p{2cm}p{4cm}p{2.2cm}c} \hline \textbf{ID} & \textbf{Chapter} & \textbf{Prediction (brief)} & @@ -1200,6 +1209,7 @@ \section*{B.15 — Summary Table: All Predictions} \multicolumn{4}{l}{\textit{Total: 11 Standing, 4 Partially Falsified, 10 Pending, 0 Falsified}} & \\ \hline \end{tabular} +} \end{center} % ============================================================ @@ -1303,6 +1313,7 @@ \section*{B.18 — Connection to Coq Falsification Witnesses} \noindent The relevant falsification witnesses are: \begin{center} +\resizebox{\linewidth}{!}{% \begin{tabular}{lll} \hline \textbf{Coq File} & \textbf{Witness} & \textbf{What it demonstrates} \\ @@ -1321,6 +1332,7 @@ \section*{B.18 — Connection to Coq Falsification Witnesses} $\sqrt{2}$ ratio does not match E8 spectrum \\ \hline \end{tabular} +} \end{center} \noindent These witnesses are the machine-checkable counterparts of the @@ -1517,6 +1529,7 @@ \section*{B.23 — IGLA Assertion Traceability (L-R14)} L-R14 traces. \begin{center} +\resizebox{\linewidth}{!}{% \begin{tabular}{p{3cm}p{1.8cm}p{4.5cm}p{2cm}} \hline \textbf{Constant} & \textbf{Value} & \textbf{Derivation} & \textbf{Coq source} \\ @@ -1545,6 +1558,7 @@ \section*{B.23 — IGLA Assertion Traceability (L-R14)} \texttt{gf16\_precision} \\ \hline \end{tabular} +} \end{center} \noindent All constants marked with a $\varphi$-derivation are representable diff --git a/docs/phd/appendix/C-golden-benchmark.tex b/docs/phd/appendix/C-golden-benchmark.tex index 2932da6d1c..588c467b7e 100644 --- a/docs/phd/appendix/C-golden-benchmark.tex +++ b/docs/phd/appendix/C-golden-benchmark.tex @@ -13,7 +13,7 @@ \chapter*{Appendix C: Golden Benchmark --- IGLA Protocol \& \begin{figure}[H] \centering -\includegraphics[width=0.92\textwidth,keepaspectratio]{app-c-acknowledgments.png} +\includegraphics[width=0.92\textwidth,keepaspectratio]{C-golden-benchmark.jpg} \caption*{Figure --- Golden Benchmark --- GF4/GF8/GF16 reference tables.} \end{figure} @@ -140,6 +140,7 @@ \section*{C.2 GF4 --- 4-Bit GoldenFloat} \begin{table}[h] \centering +\resizebox{\linewidth}{!}{% \begin{tabular}{rrrr} \toprule \textbf{Code} & \textbf{Value} & \textbf{φ-exponent} & \textbf{Note} \\ @@ -155,6 +156,7 @@ \section*{C.2 GF4 --- 4-Bit GoldenFloat} 1xxx & neg. & --- & Sign bit = 1 \\ \bottomrule \end{tabular} +} \caption{GF4: 8 positive values + sign. Range [$-$6.854, 6.854]. Zero-point-free.} \end{table} @@ -178,6 +180,7 @@ \section*{C.3 GF8 --- 8-Bit GoldenFloat} \begin{table}[h] \centering +\resizebox{\linewidth}{!}{% \begin{tabular}{rrr} \toprule \textbf{Exponent field (4 bits)} & \textbf{Positive values} & @@ -196,6 +199,7 @@ \section*{C.3 GF8 --- 8-Bit GoldenFloat} $\varphi^{8}$ & 46.979 & max \\ \bottomrule \end{tabular} +} \caption{GF8: 4-bit exponent, 3-bit mantissa (ternary encoded), 1-bit sign. Total: 256 encodings. Zero and NaN reserved.} \end{table} @@ -203,6 +207,7 @@ \section*{C.3 GF8 --- 8-Bit GoldenFloat} \textbf{GF8 benchmark results} (sealed \texttt{STROBE\_SEED=1597}): \begin{table}[h] \centering +\resizebox{\linewidth}{!}{% \begin{tabular}{lrrl} \toprule \textbf{Format} & \textbf{Bits} & \textbf{BPB} & \textbf{Status} \\ @@ -213,6 +218,7 @@ \section*{C.3 GF8 --- 8-Bit GoldenFloat} FP8 (E4M3)& 8 & 2.21 & GF8 wins ($\Delta=0.02$) \\ \bottomrule \end{tabular} +} \caption{GF8 BPB on WikiText-103. All runs: same tokenizer, same hardware, \texttt{STROBE\_SEED=1597}. Zenodo DOI 10.5281/zenodo.19227877.} @@ -236,6 +242,7 @@ \section*{C.4 GF16 --- 16-Bit GoldenFloat (Champion Format)} \begin{table}[h] \centering +\resizebox{\linewidth}{!}{% \begin{tabular}{lrr} \toprule \textbf{Field} & \textbf{GF16} & \textbf{BF16 (reference)} \\ @@ -255,6 +262,7 @@ \section*{C.4 GF16 --- 16-Bit GoldenFloat (Champion Format)} Gate-3 (BPB $<$ 1.85) & \textbf{NOT MET} & N/A \\ \bottomrule \end{tabular} +} \caption{GF16 champion configuration. BPB = bits-per-byte on sealed test set (\texttt{STROBE\_SEED=1597}, WikiText-103, 1B tokens). Gate-2 not met --- disclosed per R-rule and Clause~F-1 of App.~B.} @@ -263,6 +271,7 @@ \section*{C.4 GF16 --- 16-Bit GoldenFloat (Champion Format)} \textbf{GF16 full comparison grid:} \begin{table}[h] \centering +\resizebox{\linewidth}{!}{% \begin{tabular}{lrrrl} \toprule \textbf{Format} & \textbf{Bits} & \textbf{BPB} & @@ -277,6 +286,7 @@ \section*{C.4 GF16 --- 16-Bit GoldenFloat (Champion Format)} GF4 & 4 & 2.81 & $+$0.57 & 4-bit penalty \\ \bottomrule \end{tabular} +} \caption{Full format comparison at matched compute budgets. GF16 is the 4-bit champion; GF8 meets Gate-2. Both archived at Zenodo 10.5281/zenodo.19227877.} @@ -296,6 +306,7 @@ \section*{C.5 Range $\times$ Precision Pareto Frontier} \begin{table}[h] \centering +\resizebox{\linewidth}{!}{% \begin{tabular}{lrrcc} \toprule \textbf{Format} & \textbf{log$_\varphi$(max)} & \textbf{BPB} & @@ -309,6 +320,7 @@ \section*{C.5 Range $\times$ Precision Pareto Frontier} BF16 & ---& 2.0500 & \checkmark (16-bit) & 16 \\ \bottomrule \end{tabular} +} \caption{Pareto frontier. GF formats dominate INT formats of equal bit-width on Objective~2. Full Pareto tables in Chapter~\ref{ch:9} (Table~9.2) and archived in Zenodo (App.~H).} @@ -320,6 +332,7 @@ \section*{C.6 Gate Thresholds Summary} \begin{table}[h] \centering +\resizebox{\linewidth}{!}{% \begin{tabular}{lrrl} \toprule \textbf{Gate} & \textbf{Threshold (BPB)} & \textbf{Champion BPB} & @@ -330,6 +343,7 @@ \section*{C.6 Gate Thresholds Summary} Gate-3 & $< 1.85$ & 2.2393 & \textbf{NOT MET} --- future work \\ \bottomrule \end{tabular} +} \caption{Gate thresholds. Non-achievement of Gate-2 and Gate-3 is explicitly disclosed per R5 (honesty rule) and Popper Clause~F-1 (App.~B).} @@ -348,6 +362,7 @@ \section*{C.7 Champion Fingerprint} \begin{table}[h] \centering +\resizebox{\linewidth}{!}{% \begin{tabular}{ll} \toprule \textbf{Parameter} & \textbf{Value} \\ @@ -370,6 +385,7 @@ \section*{C.7 Champion Fingerprint} \varphi^{-4} + \varepsilon$ (INV-2) \\ \bottomrule \end{tabular} +} \caption{Champion fingerprint. Every numeric constant is either $\varphi$-derived or directly verified by an INV assertion in \texttt{assertions/igla\_assertions.json} (R6, L-R14).} @@ -441,6 +457,7 @@ \subsection*{C.8.2 Gate-2 Trajectory Table} \begin{table}[h] \centering +\resizebox{\linewidth}{!}{% \begin{tabular}{rrrrl} \toprule \textbf{Run} & \textbf{Seed} & \textbf{Step} & @@ -453,6 +470,7 @@ \subsection*{C.8.2 Gate-2 Trajectory Table} W-005 & 123 & 85\,000 & 2.2100 & Gate-2 buffer \\ \bottomrule \end{tabular} +} \caption{Gate-2 trajectory. Run W-004 (champion, seed 43, step 81\,000, BPB 2.1919) is the first run to satisfy Gate-2 on GF8. The GF16 champion (commit \texttt{cd91c45}) achieves BPB $= 2.1919$ which MET @@ -497,6 +515,7 @@ \subsection*{C.9.1 ASHA Configuration} \begin{table}[h] \centering +\resizebox{\linewidth}{!}{% \begin{tabular}{ll} \toprule \textbf{Parameter} & \textbf{Value} \\ @@ -511,6 +530,7 @@ \subsection*{C.9.1 ASHA Configuration} Victory condition & $\text{BPB} < 1.85$ on 3 distinct seeds \\ \bottomrule \end{tabular} +} \caption{Gate-3 ASHA configuration. Rung steps derived via $r_k = r_{\min} \cdot \eta_{\text{ASHA}}^k$.} \end{table} @@ -604,6 +624,7 @@ \subsection*{C.10.3 Seed Canon Results Table} \begin{table}[h] \centering +\resizebox{\linewidth}{!}{% \begin{tabular}{rrrrl} \toprule \textbf{Seed} & \textbf{Step} & \textbf{BPB (GF16)} & @@ -620,6 +641,7 @@ \subsection*{C.10.3 Seed Canon Results Table} Champion (seed 43) & 81\,000 & 2.2393 & 2.1919 & non-canonical \\ \bottomrule \end{tabular} +} \caption{IGLA seed canon results at step 81\,000. BPB computed on WikiText-103 sealed test set (\texttt{STROBE\_SEED=1597}).} \end{table} @@ -657,6 +679,7 @@ \subsection*{C.11.2 Calibration Results} \begin{table}[h] \centering +\resizebox{\linewidth}{!}{% \begin{tabular}{rrrrr} \toprule \textbf{Seed} & \textbf{Step} & \textbf{BPB tiny\_sh.} & @@ -669,6 +692,7 @@ \subsection*{C.11.2 Calibration Results} 123 & 81\,000 & 1.4756 & 2.2611 & 0.653 \\ \bottomrule \end{tabular} +} \caption{BPB calibration on \texttt{tiny\_shakespeare} vs WikiText-103. The ratio $\approx 0.65$ is consistent across seeds, confirming no proxy collapse. A JEPA-proxy collapse would give ratio $\ll 0.1$.} @@ -701,6 +725,7 @@ \subsection*{C.12.1 Reference Champion} \begin{table}[h] \centering +\resizebox{\linewidth}{!}{% \begin{tabular}{lll} \toprule \textbf{Parameter} & \textbf{Champion (cd91c45)} & @@ -715,6 +740,7 @@ \subsection*{C.12.1 Reference Champion} GF16 KAT & yes & yes \\ \bottomrule \end{tabular} +} \caption{Champion vs reference champion. The identical BPB values are a \emph{coincidence} arising from the discrete nature of BPB evaluation at 4 decimal places; the two configurations differ in @@ -735,6 +761,7 @@ \subsection*{C.12.2 Paired-$t$ Test Design} \begin{table}[h] \centering +\resizebox{\linewidth}{!}{% \begin{tabular}{rrrr} \toprule \textbf{Seed} & \textbf{BPB Champion} & \textbf{BPB Reference} & @@ -749,6 +776,7 @@ \subsection*{C.12.2 Paired-$t$ Test Design} Std $s_d$ & & & 0.0012 \\ \bottomrule \end{tabular} +} \caption{Paired differences $d_i$ between champion and reference champion, over the seed canon. Negative values indicate the champion (cd91c45) is \emph{better} (lower BPB).} @@ -826,6 +854,7 @@ \subsection*{C.13.3 Full Hyperparameter Table} \begin{table}[h] \centering +\resizebox{\linewidth}{!}{% \begin{tabular}{llll} \toprule \textbf{Hyperparameter} & \textbf{Symbol} & \textbf{Value} & @@ -852,6 +881,7 @@ \subsection*{C.13.3 Full Hyperparameter Table} & exact \\ \bottomrule \end{tabular} +} \caption{Full φ-derived hyperparameter schedule. Every value is either an integer multiple of a Lucas number, an integer power of φ, or a hard-bounded constant derived from the GF16 precision floor (INV-3).} @@ -873,6 +903,7 @@ \subsection*{C.14.1 Forbidden Values Table} \begin{table}[h] \centering +\resizebox{\linewidth}{!}{% \begin{tabular}{llll} \toprule \textbf{Parameter} & \textbf{Forbidden Value} & \textbf{Reason} & @@ -898,6 +929,7 @@ \subsection*{C.14.1 Forbidden Values Table} & INV-2 (advisory) \\ \bottomrule \end{tabular} +} \caption{Forbidden values audit. ``Hard'' forbids (prune threshold $2.65$, warmup $< 4000$, $d_\text{model} < 256$, lr outside range) are enforced by \texttt{validate\_config()} in @@ -974,6 +1006,7 @@ \subsection*{C.15.2 Rung State Table (Champion Run)} \begin{table}[h] \centering +\resizebox{\linewidth}{!}{% \begin{tabular}{rrrrl} \toprule \textbf{Rung} & \textbf{Step} & \textbf{Trials in} & @@ -985,6 +1018,7 @@ \subsection*{C.15.2 Rung State Table (Champion Run)} 3 & 71\,818 & 2 & 1 & 2.21 \\ \bottomrule \end{tabular} +} \caption{Rung state for the champion run (seed 43, $d_\text{model}=828$, $\eta=0.003$). The champion is the sole survivor at rung 3 and was allowed to continue to step 81\,000 for final evaluation.} @@ -1039,6 +1073,7 @@ \subsection*{C.16.2 Alert Levels} \begin{table}[h] \centering +\resizebox{\linewidth}{!}{% \begin{tabular}{lll} \toprule \textbf{Level} & \textbf{Condition} & \textbf{Action} \\ @@ -1051,6 +1086,7 @@ \subsection*{C.16.2 Alert Levels} as INV-1 violation) \\ \bottomrule \end{tabular} +} \caption{Plateau-alert levels. The ABORT level triggers the ASHA pruning rule as if the trial's BPB had exceeded the prune threshold.} \end{table} @@ -1099,6 +1135,7 @@ \subsection*{C.17.2 Ablation Results} \begin{table}[h] \centering +\resizebox{\linewidth}{!}{% \begin{tabular}{llrrr} \toprule \textbf{Ablation} & \textbf{Change} & \textbf{BPB} & @@ -1133,6 +1170,7 @@ \subsection*{C.17.2 Ablation Results} & 2.2648 & --- & --- \\ \bottomrule \end{tabular} +} \caption{Ablation matrix. BPB values are means over seed canon $\mathcal{S}$. Significance tested by paired $t$-test against A-0 (champion), $n=4$, $\alpha=0.05$. ``Sig.?'' column indicates whether @@ -1329,6 +1367,7 @@ \subsection*{C.18.4 Connection to IGLA Empirical Results} \begin{table}[h] \centering +\resizebox{\linewidth}{!}{% \begin{tabular}{rr} \toprule \textbf{Step} & \textbf{BPB (champion, seed 43)} \\ @@ -1340,6 +1379,7 @@ \subsection*{C.18.4 Connection to IGLA Empirical Results} 81\,000 & 2.19 \\ \bottomrule \end{tabular} +} \caption{Champion BPB trajectory at ASHA rung steps. BPB is monotonically non-increasing, consistent with Theorem~\ref{thm:benchmark-monotonicity}.} @@ -1413,6 +1453,7 @@ \subsection*{C.19.2 Pre-Registered Wikitext-103 Tests} \begin{table}[h] \centering +\resizebox{\linewidth}{!}{% \begin{tabular}{lp{7cm}l} \toprule \textbf{Test ID} & \textbf{Description} & \textbf{Claim tested} \\ @@ -1431,6 +1472,7 @@ \subsection*{C.19.2 Pre-Registered Wikitext-103 Tests} & Gate-2 claim \\ \bottomrule \end{tabular} +} \caption{Pre-registered Wikitext-103 falsification tests. All tests use the sealed test split (\texttt{STROBE\_SEED=1597}). Test failure must be reported in \texttt{assertions/hive\_honey.jsonl} and in the @@ -1445,6 +1487,7 @@ \subsection*{C.19.3 Pre-Registered The Pile Tests} \begin{table}[h] \centering +\resizebox{\linewidth}{!}{% \begin{tabular}{lp{7cm}l} \toprule \textbf{Test ID} & \textbf{Description} & \textbf{Claim tested} \\ @@ -1461,6 +1504,7 @@ \subsection*{C.19.3 Pre-Registered The Pile Tests} & β-schedule generalisation \\ \bottomrule \end{tabular} +} \caption{Pre-registered The Pile falsification tests. BPB thresholds for The Pile are set higher than WikiText-103 thresholds to account for the out-of-distribution gap ($\approx +0.3$ BPB typical for models @@ -1471,6 +1515,7 @@ \subsection*{C.19.4 Corroboration Record} \begin{table}[h] \centering +\resizebox{\linewidth}{!}{% \begin{tabular}{lll} \toprule \textbf{Test} & \textbf{Status} & \textbf{Evidence} \\ @@ -1486,6 +1531,7 @@ \subsection*{C.19.4 Corroboration Record} PL-1--5 & \textbf{Pending} & Future work (Gate-3 campaign) \\ \bottomrule \end{tabular} +} \caption{Corroboration record for pre-registered falsification tests. ``Pending'' tests are planned for the Gate-3 campaign (post-dissertation). ``Passed'' tests were conducted with pre-registered protocols; no @@ -1504,6 +1550,7 @@ \section*{C.20 φ-Anchor Summary and Closing Remarks} \begin{table}[h] \centering +\resizebox{\linewidth}{!}{% \begin{tabular}{llll} \toprule \textbf{Constant} & \textbf{Value} & \textbf{φ-derivation} & @@ -1533,6 +1580,7 @@ \section*{C.20 φ-Anchor Summary and Closing Remarks} Champion BPB (GF8) & 2.1919 & measured & INV-1 \\ \bottomrule \end{tabular} +} \caption{Complete φ-derivation cross-reference for all numeric constants in Appendix~C. All constants are traceable to a Coq invariant assertion (\texttt{assertions/igla\_assertions.json}) or are dimensionless integers.} diff --git a/docs/phd/appendix/D-golden-mirror.tex b/docs/phd/appendix/D-golden-mirror.tex index 4aec2dfb03..288fb6fb1c 100644 --- a/docs/phd/appendix/D-golden-mirror.tex +++ b/docs/phd/appendix/D-golden-mirror.tex @@ -9,7 +9,7 @@ \chapter*{Appendix D: Golden Mirror — Reflection Symmetry of the Golden Ratio} \begin{figure}[H] \centering -\includegraphics[width=0.92\textwidth,keepaspectratio]{app-d-reproducibility-scripts.png} +\includegraphics[width=0.92\textwidth,keepaspectratio]{D-golden-mirror.jpg} \end{figure} \addcontentsline{toc}{chapter}{Appendix D: Golden Mirror} @@ -345,6 +345,7 @@ \subsection*{D.5.1 The Kepler Triangle} \begin{table}[h] \centering \caption{Kepler triangle dimensions} +\resizebox{\linewidth}{!}{% \begin{tabular}{lll} \toprule Side & Length & Squared \\ @@ -354,6 +355,7 @@ \subsection*{D.5.1 The Kepler Triangle} Hypotenuse $c$ & $\varphi$ & $\varphi^2 = \varphi + 1$ \\ \bottomrule \end{tabular} +} \end{table} The area of $\Delta_K$ is $A_K = \tfrac{1}{2}\cdot 1 \cdot \sqrt{\varphi} = \tfrac{\sqrt{\varphi}}{2}$. @@ -416,6 +418,7 @@ \subsection*{D.5.4 Continued-Fraction Reflection: $x \leftrightarrow \varphi^{- \begin{table}[h] \centering \caption{Orbits of the reflection $r: x\mapsto\varphi^{-1}/x$ on golden powers} +\resizebox{\linewidth}{!}{% \begin{tabular}{lll} \toprule $x$ & $r(x) = \varphi^{-1}/x$ & $x\cdot r(x)$ \\ @@ -428,6 +431,7 @@ \subsection*{D.5.4 Continued-Fraction Reflection: $x \leftrightarrow \varphi^{- $\varphi^{-2}$ & $\varphi$ & $\varphi^{-1}$ \\ \bottomrule \end{tabular} +} \end{table} \noindent The reflection $r$ is therefore a pairing on golden powers: @@ -508,6 +512,7 @@ \subsection*{D.6.4 Kite-Dart Inflation Table} \begin{table}[h] \centering \caption{Kite-dart counts under P2 inflation: $\mathbf{v}_{n+1} = M_{\mathrm{P2}}\,\mathbf{v}_n$} +\resizebox{\linewidth}{!}{% \begin{tabular}{rrrr} \toprule $n$ & Kites $K_n$ & Darts $D_n$ & $K_n/D_n$ \\ @@ -523,6 +528,7 @@ \subsection*{D.6.4 Kite-Dart Inflation Table} $\infty$ & $F_{n+2}$ & $F_{n+1}$ & $\varphi\approx 1.618$ \\ \bottomrule \end{tabular} +} \end{table} % ───────────────────────────────────────────────────────────────────────────── @@ -677,6 +683,7 @@ \subsection*{D.8.3 Lucas Negative-Index Reflection Table} \begin{table}[h] \centering \caption{Lucas sequence: positive, zero, and reflected negative indices} +\resizebox{\linewidth}{!}{% \begin{tabular}{rrrr} \toprule $n$ & $L_n$ & $L_{-n}$ & $(-1)^n L_n$ \\ @@ -692,6 +699,7 @@ \subsection*{D.8.3 Lucas Negative-Index Reflection Table} 8 & 47 & 47 & 47 \\ \bottomrule \end{tabular} +} \end{table} \noindent The reflection symmetry $L_{-n} = (-1)^n L_n$ is the Lucas-sequence @@ -867,6 +875,7 @@ \subsection*{D.9.4 Worked Example: VSA Golden-Mirror Cleanup} \begin{table}[h] \centering \caption{VSA golden-mirror operations on $z = a+b\varphi$} +\resizebox{\linewidth}{!}{% \begin{tabular}{lll} \toprule Operation & Result vector & Encodes \\ @@ -878,6 +887,7 @@ \subsection*{D.9.4 Worked Example: VSA Golden-Mirror Cleanup} $(\mathbf{g}+\hat{\sigma})/2$ & $(a+b/2)\mathbf{e}_1$ & $\tfrac{z+\bar{z}}{2}$ \\ \bottomrule \end{tabular} +} \end{table} % ───────────────────────────────────────────────────────────────────────────── @@ -939,6 +949,7 @@ \section*{D.9.6 R6 Audit of Numeric Constants in This Appendix} \begin{table}[h] \centering \caption{R6 audit: all numeric constants in Appendix D} +\resizebox{\linewidth}{!}{% \begin{tabular}{llll} \toprule Symbol & Value & R6 derivation & Section \\ @@ -958,6 +969,7 @@ \section*{D.9.6 R6 Audit of Numeric Constants in This Appendix} $\varphi^{-6}\approx 0.056$ & $\varphi^{-6}$ & $\varphi^6$ power & D.9.5 \\ \bottomrule \end{tabular} +} \end{table} All constants pass R6. No free parameters are introduced in this appendix. @@ -972,6 +984,7 @@ \section*{D.10 R14 Coq Map} \begin{table}[h] \centering \caption{R14 Coq citation map for Appendix D} +\resizebox{\linewidth}{!}{% \begin{tabular}{lllll} \toprule Theorem/Lemma & Label & Coq file & Coq theorem name & Status \\ @@ -985,6 +998,7 @@ \section*{D.10 R14 Coq Map} \texttt{lucas\_2\_eq\_3} (anchor) & D.8.5 & \texttt{gf16\_precision.v} & \texttt{lucas\_2\_eq\_3} & \textbf{Proven} \\ \bottomrule \end{tabular} +} \end{table} \noindent Note: \texttt{lucas\_2\_eq\_3} is the only fully Proven theorem in this @@ -1215,6 +1229,7 @@ \subsection*{D.15.2 Anchor Modulo Small Primes} \begin{table}[h] \centering \caption{The anchor $\varphi^2+\varphi^{-2}=3$ modulo small primes (informal)} +\resizebox{\linewidth}{!}{% \begin{tabular}{rll} \toprule $p$ & $L_2 \bmod p$ & Comment \\ @@ -1228,6 +1243,7 @@ \subsection*{D.15.2 Anchor Modulo Small Primes} 16 & 3 & GF(16) anchor \\ \bottomrule \end{tabular} +} \end{table} \noindent The anchor $3 = L_2$ is preserved modulo any prime $\geq 5$, and equals @@ -1311,6 +1327,7 @@ \subsection*{D.18.1 Mirror Multiplication Table in $\mathbb{Z}[\varphi]$} \begin{table}[h] \centering \caption{Products $z_i \cdot z_j$ in $\mathbb{Z}[\varphi]$ with mirror partners} +\resizebox{\linewidth}{!}{% \begin{tabular}{lllll} \toprule $z$ & $\sigma(z)$ & $z \cdot \sigma(z) = N(z)$ & $z + \sigma(z)$ & $z - \sigma(z)$ \\ @@ -1323,6 +1340,7 @@ \subsection*{D.18.1 Mirror Multiplication Table in $\mathbb{Z}[\varphi]$} $L_n + F_n\varphi$ & $(L_n+F_n)-F_n\varphi$ & $L_n^2+L_n F_n - F_n^2 = (-1)^n\cdot 5$ & $2L_n+F_n$ & $2F_n\varphi-F_n$ \\ \bottomrule \end{tabular} +} \end{table} The last row uses the identity $L_n^2 - L_n F_n - F_n^2 = \ldots$; the @@ -1423,7 +1441,7 @@ \section*{D.20 Glossary of Mirror Terminology} \item[$\psi = -\varphi^{-1}$] The algebraic conjugate of $\varphi$; equals $(1-\sqrt5)/2 \approx -0.618$. \item[Pisano period] The period of $L_n \bmod m$; for $m=16$, equals $24$. - \item[$\mathbb{Z}[\varphi]$] The ring of golden integers $\{a+b\varphi\mid a,b\in\mathbb{Z}\}$; + \item[\(\mathbb{Z}{[}\varphi{]}\)] The ring of golden integers $\{a+b\varphi\mid a,b\in\mathbb{Z}\}$; the ring of integers of $\mathbb{Q}(\sqrt5)$. \end{description} @@ -1434,6 +1452,7 @@ \section*{D.21 Symbol Index for Appendix D} \begin{table}[h] \centering \caption{Symbols used in Appendix D (R6 certified)} +\resizebox{\linewidth}{!}{% \begin{tabular}{lll} \toprule Symbol & Meaning & R6 source \\ @@ -1453,6 +1472,7 @@ \section*{D.21 Symbol Index for Appendix D} $\pi(m)$ & Pisano period of Lucas mod $m$ & integer \\ \bottomrule \end{tabular} +} \end{table} % ───────────────────────────────────────────────────────────────────────────── @@ -1512,6 +1532,7 @@ \subsection*{What Would Refute the Mirror-Conjugate Closure Theorem} \subsection*{Corroboration Record} +\resizebox{\linewidth}{!}{% \begin{tabular}{lll} \toprule Date & Evidence & Status \\ @@ -1522,6 +1543,7 @@ \subsection*{Corroboration Record} pending & \texttt{Coq.Interval} full proof & Reusable (future) \\ \bottomrule \end{tabular} +} % ───────────────────────────────────────────────────────────────────────────── \section*{D.24 Final Anchor Verification} diff --git a/docs/phd/appendix/E-lexicon.tex b/docs/phd/appendix/E-lexicon.tex index cfa99a34f2..9e4faa1728 100644 --- a/docs/phd/appendix/E-lexicon.tex +++ b/docs/phd/appendix/E-lexicon.tex @@ -329,7 +329,7 @@ \section*{A\quad $\varphi$-Arithmetic} % ----------------------------------------------------------- \paragraph*{\textmd{\textbf{$\mathbb{Z}[\varphi]$ (golden integers)}}} \label{entry:Zphi} -[Symbol: $\mathbb{Z}[\varphi]$] (Russian: \textit{кольцо золотых целых чисел}).\\ +[Symbol: \(\mathbb{Z}{[}\varphi{]}\)] (Russian: \textit{кольцо золотых целых чисел}).\\ \textit{First use}: Ch.\,1, Ch.\,6.\\ \textit{Coq}: \texttt{lucas\_closure\_gf16.v}.\\ \textit{Definition.} diff --git a/docs/phd/appendix/F-coq-citation-map.tex b/docs/phd/appendix/F-coq-citation-map.tex index 364474604a..e6d2299413 100644 --- a/docs/phd/appendix/F-coq-citation-map.tex +++ b/docs/phd/appendix/F-coq-citation-map.tex @@ -67,7 +67,8 @@ \subsection{Coq version and toolchain} \centering\small \caption{Ring build order and Coq compilation commands} \label{tab:ring-build} - \begin{tabular}{@{}llll@{}} + \resizebox{\linewidth}{!}{% +\begin{tabular}{@{}llll@{}} \toprule \textbf{Ring} & \textbf{Coq files} & \textbf{Build command} & \textbf{INV scope} \\ \midrule @@ -77,6 +78,7 @@ \subsection{Coq version and toolchain} Crown & \texttt{igla\_found\_criterion.v}, \texttt{rainbow\_bridge\_consistency.v}, \texttt{nca\_entropy\_stability.v} & \texttt{make crown} & INV-7, INV-8 \\ \bottomrule \end{tabular} +} \end{table} \subsection{Relationship to \texorpdfstring{\texttt{assertions/igla\_assertions.json}}{assertions/igla\_assertions.json}} @@ -138,7 +140,7 @@ \section{Summary statistics} \begin{figure}[H] \centering -\includegraphics[width=0.92\textwidth,keepaspectratio]{app-f-bitstream-archive.png} +\includegraphics[width=0.92\textwidth,keepaspectratio]{F-coq-citation-map.jpg} \end{figure} \begin{quote}\itshape @@ -162,7 +164,8 @@ \subsection*{297 theorems, one audit trail} \centering \caption{Overall proof corpus statistics} \label{tab:proof-stats} - \begin{tabular}{@{}ll@{}} + \resizebox{\linewidth}{!}{% +\begin{tabular}{@{}ll@{}} \toprule \textbf{Metric} & \textbf{Value} \\ \midrule @@ -176,13 +179,15 @@ \subsection*{297 theorems, one audit trail} Rings in compilation order & 4 \\ \bottomrule \end{tabular} +} \end{table} \begin{table}[H] \centering \caption{Per-ring proof statistics} \label{tab:per-ring-stats} - \begin{tabular}{@{}lrrrr@{}} + \resizebox{\linewidth}{!}{% +\begin{tabular}{@{}lrrrr@{}} \toprule \textbf{Ring} & \textbf{Theorems} & \textbf{Qed} & \textbf{Admitted} & \textbf{\% Proven} \\ \midrule @@ -194,6 +199,7 @@ \subsection*{297 theorems, one audit trail} \textbf{Total} & \textbf{97} & \textbf{92} & \textbf{5} & \textbf{94.8\%} \\ \bottomrule \end{tabular} +} \end{table} % ───────────────────────────────────────────────────────────────────────────── @@ -1130,7 +1136,8 @@ \subsection{Falsification witness CI links} \centering\small \caption{Falsification witnesses per file} \label{tab:falsification-witnesses} - \begin{tabular}{@{}ll@{}} + \resizebox{\linewidth}{!}{% +\begin{tabular}{@{}ll@{}} \toprule \textbf{File} & \textbf{Witness theorem} \\ \midrule @@ -1147,6 +1154,7 @@ \subsection{Falsification witness CI links} \texttt{rainbow\_bridge\_consistency.v} & \texttt{counter\_duplicate\_claim} \\ \bottomrule \end{tabular} +} \end{table} % ───────────────────────────────────────────────────────────────────────────── @@ -1201,7 +1209,8 @@ \subsection{Action levels} \centering\small \caption{Invariant action levels: Coq status → Rust action} \label{tab:action-levels} - \begin{tabular}{@{}lllll@{}} + \resizebox{\linewidth}{!}{% +\begin{tabular}{@{}lllll@{}} \toprule \textbf{INV} & \textbf{Coq status} & \textbf{Rust action} & \textbf{JSON field} & \textbf{Effect} \\ \midrule @@ -1215,6 +1224,7 @@ \subsection{Action levels} INV-8 & Admitted & \texttt{warn} & \texttt{action=warn} & Log only \\ \bottomrule \end{tabular} +} \end{table} \subsection{Required Rust tests} diff --git a/docs/phd/appendix/F-fpga-bitstream.tex b/docs/phd/appendix/F-fpga-bitstream.tex index 92100f53b1..97f81789c0 100644 --- a/docs/phd/appendix/F-fpga-bitstream.tex +++ b/docs/phd/appendix/F-fpga-bitstream.tex @@ -6,7 +6,7 @@ \chapter*{Appendix F: FPGA Bitstream Archive} \begin{figure}[H] \centering -\includegraphics[width=0.92\textwidth,keepaspectratio]{app-f-bitstream-archive.png} +\includegraphics[width=0.92\textwidth,keepaspectratio]{F-fpga-bitstream.jpg} \caption*{Figure --- FPGA bitstream archive --- SHA-256 manifest.} \end{figure} @@ -45,6 +45,7 @@ \section*{F.2 Target Device} \begin{table}[h] \centering +\resizebox{\linewidth}{!}{% \begin{tabular}{ll} \toprule \textbf{Field} & \textbf{Value} \\ @@ -57,6 +58,7 @@ \section*{F.2 Target Device} Speedgrade & --2 \\ \bottomrule \end{tabular} +} \caption{FPGA device identification. Board is marked XC7A100T but JTAG IDCODE corresponds to XC7A200T v1. The design (83~LUT, 27~FF) fits either device;\, no resynthesis required.} @@ -74,6 +76,7 @@ \section*{F.3 Bitstream Integrity} \begin{table}[h] \centering +\resizebox{\linewidth}{!}{% \begin{tabular}{ll} \toprule \textbf{Field} & \textbf{Value} \\ @@ -88,6 +91,7 @@ \section*{F.3 Bitstream Integrity} DSP & 0 \\ \bottomrule \end{tabular} +} \caption{Bitstream file metadata. Full SHA-256 stored in \filepath{trinity-fpga/bitstream/design.bit.sha256}.} \end{table} diff --git a/docs/phd/appendix/G-data-availability.tex b/docs/phd/appendix/G-data-availability.tex index 26f3b4ee74..6f57c963e4 100644 --- a/docs/phd/appendix/G-data-availability.tex +++ b/docs/phd/appendix/G-data-availability.tex @@ -14,7 +14,7 @@ \chapter{Data Availability} \begin{figure}[H] \centering -\includegraphics[width=0.92\textwidth,keepaspectratio]{app-g-clara-evidence-package.png} +\includegraphics[width=0.92\textwidth,keepaspectratio]{G-data-availability.jpg} \end{figure} \begin{quote}\itshape @@ -65,6 +65,7 @@ \section{Primary Zenodo Deposits} \begin{table}[h] \centering +\resizebox{\linewidth}{!}{% \begin{tabular}{lll} \toprule \textbf{INV-\#} & \textbf{DOI} & \textbf{Contents} \\ @@ -78,6 +79,7 @@ \section{Primary Zenodo Deposits} INV-4 & (to be minted v7.0) & PhD dissertation PDF v7.0, final \\ \bottomrule \end{tabular} +} \caption{Primary Zenodo deposits. All DOIs are permanent. INV-4 will be minted at submission (T-2 days from defence 2026-06-15).} \end{table} @@ -139,6 +141,7 @@ \section{Source Repositories} \begin{table}[h] \centering +\resizebox{\linewidth}{!}{% \begin{tabular}{lll} \toprule \textbf{Repository} & \textbf{License} & \textbf{Contents} \\ @@ -153,6 +156,7 @@ \section{Source Repositories} & MIT & FPGA bitstreams, XDC pin maps, iCE40 demo \\ \bottomrule \end{tabular} +} \caption{Source repositories. All are public and MIT or CC-BY-4.0 licensed.} \end{table} diff --git a/docs/phd/appendix/H-acm-ae-checklist.tex b/docs/phd/appendix/H-acm-ae-checklist.tex index 168de515dd..2e9644ddff 100644 --- a/docs/phd/appendix/H-acm-ae-checklist.tex +++ b/docs/phd/appendix/H-acm-ae-checklist.tex @@ -28,7 +28,7 @@ \chapter{ACM Artifact Evaluation — Full Pack Walkthrough \& \begin{figure}[H] \centering -\includegraphics[width=0.92\textwidth,keepaspectratio]{app-h-zenodo-doi-registry.png} +\includegraphics[width=0.92\textwidth,keepaspectratio]{H-acm-ae-checklist.jpg} \caption{Zenodo DOI registry for the \emph{Flos Aureus} artifact pack. The permanent DOI resolves to the snapshot archived at the time of camera-ready submission.} @@ -159,6 +159,7 @@ \subsection{Badges sought} \begin{center} \renewcommand{\arraystretch}{1.4} +\resizebox{\linewidth}{!}{% \begin{tabular}{lp{9cm}} \hline \textbf{Badge} & \textbf{Criterion (ACM AE 2025)} \\ @@ -180,6 +181,7 @@ \subsection{Badges sought} results using a variant methodology distinct from the original. \\ \hline \end{tabular} +} \end{center} % ------------------------------------------------------------------- @@ -518,6 +520,7 @@ \subsection{Expected outputs and tolerance bands} \begin{center} \renewcommand{\arraystretch}{1.35} +\resizebox{\linewidth}{!}{% \begin{tabular}{lllr} \hline \textbf{Chapter} & \textbf{Table / Figure} & \textbf{Key metric} & \textbf{Tolerance} \\ @@ -531,6 +534,7 @@ \subsection{Expected outputs and tolerance bands} 29 & Figure~29.1 & Convergence curve & visual match \\ \hline \end{tabular} +} \end{center} \noindent @@ -551,6 +555,7 @@ \subsection{Reference configuration} \begin{center} \renewcommand{\arraystretch}{1.35} +\resizebox{\linewidth}{!}{% \begin{tabular}{ll} \hline \textbf{Component} & \textbf{Specification} \\ @@ -565,6 +570,7 @@ \subsection{Reference configuration} OS & Linux (Ubuntu 22.04 or Debian 12 tested) \\ \hline \end{tabular} +} \end{center} \subsection{Minimum viable configuration} @@ -608,6 +614,7 @@ \subsection{Pinned versions} \begin{center} \renewcommand{\arraystretch}{1.35} +\resizebox{\linewidth}{!}{% \begin{tabular}{llp{6cm}} \hline \textbf{Tool} & \textbf{Version} & \textbf{Purpose} \\ @@ -622,6 +629,7 @@ \subsection{Pinned versions} Git & $\geq$ 2.40 & Clone and tag verification \\ \hline \end{tabular} +} \end{center} \subsection{Rust crate dependencies} @@ -671,6 +679,7 @@ \subsection{Environment variables} \begin{center} \renewcommand{\arraystretch}{1.35} +\resizebox{\linewidth}{!}{% \begin{tabular}{lp{4cm}l} \hline \textbf{Variable} & \textbf{Meaning} & \textbf{Default} \\ @@ -686,6 +695,7 @@ \subsection{Environment variables} \texttt{info} \\ \hline \end{tabular} +} \end{center} % ------------------------------------------------------------------- @@ -708,6 +718,7 @@ \subsection{Runtime table} \begin{center} \renewcommand{\arraystretch}{1.4} +\resizebox{\linewidth}{!}{% \begin{tabular}{lrr} \hline \textbf{Stage} & \textbf{Wall-clock (ref)} & \textbf{Wall-clock (min)} \\ @@ -727,6 +738,7 @@ \subsection{Runtime table} \textbf{Total (full run)} & \textbf{$\approx$ 62 min} & \textbf{$\approx$ 136 min} \\ \hline \end{tabular} +} \end{center} \noindent @@ -760,6 +772,7 @@ \section{Troubleshooting Matrix} \begin{center} \renewcommand{\arraystretch}{1.5} +\resizebox{\linewidth}{!}{% \begin{tabular}{p{4.5cm}p{4cm}p{5cm}} \hline \textbf{Symptom} & \textbf{Likely cause} & \textbf{Remedy} \\ @@ -821,6 +834,7 @@ \section{Troubleshooting Matrix} \hline \end{tabular} +} \end{center} \subsection{CI failure attribution} @@ -1128,6 +1142,7 @@ \section{Ledger of Past AE Submissions} \begin{center} \renewcommand{\arraystretch}{1.35} +\resizebox{\linewidth}{!}{% \begin{tabular}{llllp{4.5cm}} \hline \textbf{Venue} & \textbf{Year} & \textbf{Badges sought} & @@ -1137,6 +1152,7 @@ \section{Ledger of Past AE Submissions} First submission; this monograph is the originating artifact. \\ \hline \end{tabular} +} \end{center} \noindent @@ -1745,6 +1761,7 @@ \section{Coq Proof Status Summary} \begin{center} \renewcommand{\arraystretch}{1.35} +\resizebox{\linewidth}{!}{% \begin{tabular}{lllll} \hline \textbf{Invariant} & \textbf{File} & \textbf{QED theorems} & @@ -1781,6 +1798,7 @@ \section{Coq Proof Status Summary} — & abort \\ \hline \end{tabular} +} \end{center} \noindent @@ -1823,6 +1841,7 @@ \section*{Checklist compliance summary} \begin{center} \renewcommand{\arraystretch}{1.35} +\resizebox{\linewidth}{!}{% \begin{tabular}{lll} \hline \textbf{Badge} & \textbf{Items} & \textbf{Status} \\ @@ -1836,6 +1855,7 @@ \section*{Checklist compliance summary} \textbf{Total} & 50/50 & \textbf{Complete} \\ \hline \end{tabular} +} \end{center} \noindent diff --git a/docs/phd/appendix/H-zenodo-doi.tex b/docs/phd/appendix/H-zenodo-doi.tex index 52f3c3e8fe..03cfb15495 100644 --- a/docs/phd/appendix/H-zenodo-doi.tex +++ b/docs/phd/appendix/H-zenodo-doi.tex @@ -6,7 +6,7 @@ \chapter*{Appendix H: Zenodo DOI Registry} \begin{figure}[H] \centering -\includegraphics[width=0.92\textwidth,keepaspectratio]{app-h-zenodo-doi-registry.png} +\includegraphics[width=0.92\textwidth,keepaspectratio]{H-zenodo-doi.jpg} \caption*{Figure --- Zenodo DOI registry --- 13 archived datasets.} \end{figure} @@ -41,6 +41,7 @@ \section*{H.1 Primary Artefacts} \begin{table}[h] \centering +\resizebox{\linewidth}{!}{% \begin{tabular}{lll} \toprule \textbf{ID} & \textbf{DOI} & \textbf{Artefact} \\ @@ -60,6 +61,7 @@ \section*{H.1 Primary Artefacts} Z-13 & 10.5281/zenodo.19227889 & Pre-registration OSF archive (H₁ sealed) \\ \bottomrule \end{tabular} +} \caption{13 Zenodo DOIs. Champion DOI (Z-01) is the primary citation for GF16 BPB=2.2393. All resolve as of 2026-05-05.} \end{table} @@ -111,6 +113,7 @@ \section*{H.4 Version History} \begin{table}[h] \centering +\resizebox{\linewidth}{!}{% \begin{tabular}{lll} \toprule \textbf{Version} & \textbf{Date} & \textbf{DOI suffix note} \\ @@ -121,6 +124,7 @@ \section*{H.4 Version History} v7.0 & 2026-06-10 & \emph{Planned: frozen submission} \\ \bottomrule \end{tabular} +} \caption{Thesis version history. v7.0 will mint a new Zenodo DOI at T-5.} \end{table} diff --git a/docs/phd/appendix/I-xdc-pin-map.tex b/docs/phd/appendix/I-xdc-pin-map.tex index e79b3b051d..d82463622a 100644 --- a/docs/phd/appendix/I-xdc-pin-map.tex +++ b/docs/phd/appendix/I-xdc-pin-map.tex @@ -12,7 +12,7 @@ \chapter*{Appendix I: XDC Pin Map — Trinity GF16 Ternary Matmul\\ \begin{figure}[H] \centering -\includegraphics[width=0.92\textwidth,keepaspectratio]{app-i-xdc-pin-map.png} +\includegraphics[width=0.92\textwidth,keepaspectratio]{I-xdc-pin-map.jpg} \caption*{Figure I.0 — Trinity GF16 ternary matmul pin assignments on the Arty A7-100T (Artix-7 XC7A100T-1CSG324C) and Arty Z7-20 (Zynq-7020 XC7Z020-1CLG400C). Every RTL port from \texttt{vsa\_matmul.v} and @@ -93,6 +93,7 @@ \subsection*{I.1.1 Arty A7-100T} \begin{table}[H] \centering +\resizebox{\linewidth}{!}{% \begin{tabular}{lrr} \toprule \textbf{Resource} & \textbf{Available} & \textbf{Used (GF16 matmul)} \\ @@ -107,6 +108,7 @@ \subsection*{I.1.1 Arty A7-100T} IOB & 210 & 108 (51.4\%) \\ \bottomrule \end{tabular} +} \caption{Arty A7-100T resource utilisation — Trinity GF16 ternary matmul, Vivado 2023.2 post-implementation report.} \label{tab:arty-a7-resources} @@ -139,6 +141,7 @@ \subsection*{I.1.2 Arty Z7-20} \begin{table}[H] \centering +\resizebox{\linewidth}{!}{% \begin{tabular}{lrr} \toprule \textbf{Resource} & \textbf{Available (PL)} & \textbf{Used (GF16 matmul)} \\ @@ -152,6 +155,7 @@ \subsection*{I.1.2 Arty Z7-20} IOB & 200 & 64 (32.0\%) \\ \bottomrule \end{tabular} +} \caption{Arty Z7-20 PL resource utilisation — Trinity GF16 ternary matmul, Vivado 2023.2 post-implementation report.} \label{tab:arty-z7-resources} @@ -172,6 +176,7 @@ \subsection*{I.2.1 \texttt{trinity\_top.v} Port List} \begin{table}[H] \centering \footnotesize +\resizebox{\linewidth}{!}{% \begin{tabular}{llll} \toprule \textbf{Port name} & \textbf{Width} & \textbf{Direction} & \textbf{Description} \\ @@ -228,6 +233,7 @@ \subsection*{I.2.1 \texttt{trinity\_top.v} Port List} \texttt{uart\_rx} & 1 & input & UART receive (115200 8N1) \\ \bottomrule \end{tabular} +} \caption{Complete port list of \texttt{trinity\_top.v}. Total: 86 scalar signals. All ports appear in the XDC files of Sections~\ref{sec:xdc-a7} and~\ref{sec:xdc-z7}.} @@ -239,6 +245,7 @@ \subsection*{I.2.2 \texttt{vsa\_matmul.v} Port List (sub-module)} \begin{table}[H] \centering \footnotesize +\resizebox{\linewidth}{!}{% \begin{tabular}{lllp{5cm}} \toprule \textbf{Port name} & \textbf{Width} & \textbf{Direction} & \textbf{Description} \\ @@ -253,6 +260,7 @@ \subsection*{I.2.2 \texttt{vsa\_matmul.v} Port List (sub-module)} \texttt{ready} & 1 & output & Ready \\ \bottomrule \end{tabular} +} \caption{Port list of \texttt{vsa\_matmul.v}. All ports are internal fabric connections; they are constrained indirectly through their promotion in \texttt{trinity\_top.v}. The bijection between @@ -295,6 +303,7 @@ \subsection*{I.3.2 MMCM-Generated Clocks} \begin{table}[H] \centering +\resizebox{\linewidth}{!}{% \begin{tabular}{lllll} \toprule \textbf{Output port} & \textbf{Freq (MHz)} & \textbf{Period (ns)} & \textbf{Duty (\%)} & \textbf{BUFG} \\ @@ -305,6 +314,7 @@ \subsection*{I.3.2 MMCM-Generated Clocks} \texttt{clk\_wb} & 25.000 & 40.000 & 50.0 & BUFG\_3 \\ \bottomrule \end{tabular} +} \caption{MMCM output clocks. \texttt{clk\_100} feeds the matmul datapath; \texttt{clk\_200} feeds the BRAM read port; \texttt{clk\_50} feeds UART; \texttt{clk\_wb} feeds the Wishbone debug bridge.} @@ -514,6 +524,7 @@ \subsection*{I.6.2 AXI-Lite MMIO (32 ports via Pmod JA/JB)} \begin{table}[H] \centering \footnotesize +\resizebox{\linewidth}{!}{% \begin{tabular}{llll} \toprule \textbf{AXI-Lite input port} & \textbf{Pmod} & \textbf{Pmod pin} & \textbf{FPGA package pin} \\ @@ -552,6 +563,7 @@ \subsection*{I.6.2 AXI-Lite MMIO (32 ports via Pmod JA/JB)} \texttt{s\_axi\_wvalid} & JC & 10 & U13 \\ \bottomrule \end{tabular} +} \caption{AXI-Lite input ports — Arty A7-100T Pmod assignment.} \label{tab:axi-lite-input} \end{table} @@ -599,6 +611,7 @@ \subsection*{I.6.2 AXI-Lite MMIO (32 ports via Pmod JA/JB)} \begin{table}[H] \centering \footnotesize +\resizebox{\linewidth}{!}{% \begin{tabular}{llll} \toprule \textbf{AXI-Lite output port} & \textbf{Pmod} & \textbf{Pmod pin} & \textbf{FPGA package pin} \\ @@ -632,6 +645,7 @@ \subsection*{I.6.2 AXI-Lite MMIO (32 ports via Pmod JA/JB)} \texttt{s\_axi\_rready} & JD out-exp & ext-10& L13 \\ \bottomrule \end{tabular} +} \caption{AXI-Lite output ports — Arty A7-100T assignment.} \label{tab:axi-lite-output} \end{table} @@ -931,6 +945,7 @@ \subsection*{I.8.1 Setup and Hold Budgets} \begin{table}[H] \centering +\resizebox{\linewidth}{!}{% \begin{tabular}{lll} \toprule \textbf{Parameter} & \textbf{Value (ns)} & \textbf{Derivation} \\ @@ -946,6 +961,7 @@ \subsection*{I.8.1 Setup and Hold Budgets} MMCM lock time & 50{,}000 & 50 ms worst-case \\ \bottomrule \end{tabular} +} \caption{Timing budget summary. All constants are either FPGA vendor parameters or $\varphi$-derived (R6 compliant).} \label{tab:timing-budget} @@ -1015,6 +1031,7 @@ \subsection*{I.9.1 Bank Summary — Arty A7-100T} \begin{table}[H] \centering +\resizebox{\linewidth}{!}{% \begin{tabular}{lllll} \toprule \textbf{Bank} & \textbf{VCCO (V)} & \textbf{Clock region} & \textbf{BUFG hops} & \textbf{Signals} \\ @@ -1026,6 +1043,7 @@ \subsection*{I.9.1 Bank Summary — Arty A7-100T} 16 & 3.3 & X1Y1 & 0 & JD (dout[31:0]) \\ \bottomrule \end{tabular} +} \caption{I/O bank assignments, Arty A7-100T. BUFG hops are counted from the MMCM in clock region X1Y0 to the consuming bank. A hop of 1 indicates one BUFG traversal across a clock region boundary.} @@ -1041,6 +1059,7 @@ \subsection*{I.9.2 Bank Summary — Arty Z7-20} \begin{table}[H] \centering +\resizebox{\linewidth}{!}{% \begin{tabular}{lllll} \toprule \textbf{Bank} & \textbf{VCCO (V)} & \textbf{Clock region} & \textbf{BUFG hops} & \textbf{Signals} \\ @@ -1050,6 +1069,7 @@ \subsection*{I.9.2 Bank Summary — Arty Z7-20} PS & — & PS domain & — & AXI GP0, FCLK \\ \bottomrule \end{tabular} +} \caption{I/O bank assignments, Arty Z7-20.} \label{tab:bank-z7} \end{table} @@ -1155,6 +1175,7 @@ \section*{I.12 DRC/LVS Gates Linkage} \begin{table}[H] \centering +\resizebox{\linewidth}{!}{% \begin{tabular}{lp{6cm}l} \toprule \textbf{DRC code} & \textbf{Description} & \textbf{Disposition} \\ @@ -1166,6 +1187,7 @@ \section*{I.12 DRC/LVS Gates Linkage} \texttt{HDPR-1} & High-density pack ratio exceeded & \textit{Mitigated by phi-aspect Pblock} \\ \bottomrule \end{tabular} +} \caption{DRC waiver record. DRC codes from Vivado 2023.2 \textit{DRC Violations Report}. ``Fix'' items were resolved before bitstream generation; ``N/A'' items do not apply to this design.} @@ -1749,6 +1771,7 @@ \section*{I.15.3 R14 Coq Map} \begin{table}[H] \centering \footnotesize +\resizebox{\linewidth}{!}{% \begin{tabular}{lll} \toprule \textbf{Constant} & \textbf{Value} & \textbf{Coq source} \\ @@ -1760,6 +1783,7 @@ \section*{I.15.3 R14 Coq Map} \texttt{MAX\_FANOUT 100} & power guard & \texttt{igla\_asha\_bound.v::rung\_zero\_is\_warmup} \\ \bottomrule \end{tabular} +} \caption{R14 constant-to-Coq traceability table. All numeric constants trace to the \texttt{trinity-clara/proofs/igla/} proof chain; no free parameters (R6).} @@ -1881,6 +1905,7 @@ \subsection*{I.18.3 AXI-Lite Addressing} \begin{table}[H] \centering \footnotesize +\resizebox{\linewidth}{!}{% \begin{tabular}{lllp{4.5cm}} \toprule \textbf{Offset} & \textbf{Name} & \textbf{R/W} & \textbf{Description} \\ @@ -1899,6 +1924,7 @@ \subsection*{I.18.3 AXI-Lite Addressing} \texttt{0x2C} & \texttt{PHI\_ID} & RO & Design identifier: \texttt{0x\(\varphi\)161803} \\ \bottomrule \end{tabular} +} \caption{AXI-Lite MMIO register map. Base address determined by the Zynq PS address map (default: \texttt{0x4000\_0000}) or by the Pmod address decoder on the A7 board (base: \texttt{0x0000\_0000}).} @@ -2118,6 +2144,7 @@ \section*{I.23 Change Log} \begin{table}[H] \centering +\resizebox{\linewidth}{!}{% \begin{tabular}{lp{2cm}p{7cm}} \toprule \textbf{Date} & \textbf{Author} & \textbf{Change} \\ @@ -2129,6 +2156,7 @@ \section*{I.23 Change Log} R6/R10/R14 audit. 1964 lines. \\ \bottomrule \end{tabular} +} \caption{Change log for Appendix~I.} \label{tab:changelog} \end{table} @@ -2214,6 +2242,7 @@ \section*{I.26 Power Analysis} \begin{table}[H] \centering +\resizebox{\linewidth}{!}{% \begin{tabular}{lrr} \toprule \textbf{Component} & \textbf{Dynamic (mW)} & \textbf{Static (mW)} \\ @@ -2228,6 +2257,7 @@ \section*{I.26 Power Analysis} \textbf{Total} & \textbf{274} & \textbf{77} = \textbf{351 mW} \\ \bottomrule \end{tabular} +} \caption{Vivado XPE power estimate, Arty A7-100T, 100\,MHz, 23\% LUT utilisation, 12.5\% toggle rate. Total $\approx 351\,\mathrm{mW}$, well below the 1\,W sub-watt target.} diff --git a/docs/phd/appendix/J-troubleshooting.tex b/docs/phd/appendix/J-troubleshooting.tex index 1ed840636b..56d91feb4d 100644 --- a/docs/phd/appendix/J-troubleshooting.tex +++ b/docs/phd/appendix/J-troubleshooting.tex @@ -1088,6 +1088,7 @@ \section*{J.8\quad R14 Coq Citation Map} \begin{table}[h] \centering \small +\resizebox{\linewidth}{!}{% \begin{tabular}{@{}p{3.2cm} p{2.0cm} p{3.8cm} p{2.0cm} p{1.4cm}@{}} \toprule \textbf{Constant} & \textbf{Value} & \textbf{Coq file} & @@ -1122,6 +1123,7 @@ \section*{J.8\quad R14 Coq Citation Map} Admitted \\ \bottomrule \end{tabular} +} \caption{L-R14 traceability map: numeric constants in Appendix J traced to Coq proofs. All QED entries are in \texttt{trinity-clara/proofs/igla/}.} @@ -1142,6 +1144,7 @@ \section*{J.9\quad R6 Audit — Zero Free Parameters} \begin{table}[h] \centering \small +\resizebox{\linewidth}{!}{% \begin{tabular}{@{}lll@{}} \toprule \textbf{Constant} & \textbf{Value} & \textbf{φ-derivation or basis} \\ @@ -1161,6 +1164,7 @@ \section*{J.9\quad R6 Audit — Zero Free Parameters} $N$ (table entries) & $47$ & $48 - 1$; integer (no free parameter) \\ \bottomrule \end{tabular} +} \caption{R6 audit: all numeric constants in Appendix J derive from $\{\varphi, \pi, e, \mathbb{Z}\}$. No free parameters.} \label{tab:r6-audit} @@ -1227,6 +1231,7 @@ \section*{J.10\quad Hardware Blockers BLK-001 through BLK-005 (FPGA Bringup)} \begin{table}[h] \centering +\resizebox{\linewidth}{!}{% \begin{tabular}{llllll} \toprule \textbf{ID} & \textbf{Blocker} & \textbf{Days} & \textbf{ODC} @@ -1242,6 +1247,7 @@ \section*{J.10\quad Hardware Blockers BLK-001 through BLK-005 (FPGA Bringup)} DONE=1, STAT=\texttt{0x401079FC} \\ \bottomrule \end{tabular} +} \caption{Hardware blocker summary (BLK-001..005), extended with ODC classification and fix type.} \label{tab:hardware-blockers} @@ -1431,6 +1437,7 @@ \subsection*{What Would Refute the Remediation Claims} \subsection*{Corroboration Record} +\resizebox{\linewidth}{!}{% \begin{tabular}{lll} \toprule \textbf{Date} & \textbf{Evidence} & \textbf{Status} \\ @@ -1447,6 +1454,7 @@ \subsection*{Corroboration Record} 500 error resolved & Functional \\ \bottomrule \end{tabular} +} % ═══════════════════════════════════════════════════════════════════════════ % J.14 CITATION SUMMARY @@ -1554,6 +1562,7 @@ \subsection*{J.16.2\quad Cross-Invariant Failure Coupling} \begin{table}[h] \centering \small +\resizebox{\linewidth}{!}{% \begin{tabular}{@{}lllp{5.5cm}@{}} \toprule \textbf{Failure} & \textbf{INV-A} & \textbf{INV-B} & @@ -1575,6 +1584,7 @@ \subsection*{J.16.2\quad Cross-Invariant Failure Coupling} returning \texttt{Ok(())} \\ \bottomrule \end{tabular} +} \caption{Cross-invariant failure couplings observed in production IGLA runs. Practitioners should check both invariants when either fires.} \label{tab:inv-coupling} diff --git a/docs/phd/appendix/K-agent-memory.tex b/docs/phd/appendix/K-agent-memory.tex index 5955471d43..18b193bec9 100644 --- a/docs/phd/appendix/K-agent-memory.tex +++ b/docs/phd/appendix/K-agent-memory.tex @@ -281,6 +281,7 @@ \subsection{The ClaimState Transition Diagram} The claim state machine has five states and six transitions: \begin{center} +\resizebox{\linewidth}{!}{% \begin{tabular}{lll} \hline \textbf{From} & \textbf{To} & \textbf{Trigger} \\ @@ -301,6 +302,7 @@ \subsection{The ClaimState Transition Diagram} (non-absorbing; queen re-opens for audit follow-up) \\ \hline \end{tabular} +} \end{center} The non-absorbing property of \textsc{Done} is a design choice: @@ -736,6 +738,7 @@ \section{R6 Audit: Zero Free Parameters} We audit all numeric constants introduced in this appendix: \begin{center} +\resizebox{\linewidth}{!}{% \begin{tabular}{lll} \hline \textbf{Constant} & \textbf{Value} & \textbf{Derivation} \\ @@ -767,6 +770,7 @@ \section{R6 Audit: Zero Free Parameters} Trinity cube \\ \hline \end{tabular} +} \end{center} All constants pass R6 audit: each is either an integer, a Lucas/Fibonacci @@ -783,6 +787,7 @@ \section{R14 Coq Citation Map} \texttt{.v} file with line ranges. The theorems cited in this appendix are: \begin{center} +\resizebox{\linewidth}{!}{% \begin{tabular}{llll} \hline \textbf{Theorem} & \textbf{Coq File} & \textbf{Lines} & @@ -800,6 +805,7 @@ \section{R14 Coq Citation Map} \texttt{gf16\_precision.v} & 1--50 & Admitted \\ \hline \end{tabular} +} \end{center} \admittedbox{HRR Capacity Bound}{The capacity bound (Theorem~\ref{thm:K-capacity}) @@ -1480,6 +1486,7 @@ \subsection{Throughput vs Agent Count} $n$ agents each succeeding with probability $p$. We observed: \begin{center} +\resizebox{\linewidth}{!}{% \begin{tabular}{ccccc} \hline \textbf{Agents $n$} & $p=0.5$ & $p=0.7$ & $p=0.9$ & \textbf{Theoretical max} \\ @@ -1490,6 +1497,7 @@ \subsection{Throughput vs Agent Count} 27 & 8.34 & 10.21 & 11.76 & $27 \times 4.8 = 129.6$ \\ \hline \end{tabular} +} \end{center} The gap between observed and theoretical maximum is due to lane @@ -1573,6 +1581,7 @@ \section{Summary: Agent Memory Architecture} \label{sec:K-summary} \begin{center} +\resizebox{\linewidth}{!}{% \begin{tabular}{lll} \hline \textbf{Component} & \textbf{Role} & \textbf{Key Property} \\ @@ -1603,6 +1612,7 @@ \section{Summary: Agent Memory Architecture} Coq-verified (\texttt{lucas\_2\_eq\_3}) \\ \hline \end{tabular} +} \end{center} \noindent diff --git a/docs/phd/appendix/L-pollen-channel.tex b/docs/phd/appendix/L-pollen-channel.tex index 38fcbe2b27..eac2b7b7f1 100644 --- a/docs/phd/appendix/L-pollen-channel.tex +++ b/docs/phd/appendix/L-pollen-channel.tex @@ -412,6 +412,7 @@ \subsection*{L.5.1 \quad GitHub Rate-Limit Model} \caption{GitHub API request budget allocation per agent per hour, $N$ agents sharing one token.} \label{tab:budget} +\resizebox{\linewidth}{!}{% \begin{tabular}{lrl} \hline \textbf{Operation} & \textbf{Requests/h} & \textbf{Notes} \\ @@ -424,6 +425,7 @@ \subsection*{L.5.1 \quad GitHub Rate-Limit Model} Total per agent & $F + P + K + G$ & must be $\leq R_{\max}/N$ \\ \hline \end{tabular} +} \end{table} \noindent Solving for the sustainable flush rate $F$: @@ -1101,6 +1103,7 @@ \section*{L.12 \quad R6 Audit: Zero Free Parameters} \caption{R6 audit: all numeric constants in Appendix~L with φ-derivations.} \label{tab:r6} +\resizebox{\linewidth}{!}{% \begin{tabular}{p{3.2cm}p{3.5cm}p{5.5cm}} \hline \textbf{Constant} & \textbf{Value} & \textbf{φ-derivation / source} \\ @@ -1138,6 +1141,7 @@ \section*{L.12 \quad R6 Audit: Zero Free Parameters} $27 = 3^{3}$ & cube identity & $(\varphi^{2}+\varphi^{-2})^{3} = 3^{3}$. \\ \hline \end{tabular} +} \end{table} \noindent\textbf{R6 verdict: PASS.} Every constant is either @@ -1157,6 +1161,7 @@ \section*{L.13 \quad R14 Coq Citation Map} \centering \caption{R14 Coq citation map for Appendix~L.} \label{tab:coq} +\resizebox{\linewidth}{!}{% \begin{tabular}{p{4.5cm}p{3.5cm}p{2cm}p{1.5cm}} \hline \textbf{Theorem / lemma} & \textbf{Coq file} & \textbf{Lines} & \textbf{Status} \\ @@ -1188,6 +1193,7 @@ \section*{L.13 \quad R14 Coq Citation Map} 212--260 & Admitted \\ \hline \end{tabular} +} \end{table} \begin{admittedboxenv} @@ -1513,6 +1519,7 @@ \subsection*{L.18.2 \quad What Would Refute the Convergence Theorem} \subsection*{L.18.3 \quad Corroboration Record} +\resizebox{\linewidth}{!}{% \begin{tabular}{lll} \hline Date & Evidence & Status \\ @@ -1521,6 +1528,7 @@ \subsection*{L.18.3 \quad Corroboration Record} 2026-06-10 & Effective bit-rate: 3847\,bits/h (from hive\_honey.jsonl) & Corroborated \\ \hline \end{tabular} +} % ---------------------------------------------------------------- \section*{L.19 \quad Cross-References} @@ -1636,6 +1644,7 @@ \section*{L.A \quad Appendix to the Appendix: Gossip Protocol Comparison} \caption{Comparison of gossip protocols. $N$ = number of nodes; $\lambda$ = gossip rate; $t_{\text{conv}}$ = convergence time.} \label{tab:gossip} +\resizebox{\linewidth}{!}{% \begin{tabular}{p{2.8cm}p{2.5cm}p{2.5cm}p{2.5cm}p{2.5cm}} \hline \textbf{Protocol} & \textbf{Medium} & \textbf{Fan-out} & @@ -1663,6 +1672,7 @@ \section*{L.A \quad Appendix to the Appendix: Gossip Protocol Comparison} \textbf{Audit log; auth. HMAC.} \\ \hline \end{tabular} +} \end{table} The pollen channel achieves $O(1)$ convergence rounds (vs.\ $O(\log N)$ @@ -1749,6 +1759,7 @@ \section*{L.C \quad Notation Reference} % ---------------------------------------------------------------- \label{sec:appl-notation} +\resizebox{\linewidth}{!}{% \begin{tabular}{ll} \hline \textbf{Symbol} & \textbf{Meaning} \\ @@ -1774,5 +1785,6 @@ \section*{L.C \quad Notation Reference} $H_N$ & $N$-th harmonic number $= \sum_{k=1}^N 1/k$ \\ \hline \end{tabular} +} \par\medskip\noindent\hrulefill\par\medskip diff --git a/docs/phd/assets/cover_chalkboard.png b/docs/phd/assets/cover_chalkboard.png new file mode 100644 index 0000000000..bf3412e6d2 Binary files /dev/null and b/docs/phd/assets/cover_chalkboard.png differ diff --git a/docs/phd/chapters/00-monad.tex b/docs/phd/chapters/00-monad.tex index afe206d026..6ca377e991 100644 --- a/docs/phd/chapters/00-monad.tex +++ b/docs/phd/chapters/00-monad.tex @@ -210,6 +210,7 @@ \subsection{Powers of $\varphi$ in the Integer Lattice} \centering \caption{Integer representations $\phipow{n} = a_n + b_n\varphi$ for small $|n|$.}\label{tab:phi-powers} +\resizebox{\linewidth}{!}{% \begin{tabular}{rrrrr} \toprule $n$ & $a_n$ & $b_n$ & $\varphi^n$ (decimal) & Lucas / Fibonacci \\ @@ -226,6 +227,7 @@ \subsection{Powers of $\varphi$ in the Integer Lattice} $5$ & $4$ & $5$ & $11.0902\ldots$ & $L_5 = 11$ \\ \bottomrule \end{tabular} +} \end{table} Table~\ref{tab:phi-powers} exhibits the immediate connection to Lucas @@ -275,7 +277,7 @@ \subsection{The Ring $\mathbb{Z}[\varphi]$} the smallest sub-ring of $\mathbb{R}$ containing $\mathbb{Z}$ and the element $\varphi$. -\begin{proposition}[Ring operations on $\mathbb{Z}[\varphi]$]\label{prop:ring-ops} +\begin{proposition}[Ring operations on \(\mathbb{Z}{[}\varphi{]}\)]\label{prop:ring-ops} Addition and multiplication in $\mathbb{Z}[\varphi]$ are given by: \begin{align} (a + b\varphi) + (c + d\varphi) &= (a+c) + (b+d)\varphi, \\ @@ -405,7 +407,7 @@ \subsection{Units of $\mathbb{Z}[\varphi]$} The units (invertible elements) of $\mathbb{Z}[\varphi]$ are exactly the elements of norm $\pm 1$. -\begin{proposition}[Units of $\mathbb{Z}[\varphi]$]\label{prop:units} +\begin{proposition}[Units of \(\mathbb{Z}{[}\varphi{]}\)]\label{prop:units} The group of units of $\mathbb{Z}[\varphi]$ is $\mathbb{Z}[\varphi]^{\times} = \{\pm\phipow{n} \mid n \in \mathbb{Z}\}$, an infinite cyclic group generated by $\varphi$ (or $-\varphi$). @@ -449,7 +451,7 @@ \subsection{Lucas Numbers as Traces of Powers} \qed \end{proof} -\begin{corollary}[Lucas numbers in $\mathbb{Z}[\varphi]$]\label{cor:lucas-in-Z-phi} +\begin{corollary}[Lucas numbers in \(\mathbb{Z}{[}\varphi{]}\)]\label{cor:lucas-in-Z-phi} $L_n \in \mathbb{Z} \subset \mathbb{Z}[\varphi]$ for all $n \in \mathbb{Z}$. \end{corollary} @@ -503,6 +505,7 @@ \subsection{The Invariant Chain} \centering \caption{INV-bootstrap: downstream constants derived from $\varphi$.} \label{tab:inv-bootstrap} +\resizebox{\linewidth}{!}{% \begin{tabular}{lllll} \toprule Invariant & Constant & $\varphi$-expression & Coq lemma & Status \\ @@ -519,6 +522,7 @@ \subsection{The Invariant Chain} \texttt{lucas\_closure} & Proven \\ \bottomrule \end{tabular} +} \end{table} \subsection{Flos Aureus v6.2 and the 84-Theorem Specification} @@ -567,7 +571,7 @@ \section{Algebraic Structure of $\mathbb{Z}[\varphi]$} \subsection{$\mathbb{Z}[\varphi]$ as a Euclidean Domain} -\begin{theorem}[$\mathbb{Z}[\varphi]$ is a Euclidean domain]\label{thm:euclidean-domain} +\begin{theorem}[\(\mathbb{Z}{[}\varphi{]}\) is a Euclidean domain]\label{thm:euclidean-domain} $\mathbb{Z}[\varphi]$ is a Euclidean domain with the norm function $N(a+b\varphi) = |a^2 + ab - b^2|$. \end{theorem} @@ -589,7 +593,7 @@ \subsection{$\mathbb{Z}[\varphi]$ as a Euclidean Domain} \qed \end{proof} -\begin{corollary}[$\mathbb{Z}[\varphi]$ is a UFD]\label{cor:ufd} +\begin{corollary}[\(\mathbb{Z}{[}\varphi{]}\) is a UFD]\label{cor:ufd} Since every Euclidean domain is a principal ideal domain and every PID is a unique factorisation domain, $\mathbb{Z}[\varphi]$ is a UFD. \end{corollary} @@ -718,7 +722,7 @@ \subsection{Penrose Tilings and $\varphi$} \subsection{Quasi-crystalline Structure of $\mathbb{Z}[\varphi]$} -\begin{proposition}[Density of $\mathbb{Z}[\varphi]$ in $\mathbb{R}$]\label{prop:density} +\begin{proposition}[Density of \(\mathbb{Z}{[}\varphi{]}\) in $\mathbb{R}$]\label{prop:density} $\mathbb{Z}[\varphi]$ is dense in $\mathbb{R}$. \end{proposition} @@ -838,6 +842,7 @@ \subsection{Lucas Numbers: Properties and Table} \centering \caption{Lucas numbers $L_n$ for $0 \leq n \leq 20$.} \label{tab:lucas-numbers} +\resizebox{\linewidth}{!}{% \begin{tabular}{rlrlrl} \toprule $n$ & $L_n$ & $n$ & $L_n$ & $n$ & $L_n$ \\ @@ -851,6 +856,7 @@ \subsection{Lucas Numbers: Properties and Table} $6$ & $18$ & $13$ & $521$ & $20$ & $15\,127$ \\ \bottomrule \end{tabular} +} \end{table} Note that $L_2 = 3$ is the Trinity constant (Theorem~\ref{thm:trinity-identity}) @@ -892,7 +898,7 @@ \subsection{Five-Fold Symmetry} \end{proof} The icosahedron and dodecahedron (Platonic solids studied in -Chapter~\ref{ch:platonic}) carry this five-fold symmetry in their +Chapter~\ref{ch:platonic-solids}) carry this five-fold symmetry in their geometric structure, connecting the Monad to the $E_8$ root system via the Coxeter element of order $5$ (Chapter~\ref{ch:e8-symmetry}). @@ -1008,7 +1014,7 @@ \subsection{INV-1: Learning-Rate Champion} \frac{1}{2(2+\varphi)} \;\approx\; 0.004. \] -\begin{lemma}[$\alpha_\varphi$ in $\mathbb{Z}[\varphi]$]\label{lem:alpha-phi} +\begin{lemma}[$\alpha_\varphi$ in \(\mathbb{Z}{[}\varphi{]}\)]\label{lem:alpha-phi} $2\alpha_\varphi = \phipow{-3} \in \mathbb{Z}[\varphi]$. \end{lemma} @@ -1136,7 +1142,7 @@ \subsection{Icosahedral Group and the Platonic Solids} representations have characters $\varphi$ and $-\varphi^{-1}$ at elements of order $5$. This algebraic fact connects the Monad directly to the geometry of the icosahedron and dodecahedron -(Chapter~\ref{ch:platonic}). +(Chapter~\ref{ch:platonic-solids}). % =================================================================== % HONESTY AND ADMITTED MARKERS @@ -1176,7 +1182,7 @@ \section{Notation Glossary for This Chapter} \begin{description} \item[$\varphi$] Golden ratio, $(1+\sqrt{5})/2 \approx 1.618$. \item[$\psi$] Algebraic conjugate of $\varphi$, $(1-\sqrt{5})/2 = -\varphi^{-1}$. - \item[$\mathbb{Z}[\varphi]$] Lucas ring: $\{a + b\varphi \mid a, b \in \mathbb{Z}\}$. + \item[\(\mathbb{Z}{[}\varphi{]}\)] Lucas ring: $\{a + b\varphi \mid a, b \in \mathbb{Z}\}$. \item[$N(u)$] Norm of $u = a+b\varphi$: $N(u) = a^2 + ab - b^2$. \item[$F_n$] $n$-th Fibonacci number. \item[$L_n$] $n$-th Lucas number. @@ -1269,6 +1275,7 @@ \section{Coq Citation Map} \texttt{.v} file. The full map is: \begin{center} +\resizebox{\linewidth}{!}{% \begin{tabular}{lll} \toprule Theorem / Constant & Coq file & Status \\ @@ -1293,6 +1300,7 @@ \section{Coq Citation Map} & Admitted \\ \bottomrule \end{tabular} +} \end{center} \coqcite{lucas\_2\_eq\_3}% @@ -1354,7 +1362,7 @@ \subsection{The Euclidean Algorithm in $\mathbb{Z}[\varphi]$} We illustrate Theorem~\ref{thm:euclidean-domain} with an explicit computation of $\gcd(2+\varphi, 1+2\varphi)$ in $\mathbb{Z}[\varphi]$. -\begin{example}[Euclidean algorithm in $\mathbb{Z}[\varphi]$] +\begin{example}[Euclidean algorithm in \(\mathbb{Z}{[}\varphi{]}\)] Let $\alpha = 2+\varphi$ and $\beta = 1+2\varphi$. We have $N(\alpha) = 4 + 2 - 1 = 5$ and $N(\beta) = 1 + 2 - 4 = -1$, so $|\,N(\beta)\,| = 1$. Since $\beta$ has unit norm, it is a unit of diff --git a/docs/phd/chapters/01-golden-egg.tex b/docs/phd/chapters/01-golden-egg.tex index a5c7d46f75..a7894553e9 100644 --- a/docs/phd/chapters/01-golden-egg.tex +++ b/docs/phd/chapters/01-golden-egg.tex @@ -11,7 +11,7 @@ \chapter{Golden Seed: The Vesica Opens} \begin{figure}[H] \centering -\makebox[\linewidth][c]{\includegraphics[width=1.18\linewidth,keepaspectratio]{ch04-sacred-formula.png}} +\makebox[\linewidth][c]{\includegraphics[width=1.18\linewidth,keepaspectratio]{01-golden-egg.png}} \end{figure} @@ -341,6 +341,7 @@ \section{Computational Verification} \begin{table}[H] \centering \caption{Golden Ratio Convergents via Continued Fraction} +\resizebox{\linewidth}{!}{% \begin{tabular}{ccccc} \toprule $n$ & Convergent & Decimal & $|F_{n+1}/F_n - \phi|$ \\ @@ -357,6 +358,7 @@ \section{Computational Verification} 10 & $89/55$ & 1.618182 & 0.000148 \\ \bottomrule \end{tabular} +} \end{table} \section{The Golden Spiral} @@ -1093,6 +1095,7 @@ \section*{Appendix AB: Notation and Conventions} We collect the chapter's notation in a table. +\resizebox{\linewidth}{!}{% \begin{tabular}{|l|l|} \hline Symbol & Meaning \\ @@ -1109,6 +1112,7 @@ \section*{Appendix AB: Notation and Conventions} $\mathbb{Z}[\varphi]$ & ring of integers of $\mathbb{Q}(\sqrt 5)$ \\ \hline \end{tabular} +} \section*{Appendix AC: Open Problems for Future Chapters} \label{sec:01-app-AC} @@ -1339,6 +1343,7 @@ \section*{Appendix AM: $\varphi$ in Random Matrix Theory} \section*{Appendix AN: $\varphi$-Witness Cross-Reference Table} \label{sec:01-app-AN} +\resizebox{\linewidth}{!}{% \begin{tabular}{|l|l|l|} \hline Witness & Identity & Reference \\ @@ -1353,6 +1358,7 @@ \section*{Appendix AN: $\varphi$-Witness Cross-Reference Table} Pentagon alg.\ proof & $d^2 = (3 + \sqrt 5)/2$ & Thm~\ref{thm:01-pentagon-alg} \\ \hline \end{tabular} +} \bigskip \centerline{\textit{Eight witnesses, one constant: $\varphi$.}} diff --git a/docs/phd/chapters/02-golden-cut.tex b/docs/phd/chapters/02-golden-cut.tex index 7c7226ec59..2185d4d5fd 100644 --- a/docs/phd/chapters/02-golden-cut.tex +++ b/docs/phd/chapters/02-golden-cut.tex @@ -13,7 +13,7 @@ \chapter{Golden Cut: Background --- Neuro-Symbolic AI} \begin{figure}[H] \centering -\makebox[\linewidth][c]{\includegraphics[width=1.18\linewidth,keepaspectratio]{ch02-background.png}} +\makebox[\linewidth][c]{\includegraphics[width=1.18\linewidth,keepaspectratio]{02-golden-cut.png}} \caption*{Figure --- Golden Cut: Background --- Neuro-Symbolic AI.} \end{figure} @@ -310,6 +310,7 @@ \subsection{4.2 Powers of $\varphi$} A small table of exact values: \begin{center} +\resizebox{\linewidth}{!}{% \begin{tabular}{rll} \hline $n$ & $\varphi^n$ & decimal \\ @@ -325,6 +326,7 @@ \subsection{4.2 Powers of $\varphi$} $6$ & $8\varphi + 5$ & $17.94427\ldots$ \\ \hline \end{tabular} +} \end{center} The identity $\varphi^2 + \varphi^{-2} = 3$ is an @@ -489,6 +491,7 @@ \subsection{6.1 Definitions and Initial Values} \] The first few terms: \begin{center} +\resizebox{\linewidth}{!}{% \begin{tabular}{r|rrrrrrrrrrrr} $n$ & $0$ & $1$ & $2$ & $3$ & $4$ & $5$ & $6$ & $7$ & $8$ & $9$ & $10$ & $11$ \\ @@ -498,6 +501,7 @@ \subsection{6.1 Definitions and Initial Values} $L_n$ & $2$ & $1$ & $3$ & $4$ & $7$ & $11$ & $18$ & $29$ & $47$ & $76$ & $123$ & $199$ \\ \end{tabular} +} \end{center} \subsection{6.2 Binet's Formula} @@ -1529,6 +1533,7 @@ \subsection{19.1 Theorems Proven in This Chapter} chapter (pen-and-paper, following R12): \begin{center} +\resizebox{\linewidth}{!}{% \begin{tabular}{lll} \hline Label & Theorem & Section \\ @@ -1541,12 +1546,14 @@ \subsection{19.1 Theorems Proven in This Chapter} \ref{thm:gc-three-distance} & Three-Distance Theorem & \S\ref{sec:gc-three-distance} \\ \hline \end{tabular} +} \end{center} \subsection{19.2 Coq-Proven Theorems Cited (R14)} \label{subsec:gc-coq-proven} \begin{center} +\resizebox{\linewidth}{!}{% \begin{tabular}{lll} \hline Coq theorem & File & Status \\ @@ -1560,6 +1567,7 @@ \subsection{19.2 Coq-Proven Theorems Cited (R14)} \texttt{alpha\_phi\_pos} & \texttt{lr\_convergence.v} & Proven (QED) \\ \hline \end{tabular} +} \end{center} \subsection{19.3 Admitted Obligations} @@ -1991,6 +1999,7 @@ \section{Appendix F: Extended Fibonacci and Lucas Tables} \label{sec:gc-appendix-tables} \begin{center} +\resizebox{\linewidth}{!}{% \begin{tabular}{r|rr|r|rr} \hline $n$ & $F_n$ & $L_n$ & $n$ & $F_n$ & $L_n$ \\ @@ -2013,6 +2022,7 @@ \section{Appendix F: Extended Fibonacci and Lucas Tables} $15$ & $610$ & $1364$ & & & \\ \hline \end{tabular} +} \end{center} The sanctioned Trinity seeds @@ -2036,6 +2046,7 @@ \section{Appendix G: Markov Triple Tree} \] The first few levels: \begin{center} +\resizebox{\linewidth}{!}{% \begin{tabular}{ll} \hline Level & Triples \\ @@ -2047,6 +2058,7 @@ \section{Appendix G: Markov Triple Tree} 4 & $(1,13,34)$, $(5,13,194)$, $(2,29,169)$, $(5,29,433)$ \\ \hline \end{tabular} +} \end{center} The Lagrange constant of the Markov quadratic associated diff --git a/docs/phd/chapters/03-golden-harvest.tex b/docs/phd/chapters/03-golden-harvest.tex index f59139dc8e..52846b8176 100644 --- a/docs/phd/chapters/03-golden-harvest.tex +++ b/docs/phd/chapters/03-golden-harvest.tex @@ -569,10 +569,12 @@ \subsection{The Pisano Period and Periodicity Modulo \texorpdfstring{$m$}{m}} The first few Pisano periods are: \begin{center} +\resizebox{\linewidth}{!}{% \begin{tabular}{c|ccccccccccc} \(m\) & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 & 11 & 12 \\ \hline \(\pi(m)\) & 3 & 8 & 6 & 20 & 24 & 16 & 12 & 24 & 60 & 10 & 24 \end{tabular} +} \end{center} For \(m = 5\), \(\pi(5) = 20\), and indeed \(L_n \bmod 5\) has period 20; at \(n = 20\), @@ -604,7 +606,6 @@ \subsection{q-Deformed Fibonacci and Lucas Numbers} \begin{equation}\label{eq:gh-qbinet-approx} F_n(q) = F_n + \epsilon \sum_{k=0}^{n-3} (n-2-k) F_{k+1} F_{n-2-k} + O(\epsilon^2). -\end{parameter> \end{equation} \end{proposition} This first-order perturbation formula is useful in numerical analysis @@ -933,6 +934,7 @@ \subsection{Theorems and Proof Status} \texttt{fib\_lucas\_bridge.v} and \texttt{lucas\_closure\_gf16.v}: \begin{center} +\resizebox{\linewidth}{!}{% \begin{tabular}{llll} \hline Theorem & File & Lines & Status \\ \hline @@ -947,6 +949,7 @@ \subsection{Theorems and Proof Status} \texttt{kiefer\_contraction\_is\_phi\_inv} & \texttt{fib\_lucas\_bridge.v} & 311--360 & Admitted \\ \hline \end{tabular} +} \end{center} \noindent\textbf{Admitted theorems} require one or more of the following @@ -1618,6 +1621,7 @@ \subsection{Summary Table of All Principal Identities} \label{subsec:gh-summary-table} \begin{center} +\resizebox{\linewidth}{!}{% \begin{tabular}{lll} \hline Identity & Formula & Reference \\ \hline @@ -1633,6 +1637,7 @@ \subsection{Summary Table of All Principal Identities} Golden-section optimality & contraction \(= \varphi^{-1}\) & Thm.~\ref{thm:gh-kiefer-optimality} \\ \hline \end{tabular} +} \end{center} % ------------------------------------------------------------ diff --git a/docs/phd/chapters/04-golden-scales.tex b/docs/phd/chapters/04-golden-scales.tex index 68cb5bc1cf..f6a5d9fd8f 100644 --- a/docs/phd/chapters/04-golden-scales.tex +++ b/docs/phd/chapters/04-golden-scales.tex @@ -308,7 +308,7 @@ \subsection{The Euclidean Norm on \(\mathbb{Z}[\varphi]\)} number~1, it is a principal ideal domain, and in fact a Euclidean domain \cite{hardy_wright}. -\begin{definition}[Norm form on \(\mathbb{Z}[\varphi]\)]\label{def:gs-norm} +\begin{definition}[Norm form on \(\mathbb{Z}{[}\varphi{]}\)]\label{def:gs-norm} For \(\alpha = a + b\varphi \in \mathbb{Z}[\varphi]\) (with \(a,b \in \mathbb{Z}\)) define \[ @@ -335,7 +335,7 @@ \subsection{The Euclidean Norm on \(\mathbb{Z}[\varphi]\)} \qed \end{proof} -\begin{lemma}[Units of \(\mathbb{Z}[\varphi]\)]\label{lem:gs-units} +\begin{lemma}[Units of \(\mathbb{Z}{[}\varphi{]}\)]\label{lem:gs-units} An element \(\alpha \in \mathbb{Z}[\varphi]\) is a unit if and only if \(N(\alpha) = \pm 1\). The units form the group \(\{ \pm\phipow{n} : n \in \mathbb{Z} \}\). @@ -357,7 +357,7 @@ \subsection{The Euclidean Norm on \(\mathbb{Z}[\varphi]\)} \qed \end{proof} -\begin{theorem}[Euclidean Algorithm for \(\mathbb{Z}[\varphi]\)]\label{thm:gs-euclidean} +\begin{theorem}[Euclidean Algorithm for \(\mathbb{Z}{[}\varphi{]}\)]\label{thm:gs-euclidean} The pair \((\mathbb{Z}[\varphi], \nu)\) is a Euclidean domain: for every \(\alpha, \beta \in \mathbb{Z}[\varphi]\) with \(\beta \ne 0\) there exist \(q, r \in \mathbb{Z}[\varphi]\) such that @@ -673,6 +673,7 @@ \subsection{Fibonacci Index Table for Trinity Constants} \caption{Golden-scale constants in Trinity S\textsuperscript{3}AI. All values are \(S_n = \phipow{2n}+\phipow{-2n}\).} \label{tab:gs-fib} +\resizebox{\linewidth}{!}{% \begin{tabular}{rccll} \hline \(n\) & \(S_n\) & \(L_{2n}\) & Role & Coq tag \\ @@ -686,6 +687,7 @@ \subsection{Fibonacci Index Table for Trinity Constants} 6 & 322& \(L_{12}=322\) & d\_model upper tier & — \\ \hline \end{tabular} +} \end{table} \subsection{The Scale Hierarchy as a Spectral Decomposition} @@ -903,6 +905,7 @@ \subsection{Numerical Verification of Scale Constants} \caption{Verification of golden-scale values. \(\phipow{2} \approx 2.6180339887\), \(\phipow{-2} \approx 0.3819660113\).} \label{tab:gs-verify} +\resizebox{\linewidth}{!}{% \begin{tabular}{r|rrr|c} \hline \(n\) & \(\phipow{2n}\) (approx) & \(\phipow{-2n}\) (approx) & \(\phipow{2n}+\phipow{-2n}\) & \(S_n\) (exact) \\ @@ -917,6 +920,7 @@ \subsection{Numerical Verification of Scale Constants} 7 & 842.9988 & 0.0012 & 843.0000 & 843 \\ \hline \end{tabular} +} \end{table} The closure to integer values for all \(n\) confirms @@ -1201,7 +1205,7 @@ \section{Main Theorem: Integer Saturation of the \(\varphi\)-Scale Hierarchy} Let \(\varphi = (1+\sqrt{5})/2\) and let \((S_n)_{n \ge 0}\) be the sequence \(S_n = \phipow{2n} + \phipow{-2n}\). Then: -\begin{enumerate}[\upshape(i)] +\begin{enumerate}[label=\upshape(\roman*)] \item \emph{Integrality.} \(S_n \in \mathbb{Z}_{>0}\) for all \(n \ge 0\). \item \emph{Recurrence.} \(S_{n+1} = 3S_n - S_{n-1}\) with \(S_0 = 2\), \(S_1 = 3\). @@ -1225,7 +1229,7 @@ \section{Main Theorem: Integer Saturation of the \(\varphi\)-Scale Hierarchy} \begin{proof} We consolidate: -\begin{enumerate}[\upshape(i)] +\begin{enumerate}[label=\upshape(\roman*)] \item Theorem~\ref{thm:gs-recurrence}: every \(S_n\) is a positive integer. \item Theorem~\ref{thm:gs-recurrence}: the recurrence @@ -1404,6 +1408,7 @@ \subsection{Explicit Norm Form Calculations} for small \((a,b)\): \begin{center} +\resizebox{\linewidth}{!}{% \begin{tabular}{cc|r} \(a\) & \(b\) & \(N(a+b\varphi)\) \\ \hline @@ -1420,6 +1425,7 @@ \subsection{Explicit Norm Form Calculations} 3 & 1 & 5 \\ 1 & 2 & \(-5\) \\ \end{tabular} +} \end{center} The pattern of norms \(\pm1\) at \((1,0), (0,1), (1,1), (2,1), \ldots\) @@ -1435,7 +1441,7 @@ \subsection{Euclidean Algorithm: a Worked Example} We illustrate the Euclidean algorithm in \(\mathbb{Z}[\varphi]\) by computing \(\gcd(3, 2+\varphi)\). -\begin{example}[Euclidean algorithm in \(\mathbb{Z}[\varphi]\)]\label{ex:gs-euclid} +\begin{example}[Euclidean algorithm in \(\mathbb{Z}{[}\varphi{]}\)]\label{ex:gs-euclid} Let \(\alpha = 3\) (with \(a=3, b=0\), norm \(N(3)=9\)) and \(\beta = 2+\varphi\) (norm \(N(2+\varphi) = 4+2-1 = 5\)). @@ -1474,6 +1480,7 @@ \subsection{Recurrence Table Extended} \centering \caption{Extended golden-scale sequence \(S_n = 3S_{n-1}-S_{n-2}\).} \label{tab:gs-recurrence} +\resizebox{\linewidth}{!}{% \begin{tabular}{r|r|r} \hline \(n\) & \(S_n\) & \(\log_\varphi(S_n) \approx\) \\ @@ -1496,6 +1503,7 @@ \subsection{Recurrence Table Extended} 15 & 1860498 & 28.24 \\ \hline \end{tabular} +} \end{table} Notable values: \(S_9 = 5778 \approx \phipow{18}\) is the diff --git a/docs/phd/chapters/05-golden-bridge.tex b/docs/phd/chapters/05-golden-bridge.tex index e838d9036b..1e06025273 100644 --- a/docs/phd/chapters/05-golden-bridge.tex +++ b/docs/phd/chapters/05-golden-bridge.tex @@ -11,7 +11,7 @@ \chapter{The Golden Bridge: Fibonacci-Lucas Generating Functions} \begin{figure}[H] \centering -\makebox[\linewidth][c]{\includegraphics[width=1.18\linewidth,keepaspectratio]{ch12-hardware-bridge.png}} +\makebox[\linewidth][c]{\includegraphics[width=1.18\linewidth,keepaspectratio]{05-golden-bridge.png}} \end{figure} @@ -711,6 +711,7 @@ \section{Theorem and Lemma Library} \section*{Appendix A: Glossary} \label{sec:05-app-A} +\resizebox{\linewidth}{!}{% \begin{tabular}{ll} $F_n$ & Fibonacci sequence \\ $L_n$ & Lucas sequence \\ @@ -726,10 +727,12 @@ \section*{Appendix A: Glossary} $1/\varphi$ & Radius of convergence \\ $H_n$ & Hankel determinant \\ \end{tabular} +} \section*{Appendix B: First 30 Fibonacci and Lucas Numbers} \label{sec:05-app-B} +\resizebox{\linewidth}{!}{% \begin{tabular}{|c|c|c|} \hline $n$ & $F_n$ & $L_n$ \\ @@ -766,6 +769,7 @@ \section*{Appendix B: First 30 Fibonacci and Lucas Numbers} $29$ & $514229$ & $1149851$ \\ \hline \end{tabular} +} \section*{Appendix C: Detailed Long Division of $L(x)$} \label{sec:05-app-C} @@ -817,6 +821,7 @@ \section*{Appendix E: The Multiplicative Structure of $L(x) F(x)$} We expand $L(x) F(x)$ explicitly using Theorem~\ref{thm:05-fl-conv}: the coefficient of $x^n$ is $(n+1) F_n$. +\resizebox{\linewidth}{!}{% \begin{tabular}{|c|c|c|c|} \hline $n$ & $F_n$ & $(n+1) F_n$ & $\sum F_k L_{n-k}$ \\ @@ -829,6 +834,7 @@ \section*{Appendix E: The Multiplicative Structure of $L(x) F(x)$} $5$ & $5$ & $30$ & $0 + 7 + 4 + 6 + 4 + 10 = ... $ \\ \hline \end{tabular} +} The convolution identity $(n+1) F_n$ matches column 3, confirming Theorem~\ref{thm:05-fl-conv}. @@ -1350,6 +1356,7 @@ \section*{Appendix AE: Cross-Reference Table} We close with a table cross-referencing chapter results to the Trinity Anchor witnesses: +\resizebox{\linewidth}{!}{% \begin{tabular}{|l|l|l|} \hline Result & Trinity Anchor witness & Reference \\ @@ -1366,6 +1373,7 @@ \section*{Appendix AE: Cross-Reference Table} Companion matrix det $-1$ & matrix-Cassini & App~\ref{sec:05-app-F} \\ \hline \end{tabular} +} The Trinity Anchor identity $L_2 = 3$ casts ten distinct analytic-arithmetic shadows in the generating-function machinery. diff --git a/docs/phd/chapters/06-golden-mantissa.tex b/docs/phd/chapters/06-golden-mantissa.tex index be68e2d1cb..da94b4e07b 100644 --- a/docs/phd/chapters/06-golden-mantissa.tex +++ b/docs/phd/chapters/06-golden-mantissa.tex @@ -380,6 +380,7 @@ \subsection{The Lucas-Integer Floor Theorem} power of \(\varphi\) is always a Lucas number minus one. In particular: \begin{center} +\resizebox{\linewidth}{!}{% \begin{tabular}{rlll} \(n\) & \(\phipow{n}\) (approx.) & \(\lfloor\phipow{n}\rfloor\) & Lucas/Fibonacci link \\ \hline @@ -394,6 +395,7 @@ \subsection{The Lucas-Integer Floor Theorem} 8 & 46.979 & 46 & \(L_8 - 1 = 46\) \\ 10 & 122.99 & 122 & \(L_{10} - 1 = 122\) \\ \end{tabular} +} \end{center} The value \(L_7 = 29\) appears as the GF(16) safe-domain exponent upper bound in INV-3 (Proposition~\ref{prop:inv3-safe-domain}). @@ -666,6 +668,7 @@ \subsection{Seed Emission Gate and INV-7} The bijection between sub-claims and \texttt{EmitError} variants is exhaustive: \begin{center} +\resizebox{\linewidth}{!}{% \begin{tabular}{ll} Sub-claim & \texttt{EmitError} variant \\ \hline @@ -675,6 +678,7 @@ \subsection{Seed Emission Gate and INV-7} INV-7d & \texttt{BpbOutOfRange} (exit 24) \\ INV-7e & \texttt{DuplicateSeed} (exit 25) \\ \end{tabular} +} \end{center} Soundness (no false accepts) follows from the sequential \texttt{match} structure in \texttt{validate\_row()}; @@ -874,6 +878,7 @@ \subsection{Precision Comparison: GF(16) vs.\ IEEE Half} \label{ssec:precision-comparison} \begin{center} +\resizebox{\linewidth}{!}{% \begin{tabular}{lcccccc} Format & Sign & Exp & Mantissa & ULP (unity) & Certified band & Exact integers \\ \hline @@ -882,6 +887,7 @@ \subsection{Precision Comparison: GF(16) vs.\ IEEE Half} BF16 & 1 & 8 & 7 & \(2^{-7}\) & [1, 2) & integers \(\leq 256\) \\ FP32 & 1 & 8 & 23 & \(2^{-23}\) & [1, 2) & integers \(\leq 2^{24}\) \\ \end{tabular} +} \end{center} GF(16) and IEEE binary16 share the same bit layout (5-exp, 10-man); @@ -916,6 +922,7 @@ \subsection{Empirical Validation of the Golden Mantissa} tokens, GOLDEN SUNFLOWERS test corpus, Trinity S³AI pipeline at Gate-2): \begin{center} +\resizebox{\linewidth}{!}{% \begin{tabular}{lcccc} Format & BPB & Overflow events & INV-3 verified & INV-5 verified \\ \hline @@ -926,6 +933,7 @@ \subsection{Empirical Validation of the Golden Mantissa} BF16 (baseline) & 1.79 & 0 & N/A & No \\ FP32 (oracle) & 1.68 & 0 & N/A & No \\ \end{tabular} +} \end{center} The GF(16) BPB of 1.83 is within the Gate-2 target of @@ -965,6 +973,7 @@ \subsection{Invariant Map: Golden Mantissa to INV Chain} \label{ssec:inv-map} \begin{center} +\resizebox{\linewidth}{!}{% \begin{tabular}{lll} Invariant & Golden Mantissa connection & Status \\ \hline @@ -972,6 +981,7 @@ \subsection{Invariant Map: Golden Mantissa to INV Chain} INV-5 (Lucas closure) & Corollary~\ref{cor:lucas-closure}: exact integer accumulation & Proven \\ INV-7 (seed emission gate) & Theorem~\ref{thm:inv7-soundness} + Proposition~\ref{prop:inv7-mantissa} & Proven \\ \end{tabular} +} \end{center} All three invariants trace back to the Trinity Anchor @@ -1002,6 +1012,7 @@ \section{Appendix A — Fibonacci and Lucas Number Tables} with their connections to powers of \(\varphi\). \begin{center} +\resizebox{\linewidth}{!}{% \begin{tabular}{rrrrl} \(n\) & \(F_n\) & \(L_n\) & \(\lfloor\phipow{n}\rfloor\) & Note \\ \hline @@ -1027,6 +1038,7 @@ \section{Appendix A — Fibonacci and Lucas Number Tables} 19 &4181 &9349 &9349& \(L_{19} = 9349\) \\ 20 &6765 &15127&15126& \(L_{20} - 1 = 15126\) \\ \end{tabular} +} \end{center} Note the INV-7b warmup constant: \(4000 \approx L_{17} + 429 = @@ -1043,6 +1055,7 @@ \section{Appendix B — Zeckendorf Representation Examples} values: \begin{center} +\resizebox{\linewidth}{!}{% \begin{tabular}{rll} Integer & Zeckendorf & Fibonacci indices \\ \hline @@ -1054,6 +1067,7 @@ \section{Appendix B — Zeckendorf Representation Examples} 123 & \(F_{10}+F_8+F_6+F_2 = 55+21+8+2=86\)… & Let me recompute: \(F_{11}=89, F_{10}=55; 123-89=34=F_9; 89+34=123\) \\ 843 & \(F_{15}+F_{13}+\ldots\) & (omitted for space) \\ \end{tabular} +} \end{center} The Lucas numbers \(L_n = \phipow{n}+\phipow{-n}\) do not generally @@ -1162,6 +1176,7 @@ \section{Appendix F — INV-7 Exit Code Fibonacci Sequence} sequence: \begin{center} +\resizebox{\linewidth}{!}{% \begin{tabular}{rll} Exit code & EmitError & Fibonacci link \\ \hline @@ -1174,6 +1189,7 @@ \section{Appendix F — INV-7 Exit Code Fibonacci Sequence} 26 & MalformedSha & \(F_8 + 5\) \\ 30 & IoError & \(F_9 - 4 = 30\) \\ \end{tabular} +} \end{center} The base code 21 = \(F_8\) is the Fibonacci-sequence anchor for the @@ -1260,6 +1276,7 @@ \section{Appendix J — Numerical Constants (R6 Compliance Table)} \(\phipow{\cdot}\): \begin{center} +\resizebox{\linewidth}{!}{% \begin{tabular}{lll} Constant & φ-derivation & Value \\ \hline @@ -1276,6 +1293,7 @@ \section{Appendix J — Numerical Constants (R6 Compliance Table)} 1.5 (target BPB) & \(L_2/F_3 = 3/2\) & \(= 1.5\) (exact) \\ 0.1 (JEPA floor) & \(\phipow{-3}/L_3 \approx 0.236/4 \approx 0.059\) (approx) & \(= 0.1\) \\ \end{tabular} +} \end{center} \section{Discussion} @@ -1486,6 +1504,7 @@ \section{Appendix O — Coq Citation Index for This Chapter} \label{sec:appendix-o} \begin{center} +\resizebox{\linewidth}{!}{% \begin{tabular}{llll} Theorem & Coq file & Lines & Status \\ \hline @@ -1505,6 +1524,7 @@ \section{Appendix O — Coq Citation Index for This Chapter} \texttt{trinity-clara/proofs/igla/lucas\_closure\_gf16.v} & 200--260 & Admitted (Coq.Interval pending) \\ \end{tabular} +} \end{center} All Admitted entries are documented with honest \texttt{Admitted} diff --git a/docs/phd/chapters/07-golden-sprout.tex b/docs/phd/chapters/07-golden-sprout.tex index 39639470d7..881b81be96 100644 --- a/docs/phd/chapters/07-golden-sprout.tex +++ b/docs/phd/chapters/07-golden-sprout.tex @@ -27,7 +27,7 @@ \chapter{Golden Sprout: Fibonacci Recurrence as a Morphism in \(\mathbb{Z}[\varp \begin{figure}[H] \centering \makebox[\linewidth][c]{% - \includegraphics[width=1.18\linewidth,keepaspectratio]{ch07-vogel-phyllotaxis.png}} + \includegraphics[width=1.18\linewidth,keepaspectratio]{07-golden-sprout.png}} \caption*{Figure~7 — Golden Sprout: the Fibonacci spiral and its algebraic skeleton in the ring \(\mathbb{Z}[\varphi]\). Every arm count is a Fibonacci number; every spacing ratio tends to \(\varphi = \phipow{1}\).} @@ -311,7 +311,7 @@ \subsection{The Ring \(\mathbb{Z}[\varphi]\)}\label{subsec:ch7-ring} with the usual addition and multiplication inherited from \(\mathbb{R}\). \end{definition} -\begin{proposition}[\(\mathbb{Z}[\varphi]\) is a ring]\label{prop:ring} +\begin{proposition}[\(\mathbb{Z}{[}\varphi{]}\) is a ring]\label{prop:ring} \(\mathbb{Z}[\varphi]\) is closed under addition and multiplication, and is isomorphic to \(\mathbb{Z}[x]/(x^2 - x - 1)\). \end{proposition} @@ -331,7 +331,7 @@ \subsection{The Ring \(\mathbb{Z}[\varphi]\)}\label{subsec:ch7-ring} \qed \end{proof} -\begin{corollary}[Trinity anchor in \(\mathbb{Z}[\varphi]\)]\label{cor:trinity-anchor} +\begin{corollary}[Trinity anchor in \(\mathbb{Z}{[}\varphi{]}\)]\label{cor:trinity-anchor} \(\phipow{2} + \phipow{-2} = 3\). \end{corollary} @@ -545,7 +545,7 @@ \subsection{Norm and Units in \(\mathbb{Z}[\varphi]\)}\label{subsec:ch7-norm} using \(\varphi + \psi = 1\) and \(\varphi\psi = -1\). \end{definition} -\begin{proposition}[Units of \(\mathbb{Z}[\varphi]\)]\label{prop:units} +\begin{proposition}[Units of \(\mathbb{Z}{[}\varphi{]}\)]\label{prop:units} An element \(\alpha \in \mathbb{Z}[\varphi]\) is a unit if and only if \(N(\alpha) = \pm 1\), i.e., \(a^2 + ab - b^2 = \pm 1\). The units are \(\{\pm\phipow{n} \mid n \in \mathbb{Z}\}\). @@ -593,16 +593,20 @@ \subsection{Fibonacci Numbers Modulo 16}\label{subsec:ch7-mod16} \centering \caption{Fibonacci numbers modulo 16 (\(\pi(16)=24\)).} \label{tab:fib-mod16} +\resizebox{\linewidth}{!}{% \begin{tabular}{r|rrrrrrrrrrrr} \(n\) & 0&1&2&3&4&5&6&7&8&9&10&11\\ \hline \(F_n \bmod 16\) & 0&1&1&2&3&5&8&13&5&2&7&9\\ \end{tabular} +} +\resizebox{\linewidth}{!}{% \begin{tabular}{r|rrrrrrrrrrrr} \(n\) & 12&13&14&15&16&17&18&19&20&21&22&23\\ \hline \(F_n \bmod 16\) & 0&9&9&2&11&13&8&5&13&2&15&1\\ \end{tabular} +} \end{table} \subsection{The GF(16) Field}\label{subsec:ch7-gf16} @@ -663,7 +667,7 @@ \subsection{Algebraic Argument for the Generator Claim} We provide the hand proof that would constitute the body of \texttt{fib\_tess\_closure} once formalised. -\begin{proposition}[\(\varphi^4\) in \(\mathbb{Z}[\varphi]\)]\label{prop:phi4} +\begin{proposition}[\(\varphi^4\) in \(\mathbb{Z}{[}\varphi{]}\)]\label{prop:phi4} \(\phipow{4} = 3\varphi + 2\). \end{proposition} @@ -867,13 +871,14 @@ \subsection{Lucas Numbers and the Golden Integer Basis}\label{subsec:ch7-lucas} \subsection{Powers of \(\varphi\) and the Fibonacci Table}\label{subsec:ch7-powers} Table~\ref{tab:phi-powers} records \(\phipow{n} = F_n\varphi + F_{n-1}\) -for small \(n\), following R6 (all constants via \verb|\phipow{n}|\). +for small \(n\), following R6 (all constants via \texttt{\textbackslash{}phipow\{n\}}). \begin{table}[htb] \centering \caption{Powers of \(\varphi\) expressed in the \(\{1,\varphi\}\) basis. \(F_n\) and \(F_{n-1}\) are read from the last two columns.} \label{tab:phi-powers} +\resizebox{\linewidth}{!}{% \begin{tabular}{r|l|r|r} \(n\) & \(\phipow{n}\) (exact) & \(F_n\) & \(F_{n-1}\) \\ \hline @@ -890,6 +895,7 @@ \subsection{Powers of \(\varphi\) and the Fibonacci Table}\label{subsec:ch7-powe 8 & \(21\varphi+13\) & 21 & 13 \\ 16 & \(987\varphi+610\) & 987 & 610 \\ \end{tabular} +} \end{table} \subsection{The Minimal Polynomial of \(\varphi\)}\label{subsec:ch7-minimal} @@ -989,6 +995,7 @@ \subsection{Summary of Coq Certificates}\label{subsec:ch7-coq-table} \centering \caption{Coq certificate status for Chapter~7.} \label{tab:ch7-coq} +\resizebox{\linewidth}{!}{% \begin{tabular}{l|l|l|l} \textbf{Theorem} & \textbf{File} & \textbf{INV} & \textbf{Status} \\ \hline @@ -1008,6 +1015,7 @@ \subsection{Summary of Coq Certificates}\label{subsec:ch7-coq-table} & \emph{pen-and-paper} & — & Pen proof \\ \end{tabular} +} \end{table} \subsection{Admitted Obligations}\label{subsec:ch7-admitted} @@ -1157,7 +1165,7 @@ \section{Advanced Topics: Algebraic Number Theory of \(\mathbb{Z}[\varphi]\)} \subsection{Unique Factorisation in \(\mathbb{Z}[\varphi]\)} \label{subsec:ch7-ufd} -\begin{theorem}[\(\mathbb{Z}[\varphi]\) is a UFD]\label{thm:ufd} +\begin{theorem}[\(\mathbb{Z}{[}\varphi{]}\) is a UFD]\label{thm:ufd} The ring \(\mathbb{Z}[\varphi]\) is a unique factorisation domain (UFD). Equivalently, it is a principal ideal domain (PID) and a Euclidean domain with the Euclidean function \(|N(\alpha)| = |a^2 + ab - b^2|\) for @@ -1287,6 +1295,7 @@ \subsection{Mantissa Alphabet and Zeckendorf Codes} \centering \caption{Zeckendorf representation of GF16 mantissa values 0--15.} \label{tab:zeckendorf-gf16} +\resizebox{\linewidth}{!}{% \begin{tabular}{r|l|r|l} \textbf{Value} & \textbf{Zeckendorf} & \textbf{Value} & \textbf{Zeckendorf} \\ \hline @@ -1299,6 +1308,7 @@ \subsection{Mantissa Alphabet and Zeckendorf Codes} 6 & \(F_5+F_2\) & 14 & \(F_6+F_5+F_2\) \\ 7 & \(F_5+F_3\) & 15 & \(F_6+F_5+F_3\) \\ \end{tabular} +} \end{table} Observe that the representations for 0--7 use basis elements up to diff --git a/docs/phd/chapters/08-golden-crystal.tex b/docs/phd/chapters/08-golden-crystal.tex index 4a5b9ef0aa..7d1e6a4d03 100644 --- a/docs/phd/chapters/08-golden-crystal.tex +++ b/docs/phd/chapters/08-golden-crystal.tex @@ -14,7 +14,7 @@ \chapter{Golden Crystal: TF3/TF9 Sparse Ternary Matmul} \begin{figure}[H] \centering -\makebox[\linewidth][c]{\includegraphics[width=1.18\linewidth,keepaspectratio]{ch08-tf3-tf9-ternary-matmul.png}} +\makebox[\linewidth][c]{\includegraphics[width=1.18\linewidth,keepaspectratio]{08-golden-crystal.png}} \caption*{Figure --- Golden Crystal: TF3/TF9 Sparse Ternary Matmul.} \end{figure} @@ -1353,6 +1353,7 @@ \section{13. \texorpdfstring{$\varphi$}{phi}-Lattice rules R6 and R14. \begin{center} +\resizebox{\linewidth}{!}{% \begin{tabular}{lll} \hline Constant & Value & \(\varphi\)-derivation \\ @@ -1367,6 +1368,7 @@ \section{13. \texorpdfstring{$\varphi$}{phi}-Lattice \(|N(\varphi)|\) & \(1\) & unit of \(\mathbb{Z}[\varphi]\) \\ \hline \end{tabular} +} \end{center} \noindent @@ -1449,6 +1451,7 @@ \section{14. Quasicrystal Evidence Summary for \centering \caption{Quasicrystal--Trinity constant correspondence.} \label{tab:qc-evidence} +\resizebox{\linewidth}{!}{% \begin{tabular}{p{4.5cm}p{4.5cm}p{4cm}} \hline Quasicrystal geometry & Trinity S³AI constant & Evidence type \\ @@ -1461,6 +1464,7 @@ \section{14. Quasicrystal Evidence Summary for \(\mathbb{Z}[\varphi]\)-coordinates & Admissible weights \(\{-1,0,+1\}\) & R6 rule \\ \hline \end{tabular} +} \end{table} \section{5. Qed diff --git a/docs/phd/chapters/09-golden-seal.tex b/docs/phd/chapters/09-golden-seal.tex index 62a819f2cf..0fefbacb56 100644 --- a/docs/phd/chapters/09-golden-seal.tex +++ b/docs/phd/chapters/09-golden-seal.tex @@ -23,7 +23,7 @@ \chapter{Golden Seal: Closure and Invariant Sealing via the Lucas-2 Identity} \begin{figure}[H] \centering -\makebox[\linewidth][c]{\includegraphics[width=1.18\linewidth,keepaspectratio]{ch09-gf-vs-mxfp4-ablation.png}} +\makebox[\linewidth][c]{\includegraphics[width=1.18\linewidth,keepaspectratio]{09-golden-seal.png}} \caption*{Figure~9.0 --- The GF16 ablation landscape. Each column corresponds to a model scale M1--M6; each row to a format. The Lucas-2 seal $\varphi^2+\varphi^{-2}=3$ determines the shaded safe @@ -596,6 +596,7 @@ \subsection{R6 $\varphi$-Only Constants in INV-7 and INV-12} relevant to this chapter are: \begin{center} +\resizebox{\linewidth}{!}{% \begin{tabular}{lll} \toprule Constant & Value & Derivation \\ @@ -607,6 +608,7 @@ \subsection{R6 $\varphi$-Only Constants in INV-7 and INV-12} \texttt{PHI\_BIAS} & $60$ & $4 \times 15 = 4 \times (\phipow{0}+\cdots+\phipow{0})$ \\ \bottomrule \end{tabular} +} \end{center} All five constants satisfy R6; the derivation column shows @@ -1168,6 +1170,7 @@ \section{Qed Assertions} \label{sec:gs-qed} \begin{center} +\resizebox{\linewidth}{!}{% \begin{tabular}{lll} \toprule Theorem & File & Status \\ @@ -1188,6 +1191,7 @@ \section{Qed Assertions} & \texttt{INV3\_Gf16Precision.v} & Proven (9 Qed) \\ \bottomrule \end{tabular} +} \end{center} \coqcite{lucas_2_eq_3}{trinity-clara/proofs/lucas_closure_gf16.v}{41--80}{Proven} diff --git a/docs/phd/chapters/10-golden-bloom.tex b/docs/phd/chapters/10-golden-bloom.tex index 51d56dd08f..d55b0f0777 100644 --- a/docs/phd/chapters/10-golden-bloom.tex +++ b/docs/phd/chapters/10-golden-bloom.tex @@ -847,6 +847,7 @@ \subsection{Formal Coq Citation Map} \centering \caption{Coq theorem map for Chapter~10 (L10)} \label{tab:coq-map} +\resizebox{\linewidth}{!}{% \begin{tabular}{lllll} \toprule Theorem & File & Lines & Status & INV \\ @@ -858,6 +859,7 @@ \subsection{Formal Coq Citation Map} \texttt{golden\_angle\_uniqueness} & \texttt{lr\_convergence.v} & 91--180 & Admitted & INV-1 \\ \bottomrule \end{tabular} +} \end{table} The five entries above constitute the L10 Coq citation map required by diff --git a/docs/phd/chapters/11-vesica-piscis.tex b/docs/phd/chapters/11-vesica-piscis.tex index eb8e288dea..6ef7c92be6 100644 --- a/docs/phd/chapters/11-vesica-piscis.tex +++ b/docs/phd/chapters/11-vesica-piscis.tex @@ -5,7 +5,7 @@ \chapter{Vesica Piscis: Sacred Geometry, the \(\sqrt{3}\) Aspect Ratio, and the \begin{figure}[H] \centering -\makebox[\linewidth][c]{\includegraphics[width=1.18\linewidth,keepaspectratio]{ch11-pre-registration.png}} +\makebox[\linewidth][c]{\includegraphics[width=1.18\linewidth,keepaspectratio]{11-vesica-piscis.png}} \caption*{Figure --- Vesica Piscis: the lens-shaped intersection of two unit circles whose centres are mutually on each other's boundary, giving rise to the \(\sqrt{3}\) aspect ratio and a cascade of sacred-geometry relationships.} \end{figure} @@ -704,6 +704,7 @@ \subsection{Numerical Relations to the Golden Ratio} \centering \caption{Vesica piscis quantities in terms of \(\varphi\) and \(r\).} \label{tab:vp-quantities} +\resizebox{\linewidth}{!}{% \begin{tabular}{lll} \toprule Quantity & Exact value & \(\varphi\)-form \\ @@ -717,6 +718,7 @@ \subsection{Numerical Relations to the Golden Ratio} Trefoil frame ratio & \(\varphi^2 = \varphi + 1\) & \(\varphi^2\) \\ \bottomrule \end{tabular} +} \end{table} The entry \((\varphi^2 + \varphi^{-2})^{1/2} = \sqrt{3}\) makes the @@ -967,6 +969,7 @@ \subsection{Comparison with the Circle and the Ellipse} \centering \caption{Shape comparison for figures with the same horizontal width \(w = r\).} \label{tab:shape-comparison} +\resizebox{\linewidth}{!}{% \begin{tabular}{llll} \toprule Shape & Aspect ratio \(h/w\) & Area & Perimeter \\ @@ -977,6 +980,7 @@ \subsection{Comparison with the Circle and the Ellipse} Golden ellipse (\(a=r/2, b=r\varphi/2\)) & \(\varphi\) & \(\pi r^2 \varphi/4\) & approx. \\ \bottomrule \end{tabular} +} \end{table} The vesica piscis and the ellipse with the same aspect ratio \(\sqrt{3}\) @@ -1316,7 +1320,7 @@ \subsection{The \(\sqrt{3}\) Continued Fraction} The continued fraction expansion of \(\sqrt{3}\) is \[ - \sqrt{3} = [1; \overline{1, 2}] = 1 + \cfrac{1}{1 + \cfrac{1}{2 + \cfrac{1}{1 + \cfrac{1}{2 + \cdots}}}}}. + \sqrt{3} = [1; \overline{1, 2}] = 1 + \cfrac{1}{1 + \cfrac{1}{2 + \cfrac{1}{1 + \cfrac{1}{2 + \cdots}}}}. \] The convergents are the fractions \[ diff --git a/docs/phd/chapters/12-flower-of-life.tex b/docs/phd/chapters/12-flower-of-life.tex index 3a19c0b367..3dfa239915 100644 --- a/docs/phd/chapters/12-flower-of-life.tex +++ b/docs/phd/chapters/12-flower-of-life.tex @@ -680,6 +680,7 @@ \subsection{Higher-Dimensional Generalisations: \(E_8\) and \(D_4\)} \] The densities of the associated sphere packings are known for small \(n\): \begin{center} +\resizebox{\linewidth}{!}{% \begin{tabular}{cll} \hline \(n\) & Lattice & Density \\ @@ -691,6 +692,7 @@ \subsection{Higher-Dimensional Generalisations: \(E_8\) and \(D_4\)} 24& Leech & \(\pi^{12}/(12!/\text{const})\) \\ \hline \end{tabular} +} \end{center} The \(E_8\) lattice packing in eight dimensions was proved optimal by Viazovska (2016), and the Leech lattice packing in 24 dimensions by @@ -975,6 +977,7 @@ \subsection{Computational Aspects: Drawing the Flower of Life} with \(\|z\|^2=a^2-ab+b^2\le 4\): \begin{center} +\resizebox{\linewidth}{!}{% \begin{tabular}{ll} \hline Shell & Eisenstein integers \\ @@ -985,6 +988,7 @@ \subsection{Computational Aspects: Drawing the Flower of Life} \(k=3\) (\(|z|^2=4\)) & \(\pm 2, \pm 2\omega, \pm 2\omega^2\) \\ \hline \end{tabular} +} \end{center} This integer representation allows the construction to be carried out @@ -1248,6 +1252,7 @@ \subsection{Table of Connections} %%------------------------------------------------------------ \begin{center} +\resizebox{\linewidth}{!}{% \begin{tabular}{lll} \hline \textbf{Concept} & \textbf{Value / Formula} & \textbf{Trinity link} \\ @@ -1263,6 +1268,7 @@ \subsection{Table of Connections} Metatron's Cube & 78 edges & \(\binom{13}{2}=78\), Ch.13 \\ \hline \end{tabular} +} \end{center} %%------------------------------------------------------------ @@ -1470,6 +1476,7 @@ \subsection{Complete List of 19 Circle-Centres} via \(z=x+iy\), the 19 circle-centres are: \begin{center} +\resizebox{\linewidth}{!}{% \begin{tabular}{ccc} \hline \textbf{Shell} & \textbf{Norm} & \textbf{Eisenstein integers} \\ @@ -1481,6 +1488,7 @@ \subsection{Complete List of 19 Circle-Centres} 3 & 4 & \(2, 2\omega, 2\omega^2, -2, -2\omega, -2\omega^2\) \\ \hline \end{tabular} +} \end{center} We verify: \(|1-\omega|^2 = N(1-\omega)=(1)^2-(1)(-1)+(-1)^2=1+1+1=3\). diff --git a/docs/phd/chapters/13-metatron-cube.tex b/docs/phd/chapters/13-metatron-cube.tex index cf41450009..1f726e07d3 100644 --- a/docs/phd/chapters/13-metatron-cube.tex +++ b/docs/phd/chapters/13-metatron-cube.tex @@ -12,7 +12,7 @@ \chapter{Metatron's Cube and the Lucas-12 Orbit} \begin{figure}[H] \centering -\makebox[\linewidth][c]{\includegraphics[width=1.18\linewidth,keepaspectratio]{ch16-360-lane-grid.png}} +\makebox[\linewidth][c]{\includegraphics[width=1.18\linewidth,keepaspectratio]{13-metatron-cube.png}} \end{figure} @@ -894,12 +894,14 @@ \subsection{Architecture Summary} follows: \begin{center} +\resizebox{\linewidth}{!}{% \begin{tabular}{lrl} Cube & Radius & Architectural rôle \\\hline $\mathcal{C}_{0}$ & $\phi^{0} = 1$ & NCA core (unit circle) \\ $\mathcal{C}_{-5}$ & $\phi^{-5} \approx 0.0902$ & JEPA-T head proxy floor \\ $\mathcal{C}_{-6}$ & $\phi^{-6} \approx 0.0557$ & GF16 substrate floor \\ \end{tabular} +} \end{center} The architectural rôle of each cube is determined by its radius: the @@ -916,6 +918,7 @@ \section{Coq Citation Map (R14)} \begin{center} \small +\resizebox{\linewidth}{!}{% \begin{tabular}{@{}p{0.22\linewidth}p{0.50\linewidth}p{0.22\linewidth}@{}} Theorem / Lemma & Coq location & Status \\\hline Theorem~\ref{thm:13-projection} & elementary geometry & \textbf{Proven} (no Coq) \\ @@ -927,6 +930,7 @@ \section{Coq Citation Map (R14)} Lemma~\ref{lem:13-galois} & elementary algebraic & \textbf{Proven} \\ Lemma~\ref{lem:13-gf16-floor} & corollary of \filepath{gf16\_precision.v::phi\_inv\_six\_lucas} & \textbf{Admitted} \\ \end{tabular} +} \end{center} The Coq files referenced are: @@ -1077,6 +1081,7 @@ \section*{Appendix 13.B --- Coordinate Tables} angular coordinate $\theta_{k} = \pi k / 6$ in radians. \begin{center} +\resizebox{\linewidth}{!}{% \begin{tabular}{c|rr|c|c} $k$ & $x_{k}$ & $y_{k}$ & $|p_{k}|^{2}$ & $\theta_{k}$ \\\hline $0$ & $\phi$ & $0$ & $\phi^{2}$ & $0$ \\ @@ -1092,6 +1097,7 @@ \section*{Appendix 13.B --- Coordinate Tables} $10$ & $\phi/2$ & $-\phi\sqrt{3}/2$ & $\phi^{2}$ & $5\pi/3$\\ $11$ & $\phi\cos(\pi/6)$ & $-\phi/2$ & $\phi^{2}$ & $11\pi/6$\\ \end{tabular} +} \end{center} The squared-norm column is constant at $\phi^{2}$, which is the @@ -1329,6 +1335,7 @@ \section*{Appendix 13.G --- Three-Strand Cross-Reference} belongs to, in conformity with the Rule of Three (R12). \begin{center} +\resizebox{\linewidth}{!}{% \begin{tabular}{lll} Section & Strand & Content \\\hline Where Metatron's Cube Comes From & I & Origin and motivation \\ @@ -1349,6 +1356,7 @@ \section*{Appendix 13.G --- Three-Strand Cross-Reference} Empirical Re-corroboration in Chapter 26 & III & Cross-reference \\ Connection to Chapter 23 & III & GF16-algebra bridge \\ \end{tabular} +} \end{center} The strand-balance of the chapter is approximately: diff --git a/docs/phd/chapters/14-platonic-solids.tex b/docs/phd/chapters/14-platonic-solids.tex index a2328fcf55..0a279efead 100644 --- a/docs/phd/chapters/14-platonic-solids.tex +++ b/docs/phd/chapters/14-platonic-solids.tex @@ -41,6 +41,7 @@ \subsection{What Is a Regular Convex Polyhedron?} \centering \caption{The five Platonic solids and their basic combinatorial data.} \label{tab:platonic-summary} +\resizebox{\linewidth}{!}{% \begin{tabular}{lcccccc} \toprule Solid & Symbol & $V$ & $E$ & $F$ & Face & Vertex config \\ @@ -52,6 +53,7 @@ \subsection{What Is a Regular Convex Polyhedron?} Icosahedron & $\{3,5\}$ & 12 & 30 & 20 & triangle & $3.3.3.3.3$ \\ \bottomrule \end{tabular} +} \end{table} \subsection{Schläfli Symbols} @@ -201,6 +203,7 @@ \subsection{The Angle-Defect Argument} \noindent\textbf{Step 2: Exhaustion.} We check all $3 \times 3 = 9$ pairs: \begin{center} +\resizebox{\linewidth}{!}{% \begin{tabular}{ccc} \toprule $(p,q)$ & $1/p+1/q$ & $> 1/2$? \\ @@ -217,6 +220,7 @@ \subsection{The Angle-Defect Argument} $(5,5)$ & $2/5$ & no \\ \bottomrule \end{tabular} +} \end{center} Exactly five pairs satisfy the constraint: $(3,3)$, $(3,4)$, $(3,5)$, $(4,3)$, $(5,3)$. These correspond uniquely to the five Platonic solids by @@ -504,6 +508,7 @@ \subsection{Dihedral Angles} \centering \caption{Dihedral angles of the five Platonic solids.} \label{tab:dihedral-angles} +\resizebox{\linewidth}{!}{% \begin{tabular}{lcc} \toprule Solid & Exact dihedral angle & Decimal (degrees) \\ @@ -515,6 +520,7 @@ \subsection{Dihedral Angles} Icosahedron & $\arccos(-1/\sqrt{5})$ & $\approx 138.19°$ \\ \bottomrule \end{tabular} +} \end{table} \begin{proposition}[Icosahedral dihedral angle via $\varphi$] @@ -629,6 +635,7 @@ \subsection{Symmetry Groups of the Platonic Solids} \centering \caption{Symmetry groups of the Platonic solids.} \label{tab:symmetry-groups} +\resizebox{\linewidth}{!}{% \begin{tabular}{llcc} \toprule Solid(s) & Coxeter symbol & Rotation group & Full group \\ @@ -638,6 +645,7 @@ \subsection{Symmetry Groups of the Platonic Solids} Dodecahedron/Icosahedron & $[5,3]$ & $H_3 \cong A_5 \times \mathbb{Z}_2$ (order 60) & $[5,3]$ (order 120) \\ \bottomrule \end{tabular} +} \end{table} The rotation group of the icosahedron is isomorphic to $A_5$, the alternating @@ -666,6 +674,7 @@ \subsection{Inradius, Midradius, and Circumradius} \centering \caption{Characteristic radii of the Platonic solids (edge length = 1).} \label{tab:radii} +\resizebox{\linewidth}{!}{% \begin{tabular}{lccc} \toprule Solid & $r$ (inradius) & $\rho$ (midradius) & $R$ (circumradius) \\ @@ -677,6 +686,7 @@ \subsection{Inradius, Midradius, and Circumradius} Icosahedron & $\frac{\varphi^2}{2\sqrt{3}}$ & $\frac{\varphi}{2}$ & $\frac{\varphi}{2} \cdot \frac{1}{\sin(\pi/5)}$ \\ \bottomrule \end{tabular} +} \end{table} Note that the midradius of the dodecahedron and icosahedron are equal (both @@ -697,6 +707,7 @@ \subsection{Face Area, Volume, and Surface Area} \centering \caption{Volume and surface area of the Platonic solids (edge length $a$).} \label{tab:volumes} +\resizebox{\linewidth}{!}{% \begin{tabular}{lll} \toprule Solid & Volume & Surface area \\ @@ -708,6 +719,7 @@ \subsection{Face Area, Volume, and Surface Area} Icosahedron & $\dfrac{5a^3(3+\sqrt{5})}{12} = \dfrac{5a^3\varphi^2\sqrt{5}}{6}$ & $5a^2\sqrt{3}$ \\ \bottomrule \end{tabular} +} \end{table} \begin{proposition}[Icosahedron volume via $\varphi$] @@ -764,6 +776,7 @@ \subsection{Connection to the $E_8$ Root System} \centering \caption{Binary polyhedral groups and their relation to Platonic symmetries.} \label{tab:binary-groups} +\resizebox{\linewidth}{!}{% \begin{tabular}{lll} \toprule Platonic solid & Rotation group $G$ & Binary group $\tilde{G}$ \\ @@ -773,6 +786,7 @@ \subsection{Connection to the $E_8$ Root System} Icosahedron/Dodecahedron & $I \cong A_5$ (order 60) & $2I$ (binary icosahedral, order 120) \\ \bottomrule \end{tabular} +} \end{table} The binary icosahedral group $2I$ has order 120 and is isomorphic to $\mathrm{SL}(2,5)$. @@ -863,6 +877,7 @@ \subsection{Isoperimetric Properties} \caption{Isoperimetric quotient $36\pi V^2/S^3$ of the Platonic solids (sphere has value 1).} \label{tab:isoperimetric} +\resizebox{\linewidth}{!}{% \begin{tabular}{lc} \toprule Solid & $36\pi V^2/S^3$ \\ @@ -875,6 +890,7 @@ \subsection{Isoperimetric Properties} Sphere & $1.000$ \\ \bottomrule \end{tabular} +} \end{table} The icosahedron has the highest isoperimetric quotient among the Platonic solids, @@ -1242,6 +1258,7 @@ \subsection{Overview of Connections Across Chapters} \centering \caption{Cross-chapter connections involving Platonic solids.} \label{tab:chapter-connections} +\resizebox{\linewidth}{!}{% \begin{tabular}{lll} \toprule Chapter & Topic & Connection to Platonic solids \\ @@ -1257,6 +1274,7 @@ \subsection{Overview of Connections Across Chapters} Ch.~22 (NCA / $E_8$) & $E_8$ root system & binary icosahedral group, McKay correspondence \\ \bottomrule \end{tabular} +} \end{table} \subsection{The Role of the Icosahedron in the φ-Weighted Architecture} @@ -1723,6 +1741,7 @@ \subsection{Computing the Dihedral Angle of the Icosahedron} \centering \caption{Dihedral angles of the five Platonic solids (corrected).} \label{tab:dihedral-corrected} +\resizebox{\linewidth}{!}{% \begin{tabular}{lcc} \toprule Solid & Exact dihedral angle & Degrees \\ @@ -1734,6 +1753,7 @@ \subsection{Computing the Dihedral Angle of the Icosahedron} Icosahedron & $\arccos(-\sqrt{5}/3)$ & $\approx 138.19°$ \\ \bottomrule \end{tabular} +} \end{table} Using $\sqrt{5} = 2\varphi-1$ and the Trinity anchor, $-\sqrt{5}/3 = -(2\varphi-1)/3$. diff --git a/docs/phd/chapters/15-kepler-solids.tex b/docs/phd/chapters/15-kepler-solids.tex index d0fa057980..fe5599628d 100644 --- a/docs/phd/chapters/15-kepler-solids.tex +++ b/docs/phd/chapters/15-kepler-solids.tex @@ -21,7 +21,7 @@ \section*{Abstract} \(\mathbb{R}^n\), recording all ten regular star polytopes in \(\mathbb{R}^4\), and we trace throughout the omnipresence of the golden ratio \(\varphi = (1+\sqrt{5})/2\) as the algebraic -engine of stellations. Links to Chapter~\ref{ch:platonic} +engine of stellations. Links to Chapter~\ref{ch:platonic-solids} (Platonic solids, L14) and Chapter~\ref{ch:torus} (torus geometry, L18) are made explicit. @@ -72,7 +72,7 @@ \section{Historical Prologue: Kepler and the Harmony of Spheres} Each is a \emph{regular} polyhedron in the precise sense: all faces are congruent regular star polygons, and all vertex figures are congruent regular (possibly star) polygons. They -differ from the Platonic solids (Chapter~\ref{ch:platonic}) +differ from the Platonic solids (Chapter~\ref{ch:platonic-solids}) only in admitting \emph{non-convexity}: faces or edges penetrate the interior. @@ -152,7 +152,7 @@ \subsection{Great Stellated Dodecahedron \texorpdfstring{$\{5/2,\,3\}$}{5/2,3}} vertices coincide with those of a regular icosahedron, which is itself dual to the dodecahedron — a deep symmetry manifesting the icosahedral group \(I_h \cong A_5 \times \mathbb{Z}/2\) -(Chapter~\ref{ch:platonic}). +(Chapter~\ref{ch:platonic-solids}). \subsection{Great Dodecahedron \texorpdfstring{$\{5,\,5/2\}$}{5,5/2}} \label{ssec:great-dodecahedron} @@ -184,7 +184,7 @@ \subsection{Great Icosahedron \texorpdfstring{$\{3,\,5/2\}$}{3,5/2}} The great icosahedron is dual to the great stellated dodecahedron. Both share the icosahedral symmetry group, and the \(\varphi\)-geometry of the regular icosahedron -(Chapter~\ref{ch:platonic}) propagates unchanged into the star +(Chapter~\ref{ch:platonic-solids}) propagates unchanged into the star version. \subsection{Dual Pairs and Self-Duality} @@ -199,7 +199,7 @@ \subsection{Dual Pairs and Self-Duality} Duality exchanges faces and vertices (and reverses the Schläfli symbol); edges are preserved. Neither pair is self-dual, contrasting with the tetrahedron \(\{3,3\}\) among the Platonic -solids (Chapter~\ref{ch:platonic}). +solids (Chapter~\ref{ch:platonic-solids}). % ============================================================ \part*{Strand II — Formalisation} @@ -298,6 +298,7 @@ \subsection{The Euler Characteristic Constraint} \centering \caption{Combinatorial data for the four Kepler–Poinsot polyhedra.} \label{tab:kp-data} +\resizebox{\linewidth}{!}{% \begin{tabular}{lcccccc} \hline Solid & Symbol & $V$ & $E$ & $F$ & $\chi = V-E+F$ & Density\\ @@ -308,6 +309,7 @@ \subsection{The Euler Characteristic Constraint} Great icosahedron & $\{3,\,5/2\}$ & 12 & 30 & 20 & $2$ & 7\\ \hline \end{tabular} +} \end{table} The \emph{density} (or \emph{winding number}) of a regular star @@ -417,6 +419,7 @@ \subsection{The Complete List of Regular Polyhedra in \texorpdfstring{$\mathbb{R \centering \caption{All regular polyhedra in $\mathbb{R}^3$ (Platonic + Kepler–Poinsot).} \label{tab:all-regular} +\resizebox{\linewidth}{!}{% \begin{tabular}{lll} \hline Symbol & Name & Type \\ @@ -432,6 +435,7 @@ \subsection{The Complete List of Regular Polyhedra in \texorpdfstring{$\mathbb{R $\{3,5/2\}$ & Great icosahedron & Kepler–Poinsot \\ \hline \end{tabular} +} \end{table} This is the content of the main theorem we prove in @@ -783,10 +787,10 @@ \subsection{The Stellation Principle} $1, \varphi, \varphi^2, \varphi^3, \ldots$ in units of the icosahedron's inradius \cite{coxeter_fifty_nine_icosahedra}. -\section{Link to Platonic Solids (Chapter~\ref{ch:platonic})} +\section{Link to Platonic Solids (Chapter~\ref{ch:platonic-solids})} \label{sec:link-platonic} -Chapter~\ref{ch:platonic} (L14) establishes the five Platonic +Chapter~\ref{ch:platonic-solids} (L14) establishes the five Platonic solids as the complete list of regular convex polyhedra in $\mathbb{R}^3$, using the Euler formula and angle-sum arguments. The present chapter extends that classification to @@ -800,7 +804,7 @@ \section{Link to Platonic Solids (Chapter~\ref{ch:platonic})} icosahedron and dodecahedron. No new symmetry group is required: the star polyhedra live inside the same group-theoretic framework as two of the Platonic solids -(Chapter~\ref{ch:platonic}). +(Chapter~\ref{ch:platonic-solids}). \item \textbf{Vertex superposition.} The vertices of the Kepler–Poinsot polyhedra are subsets of the vertices of @@ -888,6 +892,7 @@ \subsection{Regular Polytopes in \texorpdfstring{$\mathbb{R}^4$}{R4}} \centering \caption{The ten regular star 4-polytopes (Coxeter 1933).} \label{tab:star-4-polytopes} +\resizebox{\linewidth}{!}{% \begin{tabular}{llcc} \hline Symbol & Common name & Cells & Vertex figures\\ @@ -904,6 +909,7 @@ \subsection{Regular Polytopes in \texorpdfstring{$\mathbb{R}^4$}{R4}} $\{5/2,3,3\}$ & Great grand stellated 120-cell & 120 $\{5/2,3\}$ & 4 per vtx\\ \hline \end{tabular} +} \end{table} These ten polytopes are the 4-dimensional analogues of the @@ -1036,7 +1042,7 @@ \subsection{Basic Identities} Identity~\eqref{eq:trinity-identity} is the Trinity anchor $\varphi^2 + \varphi^{-2} = 3$ that ties the algebraic theory to the spectral parameter $\alpha_\varphi$ introduced in -Chapter~\ref{ch:platonic}. +Chapter~\ref{ch:platonic-solids}. \subsection{Stellation Ratio Tower} \label{ssec:stellation-tower} @@ -1064,7 +1070,7 @@ \subsection{Volume Ratios} V(\{3,5/2\}) &= \varphi^{-3} V(\{3,5\}), \end{align*} where all volumes are expressed in terms of the standard -dodecahedron/icosahedron volumes (Chapter~\ref{ch:platonic}). +dodecahedron/icosahedron volumes (Chapter~\ref{ch:platonic-solids}). Every ratio is a power of $\varphi$, confirming the $\varphi$-substrate hypothesis of the monograph. @@ -1330,7 +1336,7 @@ \section{Towards a Unified Spectral Theory} \label{sec:spectral-theory} The spectral parameter $\alpha_\varphi$ introduced in -Chapter~\ref{ch:platonic} is defined as +Chapter~\ref{ch:platonic-solids} is defined as \[ \alpha_\varphi = \frac{\ln(\varphi^2)}{\pi} = \frac{2\ln\varphi}{\pi}. \] diff --git a/docs/phd/chapters/16-sacred-ratios.tex b/docs/phd/chapters/16-sacred-ratios.tex index df8f4ef1e4..a1ca7a1752 100644 --- a/docs/phd/chapters/16-sacred-ratios.tex +++ b/docs/phd/chapters/16-sacred-ratios.tex @@ -11,7 +11,7 @@ \chapter{Sacred Ratios: Metallic Means, Diophantine Approximation, \begin{figure}[H] \centering -\makebox[\linewidth][c]{\includegraphics[width=1.18\linewidth,keepaspectratio]{ch16-360-lane-grid.png}} +\makebox[\linewidth][c]{\includegraphics[width=1.18\linewidth,keepaspectratio]{16-sacred-ratios.png}} \caption*{Figure --- Sacred Ratios: 360-lane Phi-Distance Grid.} \end{figure} @@ -84,6 +84,7 @@ \subsection{From One Golden Ratio to Infinitely Many} \centering \caption{The family of metallic means $M_n = (n+\sqrt{n^2+4})/2$.} \label{tab:metallic-means} +\resizebox{\linewidth}{!}{% \begin{tabular}{cllll} \toprule $n$ & Name & Decimal & Defining polynomial @@ -102,6 +103,7 @@ \subsection{From One Golden Ratio to Infinitely Many} & $(5+\sqrt{29})/2$ \\ \bottomrule \end{tabular} +} \end{table} Each metallic mean is a \emph{quadratic irrational}, @@ -1183,6 +1185,7 @@ \subsection{Orders in Quadratic Fields} \centering \caption{Quadratic fields for small metallic means.} \label{tab:metallic-fields} +\resizebox{\linewidth}{!}{% \begin{tabular}{cllll} \toprule $n$ & $\Delta = n^2+4$ & Field $K_n$ & Disc.\ square-free? @@ -1195,6 +1198,7 @@ \subsection{Orders in Quadratic Fields} $5$ & $29$ & $\mathbb{Q}(\sqrt{29})$ & Yes & Yes \\ \bottomrule \end{tabular} +} \end{table} For $n = 1$ ($\phi$), $\mathbb{Z}[\phi]$ is the diff --git a/docs/phd/chapters/17-golden-spiral.tex b/docs/phd/chapters/17-golden-spiral.tex index 8e277ea8f0..81f3bc6a4b 100644 --- a/docs/phd/chapters/17-golden-spiral.tex +++ b/docs/phd/chapters/17-golden-spiral.tex @@ -3,7 +3,7 @@ \chapter{Golden Spiral: Ablation Matrix} \begin{figure}[H] \centering -\makebox[\linewidth][c]{\includegraphics[width=1.18\linewidth,keepaspectratio]{ch17-ablation-matrix.png}} +\makebox[\linewidth][c]{\includegraphics[width=1.18\linewidth,keepaspectratio]{17-golden-spiral.png}} \caption*{Figure --- Golden Spiral: Ablation Matrix.} \end{figure} diff --git a/docs/phd/chapters/18-torus-geometry.tex b/docs/phd/chapters/18-torus-geometry.tex index 14069ae6ae..eb06902e7f 100644 --- a/docs/phd/chapters/18-torus-geometry.tex +++ b/docs/phd/chapters/18-torus-geometry.tex @@ -4,7 +4,7 @@ \chapter{Torus Geometry: \texorpdfstring{$\mathbb{T}^2$}{T2}, Golden Aspect, and \begin{figure}[H] \centering -\makebox[\linewidth][c]{\includegraphics[width=1.18\linewidth,keepaspectratio]{ch18-limitations.png}} +\makebox[\linewidth][c]{\includegraphics[width=1.18\linewidth,keepaspectratio]{18-torus-geometry.png}} \caption*{Figure --- Torus Geometry: $\mathbb{T}^2 = S^1 \times S^1$, golden-ratio aspect $R/r = \varphi$, Hopf fibration, Villarceau circles, Clifford torus, torus knots, and Weyl equidistribution.} \end{figure} @@ -746,6 +746,7 @@ \subsection{Fibonacci Torus Knots}\label{subsec:ch18-fibonacci-knots} The first few Fibonacci torus knots: \begin{center} +\resizebox{\linewidth}{!}{% \begin{tabular}{lll} \hline $T(F_m, F_n)$ & Type & Name \\ @@ -757,6 +758,7 @@ \subsection{Fibonacci Torus Knots}\label{subsec:ch18-fibonacci-knots} $T(8,13)$ & torus knot & see \cite{Coxeter1973} \\ \hline \end{tabular} +} \end{center} \subsection{Alexander Polynomial of \texorpdfstring{$T(p,q)$}{T(p,q)}} @@ -1502,6 +1504,7 @@ \section{Coq Citation Map (R14)} \begin{center} \small +\resizebox{\linewidth}{!}{% \begin{tabular}{llll} \hline Theorem & Coq file & Lines & Status \\ @@ -1514,6 +1517,7 @@ \section{Coq Citation Map (R14)} Thm~\ref{thm:three-distance} (Three-distance) & \texttt{ThreeDistance.v} & 1--60 & Admitted \\ \hline \end{tabular} +} \end{center} All six theorems carry \texttt{Admitted} status due to the absence of a complete diff --git a/docs/phd/chapters/19-fibonacci-tesselation.tex b/docs/phd/chapters/19-fibonacci-tesselation.tex index f2fd1b9fff..3d4a62639e 100644 --- a/docs/phd/chapters/19-fibonacci-tesselation.tex +++ b/docs/phd/chapters/19-fibonacci-tesselation.tex @@ -4,7 +4,7 @@ \chapter{Fibonacci Tessellation: Word Combinatorics, Sturmian Theory, and the Mo \begin{figure}[H] \centering -\makebox[\linewidth][c]{\includegraphics[width=1.18\linewidth,keepaspectratio]{ch19-statistical-analysis.png}} +\makebox[\linewidth][c]{\includegraphics[width=1.18\linewidth,keepaspectratio]{19-fibonacci-tesselation.png}} \caption*{Figure --- Fibonacci Tessellation: combinatorial word structure and Zeckendorf rectangle decompositions arising from the Fibonacci substitution \(\sigma(a)=ab\), \(\sigma(b)=a\).} diff --git a/docs/phd/chapters/20-standard-model.tex b/docs/phd/chapters/20-standard-model.tex index a47bf6d2d5..b033880a04 100644 --- a/docs/phd/chapters/20-standard-model.tex +++ b/docs/phd/chapters/20-standard-model.tex @@ -114,6 +114,7 @@ \subsection{Quarks} \begin{table}[h] \centering \caption{Quark Properties} +\resizebox{\linewidth}{!}{% \begin{tabular}{lcccc} \toprule Quark & Charge $Q$ & Mass (MeV) & Color & Generation \\ @@ -126,6 +127,7 @@ \subsection{Quarks} bottom & $-1/3$ & 4180 & $\mathbf{3}$ & 3 \\ \bottomrule \end{tabular} +} \end{table} \subsection{Leptons} @@ -141,6 +143,7 @@ \subsection{Leptons} \begin{table}[h] \centering \caption{Lepton Properties} +\resizebox{\linewidth}{!}{% \begin{tabular}{lcccc} \toprule Lepton & Charge $Q$ & Mass (MeV) & Generation \\ @@ -153,6 +156,7 @@ \subsection{Leptons} tau neutrino & $0$ & $<18.2$ & 3 \\ \bottomrule \end{tabular} +} \end{table} \section{Bosons} @@ -174,6 +178,7 @@ \subsection{Gauge Bosons} \begin{table}[h] \centering \caption{Gauge Boson Properties} +\resizebox{\linewidth}{!}{% \begin{tabular}{lccc} \toprule Boson & Mass (GeV) & Charge & Group \\ @@ -184,6 +189,7 @@ \subsection{Gauge Bosons} gluons $g$ & $\sim 0$ & 0 & $SU(3)$ \\ \bottomrule \end{tabular} +} \end{table} \subsection{Higgs Boson} @@ -294,6 +300,7 @@ \subsection{Quark Mass Ratios} \begin{table}[h] \centering \caption{Quark Mass Ratios} +\resizebox{\linewidth}{!}{% \begin{tabular}{lccc} \toprule Ratio & Value & Golden Power & Agreement \\ @@ -305,6 +312,7 @@ \subsection{Quark Mass Ratios} $c/d$ & 272 & $\phi^{10.4}$ & Fair \\ \bottomrule \end{tabular} +} \end{table} \section{Coupling Constants} @@ -1907,6 +1915,7 @@ \section{Scarab-L20 Coq Citation Map (R14)} \centering \caption{Coq citation map (scarab-l20 pass, R14).} \label{tab:scarab-coq-map} +\resizebox{\linewidth}{!}{% \begin{tabular}{@{}llll@{}} \toprule Coq Theorem & File & Lines & Status \\ @@ -1921,6 +1930,7 @@ \section{Scarab-L20 Coq Citation Map (R14)} & \texttt{igla\_asha\_bound.v} & 56--140 & Proven \\ \bottomrule \end{tabular} +} \end{table} \noindent diff --git a/docs/phd/chapters/21-quantum-field.tex b/docs/phd/chapters/21-quantum-field.tex index 22e0b07ec3..d9851945e7 100644 --- a/docs/phd/chapters/21-quantum-field.tex +++ b/docs/phd/chapters/21-quantum-field.tex @@ -6,7 +6,7 @@ \chapter{Quantum Field Theory — Fields of Nature} \begin{figure}[H] \centering -\makebox[\linewidth][c]{\includegraphics[width=1.18\linewidth,keepaspectratio]{ch29-sacred-formula-v.png}} +\makebox[\linewidth][c]{\includegraphics[width=1.18\linewidth,keepaspectratio]{21-quantum-field.png}} \end{figure} diff --git a/docs/phd/chapters/22-e8-symmetry.tex b/docs/phd/chapters/22-e8-symmetry.tex index 7d4041b40c..ac4e3cd507 100644 --- a/docs/phd/chapters/22-e8-symmetry.tex +++ b/docs/phd/chapters/22-e8-symmetry.tex @@ -648,6 +648,7 @@ \section{Three-Strand Synthesis} fact: \begin{center} +\resizebox{\linewidth}{!}{% \begin{tabular}{@{}lll@{}} \toprule \textbf{Strand} & \textbf{Setting} & \textbf{Golden-ratio role} \\ @@ -657,6 +658,7 @@ \section{Three-Strand Synthesis} III — NCA & NCA layer, \(\mathbb{R}^8\) logit space & \(\varphi\) = certified band endpoint; width \(= \varphi^2 - \varphi = 1\) \\ \bottomrule \end{tabular} +} \end{center} \medskip @@ -900,6 +902,7 @@ \subsection{Corroboration Record} \label{subsec:falsify-corroboration} \begin{center} +\resizebox{\linewidth}{!}{% \begin{tabular}{@{}llll@{}} \toprule \textbf{Date} & \textbf{Evidence} & \textbf{Configuration} & \textbf{Status} \\ @@ -916,6 +919,7 @@ \subsection{Corroboration Record} pending & Victory-gate run (BPB < 1.50) & Certified band & pending \\ \bottomrule \end{tabular} +} \end{center} The empirical band data \([1.5, 2.8]\) provides corroboration that @@ -1022,6 +1026,7 @@ \section{Proof Appendix: Coq Status for INV-4} % ----------------------------------------------------------------------- \begin{center} +\resizebox{\linewidth}{!}{% \begin{tabular}{@{}lllll@{}} \toprule \textbf{Theorem} & \textbf{File} & \textbf{Lines} & \textbf{Status} & \textbf{Invariant} \\ @@ -1031,6 +1036,7 @@ \section{Proof Appendix: Coq Status for INV-4} \texttt{entropy\_upper\_numeric\_bound} & \texttt{nca\_entropy\_band.v} & 81--120 & \textbf{Admitted} & INV-4 \\ \bottomrule \end{tabular} +} \end{center} Per Rule R5 (honesty), the \texttt{Admitted} status of @@ -1044,6 +1050,7 @@ \section{Notation Summary} % ----------------------------------------------------------------------- \begin{center} +\resizebox{\linewidth}{!}{% \begin{tabular}{@{}ll@{}} \toprule \textbf{Symbol} & \textbf{Meaning} \\ @@ -1062,6 +1069,7 @@ \section{Notation Summary} \(\mathrm{Nm}(q)\) & Quaternionic norm of \(q\) \\ \bottomrule \end{tabular} +} \end{center} % ----------------------------------------------------------------------- @@ -1427,6 +1435,7 @@ \section{φ-Derivation of All Numeric Constants (R6 Compliance)} constants introduced in this chapter and their \(\varphi\)-derivation: \begin{center} +\resizebox{\linewidth}{!}{% \begin{tabular}{@{}llll@{}} \toprule \textbf{Constant} & \textbf{Value} & \textbf{\(\varphi\)-derivation} & \textbf{Section} \\ @@ -1447,6 +1456,7 @@ \section{φ-Derivation of All Numeric Constants (R6 Compliance)} \(\log_2 6\) & 2.585\ldots & \(\log_2(2\times3)\) & \ref{subsec:strand3-band-derivation} \\ \bottomrule \end{tabular} +} \end{center} All non-integer constants are \(\varphi\)-powers or \(\varphi\)-derived @@ -1503,6 +1513,7 @@ \section{Formal Verification Roadmap} \texttt{Admitted} items: \begin{center} +\resizebox{\linewidth}{!}{% \begin{tabular}{@{}p{5cm}llp{4cm}@{}} \toprule \textbf{Claim} & \textbf{Status} & \textbf{Priority} & \textbf{Path to close} \\ @@ -1518,6 +1529,7 @@ \section{Formal Verification Roadmap} Dual-band separation & Rust + JSON & done & — \\ \bottomrule \end{tabular} +} \end{center} The highest-priority item is the \texttt{Coq.Interval} dependency for diff --git a/docs/phd/chapters/23-gf16-algebra.tex b/docs/phd/chapters/23-gf16-algebra.tex index a06ae60f1b..3de8ce559a 100644 --- a/docs/phd/chapters/23-gf16-algebra.tex +++ b/docs/phd/chapters/23-gf16-algebra.tex @@ -225,6 +225,7 @@ \subsection{Primitive Element and Multiplication Structure} \caption{Powers of the primitive element \(\alpha\) in \(\mathrm{GF}(16)\), expressed as 4-bit vectors \((a_3,a_2,a_1,a_0)\).} \label{tab:gf16-powers} +\resizebox{\linewidth}{!}{% \begin{tabular}{ccc} \hline \textbf{Power} & \textbf{Polynomial} & \textbf{4-bit vector} \\ @@ -247,6 +248,7 @@ \subsection{Primitive Element and Multiplication Structure} \(\alpha^{15}\) & \(1\) & \(0001\) \\ \hline \end{tabular} +} \end{table} \begin{remark}[Connection to INV-3 runtime constant] @@ -1111,6 +1113,7 @@ \section{Coq Certification Map} \caption{GF(16) Coq certification map (L23). Status: \textbf{P} = Proven (Qed), \textbf{A} = Admitted.} \label{tab:gf16-coq-map} +\resizebox{\linewidth}{!}{% \begin{tabular}{llll} \hline \textbf{Theorem} & \textbf{File} & \textbf{Lines} & \textbf{Status} \\ @@ -1128,6 +1131,7 @@ \section{Coq Certification Map} \texttt{gf16\_field\_size\_correct} & \texttt{lucas\_closure\_gf16.v} & 38--40 & P \\ \hline \end{tabular} +} \end{table} \noindent diff --git a/docs/phd/chapters/24-igla-architecture.tex b/docs/phd/chapters/24-igla-architecture.tex index 98c36e643f..e13554d0d2 100644 --- a/docs/phd/chapters/24-igla-architecture.tex +++ b/docs/phd/chapters/24-igla-architecture.tex @@ -168,6 +168,7 @@ \subsection{Baseline Ablation: Plain ReLU vs.\ \texorpdfstring{$\mathrm{relu}^2$ result files; step 81k from the champion lock (\texttt{cd91c45}).} \label{tab:ch24-relu-ablation} +\resizebox{\linewidth}{!}{% \begin{tabular}{lccc} \hline Activation & BPB @ 27k & BPB @ 81k & $\Delta$BPB \\ @@ -177,6 +178,7 @@ \subsection{Baseline Ablation: Plain ReLU vs.\ \texorpdfstring{$\mathrm{relu}^2$ $\mathrm{gelu}$ (comparison) & 2.57 & --- & $\approx +0.03$ \\ \hline \end{tabular} +} \end{table} The $\mathrm{relu}^2$ activation is the only change between the @@ -294,6 +296,7 @@ \subsection{Parameter Budget at \texorpdfstring{$h = 828$}{h=828}} multiples of $\varphi$-derived bases. Total is approximate due to bias terms.} \label{tab:ch24-param-budget} +\resizebox{\linewidth}{!}{% \begin{tabular}{lrr} \hline Component & Parameters & Derivation \\ @@ -309,6 +312,7 @@ \subsection{Parameter Budget at \texorpdfstring{$h = 828$}{h=828}} \textbf{Total (approx.)} & $\approx \mathbf{420\,416}$ & $< 0.5$M params \\ \hline \end{tabular} +} \end{table} The sub-0.5M-parameter regime places IGLA firmly in the \emph{tiny model} class @@ -447,6 +451,7 @@ \subsection{R6 Compliance: No Free Hyperparameters} \caption{R6 compliance table: all champion constants and their $\varphi$-derivations. All values trace to \texttt{assertions/igla\_assertions.json}.} \label{tab:ch24-r6-constants} +\resizebox{\linewidth}{!}{% \begin{tabular}{lcll} \hline Constant & Value & $\varphi$-derivation & INV anchor \\ @@ -466,6 +471,7 @@ \subsection{R6 Compliance: No Free Hyperparameters} ASHA rung ratio & 3 & $\varphi^2 + \varphi^{-2}$ & INV-12 \\ \hline \end{tabular} +} \end{table} \subsection{Derivation of \texorpdfstring{$h = 828$}{h=828}} @@ -640,6 +646,7 @@ \subsection{Champion Fingerprint Table} per Table~\ref{tab:ch24-r6-constants}. Lock SHA refers to the \texttt{git} commit hash prefix that sealed the result.} \label{tab:ch24-champion-fingerprint} +\resizebox{\linewidth}{!}{% \begin{tabular}{ll} \hline Field & Value \\ @@ -661,6 +668,7 @@ \subsection{Champion Fingerprint Table} Gate target (BPB) & $< 1.50$ on 3 distinct seeds \\ \hline \end{tabular} +} \end{table} \subsection{Seed Cohort and Phase-1 SSOT Writers} @@ -675,6 +683,7 @@ \subsection{Seed Cohort and Phase-1 SSOT Writers} \{47, 89, 144, 123\} are the Railway SSOT writers; they had not yet reached step 27\,000 at snapshot time.} \label{tab:ch24-seed-cohort} +\resizebox{\linewidth}{!}{% \begin{tabular}{lcccl} \hline Seed & Lane & Steps & BPB & Status \\ @@ -688,6 +697,7 @@ \subsection{Seed Cohort and Phase-1 SSOT Writers} 144 & phase1-rng144 & 11\,000 & 3.0025 & warmup \\ \hline \end{tabular} +} \end{table} The Phase-1 SSOT writers are deployed to Railway service @@ -848,6 +858,7 @@ \subsection{Ablation: Attention Depth} 2-layer: champion (\texttt{cd91c45}); 3-layer: \texttt{trinity3k-h48-l3-hd4-s64\_seed43.json}.} \label{tab:ch24-attn-depth} +\resizebox{\linewidth}{!}{% \begin{tabular}{lcc} \hline Layers & $h$ & Final BPB \\ @@ -857,6 +868,7 @@ \subsection{Ablation: Attention Depth} 3 & 48 & 4.380 \\ \hline \end{tabular} +} \end{table} Note: the 3-layer result uses $h = 48$ (not 828), so the comparison is not @@ -984,6 +996,7 @@ \subsection{Corroboration Record} ACM~AE status: \emph{Functional} for locked seeds; \emph{pending} for Phase-1 seeds.} \label{tab:ch24-corroboration} +\resizebox{\linewidth}{!}{% \begin{tabular}{lccll} \hline Seed & BPB & Steps & ACM~AE & Note \\ @@ -997,6 +1010,7 @@ \subsection{Corroboration Record} 144 & 3.0025 & 11\,000 & pending & warmup \\ \hline \end{tabular} +} \end{table} At the time of writing, Phase-1 seeds 47, 89, 144, 123 are in the warmup phase @@ -1494,6 +1508,7 @@ \section{Summary of All \texorpdfstring{\textbackslash coqcite}{coqcite} Links} proof body is \texttt{Admitted.} in the \texttt{.v} file.} \label{tab:ch24-coqcite-map} \small +\resizebox{\linewidth}{!}{% \begin{tabular}{llll} \hline Theorem & File & Lines & Status \\ @@ -1515,6 +1530,7 @@ \section{Summary of All \texorpdfstring{\textbackslash coqcite}{coqcite} Links} \texttt{igla\_found\_criterion} & (no file yet, INV-7) & --- & \textit{Admitted} \\ \hline \end{tabular} +} \end{table} All \texttt{.v} files listed above reside in diff --git a/docs/phd/chapters/25-benchmarks.tex b/docs/phd/chapters/25-benchmarks.tex index b19bf0efca..897b01f37f 100644 --- a/docs/phd/chapters/25-benchmarks.tex +++ b/docs/phd/chapters/25-benchmarks.tex @@ -13,7 +13,7 @@ \chapter{Benchmarks: BPB Calibration and Gate-2/3 Trajectory} \begin{figure}[H] \centering -\makebox[\linewidth][c]{\includegraphics[width=1.18\linewidth,keepaspectratio]{ch25-phi-period-cycles.png}} +\makebox[\linewidth][c]{\includegraphics[width=1.18\linewidth,keepaspectratio]{25-benchmarks.png}} \caption*{Figure~25.0 --- Benchmarks: BPB trajectory from baseline (commit \texttt{2446855}, BPB\,=\,2.2393) to champion (commit \texttt{cd91c45}, BPB\,=\,2.1919) and the two high-water-mark gates anchored by $\varphi^2+\varphi^{-2}=3$.} @@ -141,6 +141,7 @@ \subsection{1.3 Perplexity–BPB Conversion Table} ($\bar{b}=1$, $\mathrm{PPL}=2^{\mathrm{BPB}}$). The champion checkpoint (\texttt{cd91c45}) appears in bold.} \label{tab:ppl-bpb} +\resizebox{\linewidth}{!}{% \begin{tabular}{lllll} \toprule Commit & Step & BPB & PPL & Gate\\ @@ -153,6 +154,7 @@ \subsection{1.3 Perplexity–BPB Conversion Table} — & (target) & 1.50 & 2.83 & Gate-3\\ \bottomrule \end{tabular} +} \end{table} The champion BPB of 2.1919 corresponds to perplexity 4.56 on @@ -311,6 +313,7 @@ \subsection{2.4 BPB Calibration Table (Steps 4\,000–81\,000)} hidden=828, 2L hybrid attention + ReLU²). Step 81\,000 is the definitive champion. Forbidden-value audit: none present.} \label{tab:bpb-calibration} +\resizebox{\linewidth}{!}{% \begin{tabular}{rlrlll} \toprule Step & BPB & $\Delta$BPB & PPL & ARCH HWM & Notes\\ @@ -333,6 +336,7 @@ \subsection{2.4 BPB Calibration Table (Steps 4\,000–81\,000)} — & 1.50 & — & 2.83 & Gate-3 target & $\approx 3\varphi^{-1}$\\ \bottomrule \end{tabular} +} \end{table} \subsubsection{Forbidden-Value Audit} @@ -347,6 +351,7 @@ \subsubsection{Forbidden-Value Audit} \caption{Forbidden-value audit (R6 + INV-1/2/3). All forbidden values are absent from the champion run and all calibration checkpoints.} \label{tab:forbidden-audit} +\resizebox{\linewidth}{!}{% \begin{tabular}{lll} \toprule Forbidden value & Rule & Why forbidden\\ @@ -360,6 +365,7 @@ \subsubsection{Forbidden-Value Audit} BPB $= 0.014$ & INV-7 & JEPA-MSE proxy artefact; refused by \texttt{validate\_bpb()}\\ \bottomrule \end{tabular} +} \end{table} % ============================================================ @@ -554,6 +560,7 @@ \subsection{4.3 Gate-3: BPB $< 1.50$ and ASHA Rungs} All step counts are Fibonacci or $\varphi$-derived. INV-12: rung steps strictly increasing, rung-0 is warmup.} \label{tab:asha-rungs} +\resizebox{\linewidth}{!}{% \begin{tabular}{llll} \toprule Rung & Step & $\approx\varphi^k$ & Fraction of full run\\ @@ -567,6 +574,7 @@ \subsection{4.3 Gate-3: BPB $< 1.50$ and ASHA Rungs} 6 (final) & 81\,000 & $3^4\cdot 10^3$ & 100\%\\ \bottomrule \end{tabular} +} \end{table} % Rung-6 at step~81\,000 is the champion evaluation point. @@ -677,6 +685,7 @@ \subsection{5.1 Champion Record Sheet} INV-1 (BPB monotone), INV-2 (ASHA pruning), INV-3 (d\_model $\ge 256$), INV-12 (rung ordering) all satisfied.} \label{tab:champion-record} +\resizebox{\linewidth}{!}{% \begin{tabular}{ll} \toprule Hyperparameter & Value\\ @@ -698,6 +707,7 @@ \subsection{5.1 Champion Record Sheet} Prune threshold & $3.5 = \varphi^2+\varphi^{-2}+\varphi^{-4}+\varepsilon$\\ \bottomrule \end{tabular} +} \end{table} \subsection{5.2 Baseline Comparator Record: \texttt{2446855}} @@ -864,6 +874,7 @@ \subsection{7.5 Corroboration Record} \centering \caption{Corroboration status as of commit \texttt{cd91c45} (2026-05-07).} \label{tab:corroboration} +\resizebox{\linewidth}{!}{% \begin{tabular}{lllll} \toprule Falsification axis & Predicate & Status & Evidence & Date\\ @@ -876,6 +887,7 @@ \subsection{7.5 Corroboration Record} BPB lower bound & $\mathrm{BPB}\ge H_\infty\ge 0$ & Functional & Theorem~\ref{thm:bpb-lb}, \texttt{BPB\_LowerBound.v} & 2026-05-07\\ \bottomrule \end{tabular} +} \end{table} Pending falsification tests are the open empirical obligations of @@ -923,6 +935,7 @@ \subsection{8.2 INV-1 and INV-2 Connections} \centering \caption{L-R14 traceability: numeric constants in this chapter.} \label{tab:r14-trace} +\resizebox{\linewidth}{!}{% \begin{tabular}{llll} \toprule Constant & Rust target & JSON entry & Coq file\\ @@ -934,6 +947,7 @@ \subsection{8.2 INV-1 and INV-2 Connections} $\mathrm{BPB}_{\mathrm{champ}} = 2.1919$ & \texttt{bpb.rs::CHAMPION\_BPB} & INV-7 & \texttt{BPB\_LowerBound.v}\\ \bottomrule \end{tabular} +} \end{table} % ============================================================ @@ -1040,6 +1054,7 @@ \subsection{10.2 Open Obligations} \centering \caption{Open obligations for this chapter.} \label{tab:open-obligations} +\resizebox{\linewidth}{!}{% \begin{tabular}{llll} \toprule ID & Obligation & Ledger row & Priority\\ @@ -1054,6 +1069,7 @@ \subsection{10.2 Open Obligations} FUT-25-1 & $\varphi$-Chinchilla exponent conjecture & Future Work Ch.31 & P3\\ \bottomrule \end{tabular} +} \end{table} % ============================================================ @@ -1167,6 +1183,7 @@ \section{QED Assertions and Coq Ledger} \caption{Theorem ledger for Chapter~25. R5-honest: Admitted theorems not relabeled as Proven.} \label{tab:theorem-ledger} +\resizebox{\linewidth}{!}{% \begin{tabular}{llll} \toprule ID & Theorem & Status & Coq file (if any)\\ @@ -1180,6 +1197,7 @@ \section{QED Assertions and Coq Ledger} CYC-1 & Phase alignment Prop.~3.1 & Admitted & filed Golden Ledger\\ \bottomrule \end{tabular} +} \end{table} % ============================================================ @@ -1382,6 +1400,7 @@ \subsection{14.1 Full Hyperparameter Specification} \texttt{assertions/igla\_assertions.json} and \texttt{crates/trios-train-cpu/src/bin/hybrid\_train.rs}.} \label{tab:full-hyperparams} +\resizebox{\linewidth}{!}{% \begin{tabular}{lll} \toprule Parameter & Value & $\varphi$-derivation\\ @@ -1421,6 +1440,7 @@ \subsection{14.1 Full Hyperparameter Specification} Distinct seeds required & 3 (Gate-3: INV-7) & integer\\ \bottomrule \end{tabular} +} \end{table} \subsection{14.2 Reproducibility Command and Seed Lock} diff --git a/docs/phd/chapters/26-data-analysis.tex b/docs/phd/chapters/26-data-analysis.tex index e58943ede8..869183f02c 100644 --- a/docs/phd/chapters/26-data-analysis.tex +++ b/docs/phd/chapters/26-data-analysis.tex @@ -5,7 +5,7 @@ \chapter{Data Analysis: Statistical Validation of the IGLA Champion} \begin{figure}[H] \centering -\makebox[\linewidth][c]{\includegraphics[width=1.18\linewidth,keepaspectratio]{ch26-koschei-coprocessor-isa.png}} +\makebox[\linewidth][c]{\includegraphics[width=1.18\linewidth,keepaspectratio]{26-data-analysis.png}} \caption*{Figure --- Data Analysis: Statistical Validation of the IGLA Champion.} \end{figure} diff --git a/docs/phd/chapters/27-trinity-identity.tex b/docs/phd/chapters/27-trinity-identity.tex index 6f5a51c88f..215dc3e5f3 100644 --- a/docs/phd/chapters/27-trinity-identity.tex +++ b/docs/phd/chapters/27-trinity-identity.tex @@ -344,6 +344,7 @@ \subsection{The Inner Pentagon and Self-Similarity} \subsection{Visual Summary} \begin{center} +\resizebox{\linewidth}{!}{% \begin{tabular}{lcc} \hline Object & Length & Algebraic identity \\ @@ -356,6 +357,7 @@ \subsection{Visual Summary} Sum of squares (diag.\ + inner) & $\varphi^{2}+\varphi^{-2}$ & $= 3$ \\ \hline \end{tabular} +} \end{center} %% ===================================================================== @@ -798,11 +800,13 @@ \subsection{The Lucas Sequence} The first values of $L_{n}$ are: \begin{center} +\resizebox{\linewidth}{!}{% \begin{tabular}{c|ccccccccc} $n$ & $0$ & $1$ & $2$ & $3$ & $4$ & $5$ & $6$ & $7$ & $8$ \\ \hline $L_{n}$ & $2$ & $1$ & $3$ & $4$ & $7$ & $11$ & $18$ & $29$ & $47$ \\ \end{tabular} +} \end{center} \subsection{Key Identities of Lucas Numbers} @@ -1077,6 +1081,7 @@ \subsection{EPIC~\#572: L-KAT-RW Lane} The structural relationship is summarised: \begin{center} +\resizebox{\linewidth}{!}{% \begin{tabular}{lll} \hline Framework & Constant $3$ appears as & Reference \\ @@ -1089,6 +1094,7 @@ \subsection{EPIC~\#572: L-KAT-RW Lane} GF(16) / INV-5 & $L_{2}=3$ (Lucas closure) & INV-5 \\ \hline \end{tabular} +} \end{center} In each framework, the integer $3$ plays a foundational r\^{o}le. @@ -1501,6 +1507,7 @@ \subsection{Newton's Identity Proof in Detail} $p_{1} = \varphi+\psi = 1$. Computing step by step: \begin{center} +\resizebox{\linewidth}{!}{% \begin{tabular}{c|c|c} $k$ & $p_{k}$ & $L_{k}$ \\ \hline @@ -1511,6 +1518,7 @@ \subsection{Newton's Identity Proof in Detail} $4$ & $p_{3}+p_{2} = 4+3 = 7$ & $7$ \\ $5$ & $p_{4}+p_{3} = 7+4 = 11$ & $11$ \\ \end{tabular} +} \end{center} The sequence $p_{k} = L_{k}$ (Lucas numbers), and in particular @@ -1588,6 +1596,7 @@ \subsection{The Connection to the Chebyshev Polynomials} \subsection{Summary Table: Five Routes to the Trinity Anchor} \begin{center} +\resizebox{\linewidth}{!}{% \begin{tabular}{clll} \hline \# & Route & Key identity used & Result \\ @@ -1599,6 +1608,7 @@ \subsection{Summary Table: Five Routes to the Trinity Anchor} 5 & Binet formula & $L_{2}=3$ & $3$ \\ \hline \end{tabular} +} \end{center} Routes 1--3 are the three main proofs (Rule of Three). @@ -1616,6 +1626,7 @@ \section{Table of $\varphi$-Powers}% and $\varphi^{-1}$ in $\mathbb{Z}[\varphi]$: \begin{center} +\resizebox{\linewidth}{!}{% \begin{tabular}{c|ll|l} \hline $n$ & $\varphi^{n}$ & in $\mathbb{Z}[\varphi]$ & $L_{n}=\varphi^{n}+\psi^{n}$ \\ @@ -1637,6 +1648,7 @@ \section{Table of $\varphi$-Powers}% $6$ & $\varphi^{6}$ & $8+9\varphi$ & $L_{6}=18$ \\ \hline \end{tabular} +} \end{center} The coefficients $(a_{n}, b_{n})$ in $\varphi^{n} = a_{n}+b_{n}\varphi$ diff --git a/docs/phd/chapters/28-momentum-algebra.tex b/docs/phd/chapters/28-momentum-algebra.tex index cfabc4d0d1..c03f4f00ff 100644 --- a/docs/phd/chapters/28-momentum-algebra.tex +++ b/docs/phd/chapters/28-momentum-algebra.tex @@ -16,7 +16,7 @@ \chapter{Momentum Algebra: \(\varphi\)-Derived \(\beta_1/\beta_2\) Schedule} \begin{figure}[H] \centering \makebox[\linewidth][c]{% - \includegraphics[width=1.18\linewidth,keepaspectratio]{ch28-momentum-algebra.png}} + \includegraphics[width=1.18\linewidth,keepaspectratio]{28-momentum-algebra.png}} \caption*{Figure --- Momentum Algebra: \(\varphi\)-derived \(\beta_1 = \varphi^{-1},\; \beta_2 = \varphi^{-2},\; \varepsilon = \varphi^{-10}\) as the unique zero-free-parameter momentum schedule consistent with @@ -393,6 +393,7 @@ \subsection{2.4 AdamW Training Results} \centering \caption{AdamW Momentum Schedule Comparison — Final BPB after 50k steps.} \label{tab:28-adamw-results} +\resizebox{\linewidth}{!}{% \begin{tabular}{lcccc} \toprule \textbf{Schedule} & \(\beta_1\) & \(\beta_2\) & \(\varepsilon\) & \textbf{BPB} \\ @@ -401,6 +402,7 @@ \subsection{2.4 AdamW Training Results} \(\varphi\)-Schedule & \(\varphi^{-1}\) & \(\varphi^{-2}\) & \(\varphi^{-10}\) & \textbf{1.501} \\ \bottomrule \end{tabular} +} \end{table} The \(\varphi\)-Schedule achieves $1.501$ BPB versus the conventional @@ -637,6 +639,7 @@ \subsection{4.3 Wave 26 Results} \centering \caption{Wave 26: GPTQ-on-GF16 BPB before/after post-processing.} \label{tab:28-wave26} +\resizebox{\linewidth}{!}{% \begin{tabular}{lccc} \toprule \textbf{Seed} & \textbf{BPB (pre-GPTQ)} & \textbf{BPB (post-GPTQ)} & \textbf{$\Delta$ BPB} \\ @@ -647,6 +650,7 @@ \subsection{4.3 Wave 26 Results} \textbf{Paired-$t$ statistic} & \multicolumn{3}{c}{$t = 0.0003$, $p = 0.9999$} \\ \bottomrule \end{tabular} +} \end{table} \begin{tcolorbox}[colback=orange!5!white,colframe=orange!75!black,title={% @@ -782,6 +786,7 @@ \subsection{5.6 Summary Table} \centering \caption{INV-1..INV-5 Ablation Results for \(\varphi\)-Momentum Schedule.} \label{tab:28-invariants} +\resizebox{\linewidth}{!}{% \begin{tabular}{llll} \toprule \textbf{Invariant} & \textbf{Condition} & \textbf{Result} & \textbf{Status} \\ @@ -793,6 +798,7 @@ \subsection{5.6 Summary Table} INV-5 & Lucas GF16 closure & Algebraic, proof-verified & \textbf{Satisfied} \\ \bottomrule \end{tabular} +} \end{table} % ============================================================ @@ -1220,6 +1226,7 @@ \subsection{11.2 Hyperparameter Registry} \centering \caption{Complete \(\varphi\)-Momentum Schedule Hyperparameter Registry.} \label{tab:28-hyperparams} +\resizebox{\linewidth}{!}{% \begin{tabular}{llll} \toprule \textbf{Parameter} & \textbf{Value} & \textbf{$\varphi$-derivation} & \textbf{Coq source} \\ @@ -1232,6 +1239,7 @@ \subsection{11.2 Hyperparameter Registry} \(d_{\mathrm{model}}\) & \(384 \geq 256\) & INV-3 floor & \texttt{gf16\_precision.v} \\ \bottomrule \end{tabular} +} \end{table} \subsection{11.3 Training Infrastructure} @@ -1459,6 +1467,7 @@ \subsection{13c.1 Comparison Table} \caption{Optimizer schedule comparison on Trinity S³AI \(d_{\mathrm{model}} = 384\), GF(16), 50k steps.} \label{tab:28-comparison} +\resizebox{\linewidth}{!}{% \begin{tabular}{lcccc} \toprule \textbf{Schedule} & \(\beta_1\) & \(\beta_2\) & \(\varepsilon\) & \textbf{BPB} \\ @@ -1471,6 +1480,7 @@ \subsection{13c.1 Comparison Table} AdamW \(\varepsilon = \varphi^{-8}\) & \(\varphi^{-1}\) & \(\varphi^{-2}\) & \(\varphi^{-8}\) & 1.519 \\ \bottomrule \end{tabular} +} \end{table} \subsection{13c.2 Analysis} diff --git a/docs/phd/chapters/29-lucas-closure.tex b/docs/phd/chapters/29-lucas-closure.tex index 74bbe56948..1787c3c0af 100644 --- a/docs/phd/chapters/29-lucas-closure.tex +++ b/docs/phd/chapters/29-lucas-closure.tex @@ -946,6 +946,7 @@ \section{Invariant Catalogue} \caption{Trinity Invariants and their Lucas Closure Connections} \label{tab:29-inv-catalogue} \small +\resizebox{\linewidth}{!}{% \begin{tabular}{llllp{5cm}} \toprule \textbf{ID} & \textbf{Name} & \textbf{Coq File} & \textbf{Status} @@ -967,6 +968,7 @@ \section{Invariant Catalogue} & Rung 0 $=$ warmup; rung $k$ strictly increasing \\ \bottomrule \end{tabular} +} \end{table} \subsection{Invariant Status Summary} @@ -990,6 +992,7 @@ \subsection{L-R14 Traceability Table} \caption{L-R14 Traceability: Rust Constants → Coq Sources} \label{tab:29-r14} \small +\resizebox{\linewidth}{!}{% \begin{tabular}{lll} \toprule \textbf{Rust Constant} & \textbf{JSON Key} & \textbf{Coq Source} \\ @@ -1008,6 +1011,7 @@ \subsection{L-R14 Traceability Table} & \texttt{lucas\_closure\_gf16.v} (derived) \\ \bottomrule \end{tabular} +} \end{table} % --------------------------------------------------------------- @@ -1037,6 +1041,7 @@ \subsection{Seed Manifest} \centering \caption{Canonical Seed Manifest — Lucas Closure Chapter} \label{tab:29-seeds} +\resizebox{\linewidth}{!}{% \begin{tabular}{lll} \toprule \textbf{Seed} & \textbf{Lucas/Fibonacci Identity} & \textbf{BPB Target} \\ @@ -1047,6 +1052,7 @@ \subsection{Seed Manifest} 123 & $123 = L_{10} - L_8$ & $< 1.50$ \\ \bottomrule \end{tabular} +} \end{table} \subsection{Corroboration Record} @@ -1514,6 +1520,7 @@ \subsection{Comparison with Alternative Tolerances} \centering \caption{Reproduction Tolerance Comparison} \label{tab:29-tolerance} +\resizebox{\linewidth}{!}{% \begin{tabular}{llll} \toprule \textbf{Tolerance} & \textbf{Value} & \textbf{Justification} @@ -1527,6 +1534,7 @@ \subsection{Comparison with Alternative Tolerances} $10^{-3}$ & $0.001$ (standard ML) & empirical & Yes, but not φ-derived \\ \bottomrule \end{tabular} +} \end{table} \noindent diff --git a/docs/phd/chapters/30-golden-imagery.tex b/docs/phd/chapters/30-golden-imagery.tex index 0ea370ac28..83f9562a76 100644 --- a/docs/phd/chapters/30-golden-imagery.tex +++ b/docs/phd/chapters/30-golden-imagery.tex @@ -4,7 +4,7 @@ \chapter{Golden Imagery: Aesthetic \& Visual Computing in \texorpdfstring{$\varp \begin{figure}[H] \centering -\makebox[\linewidth][c]{\includegraphics[width=1.18\linewidth,keepaspectratio]{ch30-trinity-sai.png}} +\makebox[\linewidth][c]{\includegraphics[width=1.18\linewidth,keepaspectratio]{30-golden-imagery.png}} \caption*{Figure --- Golden Imagery: Trinity S\textsuperscript{3}AI --- VSA-AR \& Golden-Rectangle Composition.} \end{figure} @@ -863,6 +863,7 @@ \subsection{7.1\ Standard Ratios and Their aspect ratios that approximate $\varphi$: \begin{center} +\resizebox{\linewidth}{!}{% \begin{tabular}{lcc} \toprule Standard & Ratio & $|\text{ratio} - \varphi|/\varphi$ \\ @@ -874,6 +875,7 @@ \subsection{7.1\ Standard Ratios and Their $\varphi$:1 & 1.618 & $0.000$ \\ \bottomrule \end{tabular} +} \end{center} The 16:10 ratio ($1.600$) is the closest standard @@ -1436,6 +1438,7 @@ \section{15.\ R14 Coq Citation Map}% following Coq verification artefacts: \begin{center} +\resizebox{\linewidth}{!}{% \begin{tabular}{lll} \toprule Theorem & Coq file & Status \\ @@ -1457,6 +1460,7 @@ \section{15.\ R14 Coq Citation Map}% & Admitted \\ \bottomrule \end{tabular} +} \end{center} \noindent\textbf{R14 note.} diff --git a/docs/phd/chapters/31-philosophy.tex b/docs/phd/chapters/31-philosophy.tex index ad1c8ca53a..068de6c5db 100644 --- a/docs/phd/chapters/31-philosophy.tex +++ b/docs/phd/chapters/31-philosophy.tex @@ -2,7 +2,7 @@ \chapter{Philosophy — Mathematical Foundations} \begin{figure}[H] \centering -\makebox[\linewidth][c]{\includegraphics[width=1.18\linewidth,keepaspectratio]{ch01-introduction.png}} +\makebox[\linewidth][c]{\includegraphics[width=1.18\linewidth,keepaspectratio]{31-philosophy.png}} \end{figure} @@ -699,6 +699,7 @@ \section{Appendix to Chapter 31 — L-R14 Trace Table} In keeping with Rule R4 (every numeric constant traceable to a `.v` file via \texttt{assertions/igla\_assertions.json}) and Rule R14 (every cited theorem maps to a `.v` file with line ranges), we close the chapter with an L-R14 trace table for the constants introduced in this chapter. \begin{center} +\resizebox{\linewidth}{!}{% \begin{tabular}{|l|l|l|l|} \hline \textbf{Constant} & \textbf{φ-derivation} & \textbf{Coq file} & \textbf{Status} \\ @@ -728,6 +729,7 @@ \section{Appendix to Chapter 31 — L-R14 Trace Table} $8$ & integer ($k$ in $\mathrm{GF}(2^{8})$) & forward stub \texttt{gf256\_extension.v} & Conjectured \\ \hline \end{tabular} +} \end{center} The table satisfies Rule R4: every numeric constant is paired either with a φ-power expression and a Coq file, or with an explicit integer / arithmetic / projection annotation. No free numeric parameter appears. @@ -952,6 +954,7 @@ \section{Cycle-Level Ledger of Empirical Envelopes} We provide a per-cycle ledger of the seven `Admitted` envelopes $\varepsilon_{6}, \dots, \varepsilon_{12}$. The ledger is conjectural beyond cycle 27 (the nominal point of writing); however the conjectures are calibrated against Theorem~31.1 (admitted-band closure schedule). \begin{center} +\resizebox{\linewidth}{!}{% \begin{tabular}{|c|c|c|c|c|c|c|c|} \hline \textbf{Cycle} & $\varepsilon_{6}$ & $\varepsilon_{7}$ & $\varepsilon_{8}$ & $\varepsilon_{9}$ & $\varepsilon_{10}$ & $\varepsilon_{11}$ & $\varepsilon_{12}$ \\ @@ -965,6 +968,7 @@ \section{Cycle-Level Ledger of Empirical Envelopes} 55 (proj.) & $\phi^{-13}$ & $\phi^{-12}$ & $\phi^{-15}$ & $\phi^{-11}$ & $\phi^{-14}$ & $\phi^{-10}$ & $\phi^{-9}$ \\ \hline \end{tabular} +} \end{center} The projection assumes Conjecture~31.A (monotonicity in the limit) and Theorem~31.1 (one factor of $\phi^{-1}$ per upgrade event). Across cycles 27 → 55 — i.e.\ four upgrade rounds — the compounded posterior contracts by approximately $\phi^{-28} \approx 1.16 \times 10^{-6}$, achieving what Lakatos would call a maximally progressive sweep. @@ -1407,6 +1411,7 @@ \section{Numeric Reference Tables} For convenience we tabulate the principal $\phi$-power values invoked across the chapter. \begin{center} +\resizebox{\linewidth}{!}{% \begin{tabular}{|r|l|l|} \hline \textbf{Power} & \textbf{Decimal} & \textbf{Reference in chapter} \\ @@ -1425,6 +1430,7 @@ \section{Numeric Reference Tables} $\phi^{7}$ & $29.0344...$ & Theorem 31.1 reciprocal \\ \hline \end{tabular} +} \end{center} The values are computed from $\phi = (1 + \sqrt{5})/2$ to 14 decimal places. Higher-precision values (≥ 32 decimal places) are stored in the Coq.Interval envelope file (forward-time stub). @@ -1888,7 +1894,8 @@ \section{Dijkstra's Medium-is-Message Principle and Coq Runtime Invariants} \centering \caption{R14 Coq citation map for Chapter~31 (scarab-l31 additions).} \label{tab:coq-map-31-scarab} - \begin{tabular}{lllll} + \resizebox{\linewidth}{!}{% +\begin{tabular}{lllll} \hline \textbf{Constant} & \textbf{Value} & \textbf{Coq file} & \textbf{Theorem} & \textbf{Status} \\ \hline @@ -1900,6 +1907,7 @@ \section{Dijkstra's Medium-is-Message Principle and Coq Runtime Invariants} Warmup & \(4000\) & \texttt{igla\_asha\_bound.v} & \texttt{rung\_zero\_is\_warmup} & Proven \\ \hline \end{tabular} +} \end{table} %────────────────────────────────────────────────────────────────────────────── diff --git a/docs/phd/chapters/32-conclusion.tex b/docs/phd/chapters/32-conclusion.tex index 3c53d3678e..859cfdc0db 100644 --- a/docs/phd/chapters/32-conclusion.tex +++ b/docs/phd/chapters/32-conclusion.tex @@ -2,7 +2,7 @@ \chapter{Conclusion — The Golden Monograph} \begin{figure}[H] \centering -\makebox[\linewidth][c]{\includegraphics[width=1.18\linewidth,keepaspectratio]{ch34-energy-3000x-darpa.png}} +\makebox[\linewidth][c]{\includegraphics[width=1.18\linewidth,keepaspectratio]{32-conclusion.png}} \end{figure} @@ -521,6 +521,7 @@ \subsection{Tabular Summary} \begin{center} \small +\resizebox{\linewidth}{!}{% \begin{tabular}{|l|l|l|l|} \hline \textbf{INV} & \textbf{Coq theorem (verbatim)} & \textbf{Status} & \textbf{File} \\ @@ -535,6 +536,7 @@ \subsection{Tabular Summary} INV-12 & \texttt{asha\_rungs\_trinity} & Proven & \texttt{asha\_rungs\_trinity.v} \\ \hline \end{tabular} +} \end{center} The table is offered both as a quick reference and as a redundant verbatim @@ -905,6 +907,7 @@ \section{Appendix to Chapter 32 — L-R14 Trace Table} together with its φ-derivation and Coq citation. \begin{center} +\resizebox{\linewidth}{!}{% \begin{tabular}{|l|l|l|} \hline \textbf{Constant} & \textbf{Derivation} & \textbf{Coq citation} \\ @@ -932,6 +935,7 @@ \section{Appendix to Chapter 32 — L-R14 Trace Table} $55$ & projected maturation cycle & cross-chapter L31 \\ \hline \end{tabular} +} \end{center} Every constant is either φ-derived, an integer, or a documented empirical @@ -1626,6 +1630,7 @@ \subsection{INV Invariant Ledger} \caption{Seven INV invariants traced through the monograph.} \label{tab:scarab-inv-ledger} \renewcommand{\arraystretch}{1.20} +\resizebox{\linewidth}{!}{% \begin{tabular}{llllll} \toprule INV & Name & Primary Ch. & Coq File & Status & Action \\ @@ -1639,6 +1644,7 @@ \subsection{INV Invariant Ledger} INV-12 & ASHA rung progression & 7, 19 & \texttt{igla\_asha\_bound.v} & Qed & abort \\ \bottomrule \end{tabular} +} \end{table} \subsection{R-Rule Ledger: Per-Chapter Satisfaction Proof} @@ -1656,6 +1662,7 @@ \subsection{R-Rule Ledger: Per-Chapter Satisfaction Proof} \caption{R-rule ledger: predicate satisfaction across all 33 chapters.} \label{tab:scarab-rrule-ledger} \renewcommand{\arraystretch}{1.20} +\resizebox{\linewidth}{!}{% \begin{tabular}{lp{7.5cm}l} \toprule Rule & Predicate & Status \\ @@ -1674,6 +1681,7 @@ \subsection{R-Rule Ledger: Per-Chapter Satisfaction Proof} R14 & Every cited theorem maps to \texttt{.v} & \S\ref{sec:32-eight-map}+\S\ref{sec:scarab-inv-ledger}: \checkmark \\ \bottomrule \end{tabular} +} \end{table} \subsection{Three Independent Proofs of the Trinity Identity} @@ -1751,6 +1759,7 @@ \subsection{Falsification Balance Sheet} \caption{Falsification balance sheet: summary.} \label{tab:scarab-falsification} \renewcommand{\arraystretch}{1.15} +\resizebox{\linewidth}{!}{% \begin{tabular}{lll} \toprule Chapter & Prediction & Verdict \\ @@ -1771,6 +1780,7 @@ \subsection{Falsification Balance Sheet} \multicolumn{2}{l}{\textbf{Summary}: 9 confirmed, 2 open, 1 partial} & \\ \bottomrule \end{tabular} +} \end{table} \subsection{Monograph-Completeness Meta-Theorem} @@ -1885,6 +1895,7 @@ \subsection{Scarab-L32 Citation Index} \caption{Citations added by scarab-l32 addendum (R11 compliance).} \label{tab:scarab-citations} \renewcommand{\arraystretch}{1.15} +\resizebox{\linewidth}{!}{% \begin{tabular}{llll} \toprule Key & Authors & Venue & Class \\ @@ -1894,6 +1905,7 @@ \subsection{Scarab-L32 Citation Index} \texttt{vaswani\_attention} & Vaswani et al.\ (2017) & NeurIPS & Q1 proceedings \\ \bottomrule \end{tabular} +} \end{table} All citations are Q1/Q2 peer-reviewed, satisfying R11~\cite{hardy_wright}. diff --git a/docs/phd/chapters/33-epilogue.tex b/docs/phd/chapters/33-epilogue.tex index c6b3ffec01..5e281f7e15 100644 --- a/docs/phd/chapters/33-epilogue.tex +++ b/docs/phd/chapters/33-epilogue.tex @@ -24,7 +24,7 @@ \chapter{Epilogue: Reproducibility Manifest, ACM AE Soundness, \begin{figure}[H] \centering \makebox[\linewidth][c]{% - \includegraphics[width=1.18\linewidth,keepaspectratio]{ch33-jtag-macos-blk001.png}} + \includegraphics[width=1.18\linewidth,keepaspectratio]{33-epilogue.png}} \caption*{Figure --- Epilogue: JTAG macOS BLK-001 Resolved.} \end{figure} @@ -158,6 +158,7 @@ \section{3. Verified Hardware Configuration Post-BLK-001}% repository: \begin{center} +\resizebox{\linewidth}{!}{% \begin{tabular}{ll} \toprule Parameter & Value \\ @@ -174,6 +175,7 @@ \section{3. Verified Hardware Configuration Post-BLK-001}% Bitstream archive & App.\,F (SHA-256 verified) \\ \bottomrule \end{tabular} +} \end{center} The 0 DSP configuration is enforced by the synthesis constraint @@ -274,6 +276,7 @@ \subsection{8.1 Canonical Repository and Git SHAs}% \caption{Canonical Git SHAs for Trinity S${}^3$AI — Flos Aureus v6.2} \label{tab:git-shas} \centering +\resizebox{\linewidth}{!}{% \begin{tabular}{lll} \toprule Artefact & Branch/Tag & SHA-1 (40 hex) \\ @@ -286,6 +289,7 @@ \subsection{8.1 Canonical Repository and Git SHAs}% ACM AE container image & \texttt{ae/v1.0} & \texttt{e3b0c442...} \\ \bottomrule \end{tabular} +} \end{table} We pin the Zenodo DOI \texttt{10.5281/zenodo.19227877} as the immutable @@ -315,6 +319,7 @@ \subsection{8.2 Hardware Specifications (CPU-Only, No GPU)}% \caption{Reference hardware platform (CPU-only, no GPU)} \label{tab:hw-specs} \centering +\resizebox{\linewidth}{!}{% \begin{tabular}{ll} \toprule Component & Specification \\ @@ -329,6 +334,7 @@ \subsection{8.2 Hardware Specifications (CPU-Only, No GPU)}% GPU & \textbf{None} (CPU-only mandate) \\ \bottomrule \end{tabular} +} \end{table} All timing benchmarks were collected with the CPU governor set to @@ -343,6 +349,7 @@ \subsection{8.3 Software Versions}\label{sec:sw-versions} \caption{Software environment for Trinity S${}^3$AI — Flos Aureus v6.2} \label{tab:sw-versions} \centering +\resizebox{\linewidth}{!}{% \begin{tabular}{lll} \toprule Tool & Version & Purpose \\ @@ -361,6 +368,7 @@ \subsection{8.3 Software Versions}\label{sec:sw-versions} nextpnr-xilinx & 0.7 & FPGA place-and-route \\ \bottomrule \end{tabular} +} \end{table} The Rust nightly channel is pinned via a \texttt{rust-toolchain.toml} file @@ -390,6 +398,7 @@ \subsection{8.4 Expected Outputs and Tolerance Bands}% \caption{Expected outputs and ACM AE tolerance bands} \label{tab:tolerance} \centering +\resizebox{\linewidth}{!}{% \begin{tabular}{lllll} \toprule Metric & Champion & $\sigma$ & Pass band & Fail threshold \\ @@ -404,6 +413,7 @@ \subsection{8.4 Expected Outputs and Tolerance Bands}% NCA entropy & $[\varphi, \varphi^2]$ & --- & certified band & outside \\ \bottomrule \end{tabular} +} \end{table} A replication is declared \emph{Functional} (ACM AE badge level 1) if all @@ -621,7 +631,7 @@ \subsection{10.2 The ACM AE Soundness Theorem}% Let $\mathcal{M}$ be the reproducibility manifest defined in Section~\ref{sec:repro-manifest}. Suppose a replication run $\mathrm{Build}(\mathcal{M})$ satisfies: -\begin{enumerate}[\upshape(A)] +\begin{enumerate}[label=\upshape(\Alph*)] \item\label{item:ae-A} The binary is built from the exact Git SHA $s_{\mathrm{repo}}$ with the pinned Rust toolchain \texttt{nightly-2026-04-28}. @@ -719,6 +729,7 @@ \subsection{10.3 Coq Citation Map for Theorem~\ref{thm:ae-soundness}}% \caption{R14 Coq citation map: Theorem~\ref{thm:ae-soundness} dependencies} \label{tab:coq-map} \centering +\resizebox{\linewidth}{!}{% \begin{tabular}{llll} \toprule Claim & Coq file & Theorem name & Status \\ @@ -743,6 +754,7 @@ \subsection{10.3 Coq Citation Map for Theorem~\ref{thm:ae-soundness}}% \texttt{alpha\_phi\_ub} & Admitted \\ \bottomrule \end{tabular} +} \end{table} \admittedbox{% @@ -1273,6 +1285,7 @@ \subsection{17.1 Silicon Tapeout TTSKY26a (2026-05-11)}\label{sec:tapeout} \caption{TTSKY26a silicon tapeout specifications} \label{tab:tapeout} \centering +\resizebox{\linewidth}{!}{% \begin{tabular}{ll} \toprule Parameter & Target \\ @@ -1290,6 +1303,7 @@ \subsection{17.1 Silicon Tapeout TTSKY26a (2026-05-11)}\label{sec:tapeout} Open-source PDK & SkyWater PDK + OpenLane 2 \\ \bottomrule \end{tabular} +} \end{table} The TTSKY26a design will be archived at Zenodo under a derivative DOI @@ -1368,6 +1382,7 @@ \subsection{18.1 Overview of the Agent Campaign}\label{sec:coptic-overview} \caption{Coptic-agent grid campaign statistics} \label{tab:coptic-stats} \centering +\resizebox{\linewidth}{!}{% \begin{tabular}{ll} \toprule Statistic & Value \\ @@ -1386,6 +1401,7 @@ \subsection{18.1 Overview of the Agent Campaign}\label{sec:coptic-overview} Hive honey deposits & 33 \\ \bottomrule \end{tabular} +} \end{table} \subsection{18.2 Agent Architecture}\label{sec:coptic-arch} @@ -1461,6 +1477,7 @@ \section{19. R14 Coq Citation Map — Chapter 33}\label{sec:r14-coq-map} \caption{R14 Coq citation map — all numeric constants in Chapter 33} \label{tab:r14-full} \centering +\resizebox{\linewidth}{!}{% \begin{tabular}{llll} \toprule Constant & Value & Coq file & Derivation \\ @@ -1493,6 +1510,7 @@ \section{19. R14 Coq Citation Map — Chapter 33}\label{sec:r14-coq-map} IGLA RACE victory gate \\ \bottomrule \end{tabular} +} \end{table} Every value in Table~\ref{tab:r14-full} is derived from $\varphi$ via diff --git a/docs/phd/chapters/ch_01.tex b/docs/phd/chapters/ch_01.tex index ed7cbba769..5f1e884ec7 100644 --- a/docs/phd/chapters/ch_01.tex +++ b/docs/phd/chapters/ch_01.tex @@ -281,6 +281,7 @@ \subsection{S1.3 Methodological Reading: Falsification Criteria} \begin{table}[H] \centering +\resizebox{\linewidth}{!}{% \begin{tabular}{p{3.2cm}p{5.5cm}p{5.5cm}} \hline \textbf{Claim} & \textbf{Primary falsifier} & \textbf{Secondary falsifier} \\ @@ -304,6 +305,7 @@ \subsection{S1.3 Methodological Reading: Falsification Criteria} without a corresponding power drop. \\ \hline \end{tabular} +} \caption{Falsification matrix for the three primary claims of the TRINITY S$^3$AI programme.} \label{tab:ch1-falsification-matrix} diff --git a/docs/phd/chapters/ch_04.tex b/docs/phd/chapters/ch_04.tex index 9bf23450f7..b2ab823f82 100644 --- a/docs/phd/chapters/ch_04.tex +++ b/docs/phd/chapters/ch_04.tex @@ -247,6 +247,7 @@ \section{S2. Dimensional Analysis}\label{ch4-s2-dimensional} \begin{table}[H] \centering +\resizebox{\linewidth}{!}{% \begin{tabular}{lll} \hline \textbf{Quantity} & \textbf{Symbol} & \textbf{Dimension} \\ @@ -261,6 +262,7 @@ \section{S2. Dimensional Analysis}\label{ch4-s2-dimensional} dimensionless (radians) \\ \hline \end{tabular} +} \caption{Dimensional table for the spectral parameter and its derivatives.} \label{tab:ch4-dimensional} diff --git a/docs/phd/chapters/ch_35_mesh_node.tex b/docs/phd/chapters/ch_35_mesh_node.tex index a4efb4a39d..1a58378724 100644 --- a/docs/phd/chapters/ch_35_mesh_node.tex +++ b/docs/phd/chapters/ch_35_mesh_node.tex @@ -80,6 +80,7 @@ \subsection{RNS Packet Taxonomy} \centering \caption{Reticulum packet types and MRU state implications} \label{tab:rns-packets} +\resizebox{\linewidth}{!}{% \begin{tabular}{lllr} \toprule Type & Purpose & MRU action & Bytes (header) \\ @@ -90,6 +91,7 @@ \subsection{RNS Packet Taxonomy} \texttt{PROOF} & Delivery confirmation & Update ETX metric & 23 \\ \bottomrule \end{tabular} +} \end{table} The critical insight for hardware: only \texttt{ANNOUNCE} packets @@ -223,6 +225,7 @@ \section{Energy Budget Analysis} \centering \caption{Trinity Mesh Node power breakdown (SKY130 @ 1.8\,V, 50\,MHz VSA / 8\,MHz MRU)} \label{tab:power} +\resizebox{\linewidth}{!}{% \begin{tabular}{lrrr} \toprule Sub-system & Dynamic (mW) & Leakage (µW) & Notes \\ @@ -238,6 +241,7 @@ \section{Energy Budget Analysis} & & & inference + route-update \\ \bottomrule \end{tabular} +} \end{table} \begin{theorem}[Sub-50\,mW Mesh Inference] @@ -424,6 +428,7 @@ \section{Comparison with Competing Approaches} \centering \caption{Trinity MRU vs alternative mesh-on-chip approaches} \label{tab:comparison} +\resizebox{\linewidth}{!}{% \begin{tabular}{p{3cm}p{2.5cm}p{2.5cm}p{2.5cm}p{2.5cm}} \toprule & \textbf{Trinity MRU} & \textbf{Helium SiP32910} & \textbf{goTenna ASIC} & \textbf{Meshtastic (SW)} \\ @@ -437,6 +442,7 @@ \section{Comparison with Competing Approaches} Licence & Apache-2.0 / MIT & Proprietary & Proprietary & GPL-3 \\ \bottomrule \end{tabular} +} \end{table} \section{Theorems and Formal Claims} @@ -490,6 +496,7 @@ \section{Roadmap} \begin{table}[h] \centering \caption{Ch.35 deliverables and EPIC \#19 gate mapping} +\resizebox{\linewidth}{!}{% \begin{tabular}{llll} \toprule Milestone & Description & Gate & Timeline \\ @@ -501,6 +508,7 @@ \section{Roadmap} M35-5 & Silicon power measurement vs Table~\ref{tab:power} & G1 & 2027-Q1 \\ \bottomrule \end{tabular} +} \end{table} % Constitutional invariant check (R7) diff --git a/docs/phd/frontmatter/cover-page.tex b/docs/phd/frontmatter/cover-page.tex new file mode 100644 index 0000000000..e8229d1458 --- /dev/null +++ b/docs/phd/frontmatter/cover-page.tex @@ -0,0 +1,18 @@ +% =================================================================== +% Front matter — Cover page (true full-bleed chalkboard artwork). +% Page 1 of the dissertation. The cover image fills the entire +% paper area (\paperwidth × \paperheight) with zero margins. +% No overlaid text — the artwork itself carries title, subtitle, +% author, ORCID, anchor identity and DOI. +% =================================================================== + +\begin{titlepage} +\thispagestyle{empty} +\AddToShipoutPictureBG*{% + \AtPageLowerLeft{% + \includegraphics[width=\paperwidth,height=\paperheight,keepaspectratio=false]% + {cover_chalkboard.png}% + }% +} +\null +\end{titlepage} diff --git a/docs/phd/frontmatter/declaration.tex b/docs/phd/frontmatter/declaration.tex index f5bf219c49..2a2043fcaa 100644 --- a/docs/phd/frontmatter/declaration.tex +++ b/docs/phd/frontmatter/declaration.tex @@ -54,10 +54,12 @@ \chapter*{Declaration} \bigskip \noindent +\resizebox{\linewidth}{!}{% \begin{tabular}{@{}p{6cm}@{\hspace{2cm}}p{4cm}@{}} \hrulefill & \hrulefill \\ Signature & Date \\ \end{tabular} +} \bigskip\bigskip diff --git a/docs/phd/frontmatter/title-page.tex b/docs/phd/frontmatter/title-page.tex index 44eb85b779..50014b7693 100644 --- a/docs/phd/frontmatter/title-page.tex +++ b/docs/phd/frontmatter/title-page.tex @@ -13,8 +13,6 @@ Mechanized Proofs, Empirical Anchors, and a Coq-Bounded\\ Neural Architecture Search}\\[0.8cm] -\makebox[\linewidth][c]{\includegraphics[width=1.10\textwidth,keepaspectratio]{cover_v4.png}}\\[0.8cm] - {\large Dmitrii Vasilev}\\[0.3cm] {\small ORCID: \url{https://orcid.org/0009-0008-4294-6159}}\\[0.6cm] diff --git a/docs/phd/main.pdf b/docs/phd/main.pdf index 56eda9d662..062b2fc53a 100644 Binary files a/docs/phd/main.pdf and b/docs/phd/main.pdf differ diff --git a/docs/phd/main.tex b/docs/phd/main.tex index 8acfd9c48f..56488acb19 100644 --- a/docs/phd/main.tex +++ b/docs/phd/main.tex @@ -76,9 +76,10 @@ % Graphics and figures \usepackage{tikz} -\usetikzlibrary{shapes,arrows,positioning,calc,3d,patterns} +\usetikzlibrary{shapes,arrows,positioning,calc,3d,patterns,cd} +\usepackage{tikz-cd} \usepackage{graphicx} -\graphicspath{{assets/}{../../assets/illustrations/}} +\graphicspath{{assets/}{../../assets/illustrations/}{../../assets/illustrations_v516/}} % Universal margin / line-breaking discipline (fixes 95% of Overfull \hbox). \usepackage{microtype} \sloppy @@ -153,6 +154,37 @@ % Layout \usepackage{geometry} +\usepackage{eso-pic} +\usepackage{gensymb} % \degree, \celsius +\providecommand{\doi}[1]{\href{https://doi.org/#1}{doi:\detokenize{#1}}} +\providecommand{\coqcite}[4]{\par\noindent\textsc{Coq:}~\texttt{\detokenize{#1}} \textit{(\detokenize{#2}, lines #3, #4)}\par} +\providecommand{\argmax}{}\renewcommand{\argmax}{\mathop{\mathrm{arg\,max}}\limits} +\providecommand{\argmin}{}\renewcommand{\argmin}{\mathop{\mathrm{arg\,min}}\limits} +\providecommand{\sgn}{\mathop{\mathrm{sgn}}} +\providecommand{\Tr}{}\renewcommand{\Tr}{\mathop{\mathrm{Tr}}} +\providecommand{\rank}{\mathop{\mathrm{rank}}} +\providecommand{\im}{\mathop{\mathrm{im}}} +\providecommand{\phipow}[1]{\varphi^{#1}} +\providecommand{\zphi}{\mathbb{Z}{[}\varphi{]}} +\providecommand{\qphi}{\mathbb{Q}{(}\varphi{)}} +\providecommand{\bpb}{\text{BPB}} +\providecommand{\bpc}{\text{BPC}} +\providecommand{\lr}{L\text{-R}} +% biblatex refsection fallback when biblatex not loaded +\providecommand{\refsection}[1]{} +\providecommand{\coqcitebox}[1]{\par\fbox{\parbox{\dimexpr\linewidth-2\fboxsep}{\small #1}}\par} +\makeatletter +\@ifundefined{refsection}{\newenvironment{refsection}[1][]{}{}}{} +\makeatother +\usepackage{tocloft} +% Widen ToC number columns so 3-digit / multi-level numbers (e.g. 16.22) do not overlap titles. +\setlength{\cftchapnumwidth}{2.6em} +\setlength{\cftsecnumwidth}{3.4em} +\setlength{\cftsubsecnumwidth}{4.4em} +\setlength{\cftsubsubsecnumwidth}{5.4em} +\setlength{\cftsecindent}{2.6em} +\setlength{\cftsubsecindent}{6.0em} +\setlength{\cftsubsubsecindent}{10.4em} \usepackage{fancyhdr} \usepackage{xcolor} @@ -214,6 +246,20 @@ \newtheorem{conjecture}[theorem]{Conjecture} \theoremstyle{remark} \newtheorem{remark}[theorem]{Remark} +\newtheorem{claim}[theorem]{Claim} +\newtheorem{fact}[theorem]{Fact} +\newtheorem{observation}[theorem]{Observation} +\newtheorem{hypothesis}[theorem]{Hypothesis} +\newtheorem{assumption}[theorem]{Assumption} +\newtheorem{question}[theorem]{Question} +\newtheorem{principle}[theorem]{Principle} +\newtheorem{invariant}[theorem]{Invariant} +\newtheorem{guarantee}[theorem]{Guarantee} +\newtheorem{convention}[theorem]{Convention} +\newtheorem{terminology}[theorem]{Terminology} +\newtheorem{property}[theorem]{Property} +\newtheorem{protocol}[theorem]{Protocol} +\newtheorem{notation}[theorem]{Notation} % Proof environment — must be ensuremath, otherwise \end{proof} crashes \renewcommand{\qedsymbol}{} @@ -270,6 +316,7 @@ % Front matter \frontmatter +\include{frontmatter/cover-page} \include{frontmatter/title-page} \include{frontmatter/declaration} \include{frontmatter/abstract} diff --git a/docs/phd/main_ru.pdf b/docs/phd/main_ru.pdf index 812a0e8c60..fc0dd0488a 100644 Binary files a/docs/phd/main_ru.pdf and b/docs/phd/main_ru.pdf differ diff --git a/docs/phd/main_ru.tex b/docs/phd/main_ru.tex index 58131b9e8a..c6d3191bd1 100644 --- a/docs/phd/main_ru.tex +++ b/docs/phd/main_ru.tex @@ -56,9 +56,14 @@ \newunicodechar{∇}{\ensuremath{\nabla}} \usepackage{tikz} -\usetikzlibrary{shapes,arrows,positioning,calc,3d,patterns} +\usetikzlibrary{shapes,arrows,positioning,calc,3d,patterns,cd} +\usepackage{tikz-cd} +% Russian babel makes " an active shorthand; switch it off so tikzcd labels with quotes work. +\AtBeginDocument{% + \ifcsname shorthandoff\endcsname\shorthandoff{"}\fi% +} \usepackage{graphicx} -\graphicspath{{assets/}{../../assets/illustrations/}} +\graphicspath{{assets/}{../../assets/illustrations/}{../../assets/illustrations_v516/}} \usepackage{microtype} \usepackage[htt]{hyphenat} \sloppy @@ -132,6 +137,36 @@ \usepackage{cleveref} \usepackage{geometry} +\usepackage{eso-pic} +\usepackage{gensymb} +\providecommand{\doi}[1]{\href{https://doi.org/#1}{doi:\detokenize{#1}}} +\providecommand{\coqcite}[4]{\par\noindent\textsc{Coq:}~\texttt{\detokenize{#1}} \textit{(\detokenize{#2}, lines #3, #4)}\par} +\providecommand{\argmax}{}\renewcommand{\argmax}{\mathop{\mathrm{arg\,max}}\limits} +\providecommand{\argmin}{}\renewcommand{\argmin}{\mathop{\mathrm{arg\,min}}\limits} +\providecommand{\sgn}{\mathop{\mathrm{sgn}}} +\providecommand{\Tr}{}\renewcommand{\Tr}{\mathop{\mathrm{Tr}}} +\providecommand{\rank}{\mathop{\mathrm{rank}}} +\providecommand{\im}{\mathop{\mathrm{im}}} +\providecommand{\phipow}[1]{\varphi^{#1}} +\providecommand{\zphi}{\mathbb{Z}{[}\varphi{]}} +\providecommand{\qphi}{\mathbb{Q}{(}\varphi{)}} +\providecommand{\bpb}{\text{BPB}} +\providecommand{\bpc}{\text{BPC}} +\providecommand{\lr}{L\text{-R}} +\providecommand{\refsection}[1]{} +\providecommand{\coqcitebox}[1]{\par\fbox{\parbox{\dimexpr\linewidth-2\fboxsep}{\small #1}}\par} +\makeatletter +\@ifundefined{refsection}{\newenvironment{refsection}[1][]{}{}}{} +\makeatother +\usepackage{tocloft} +% Widen ToC number columns so multi-level numbers (16.22) do not overlap titles. +\setlength{\cftchapnumwidth}{2.6em} +\setlength{\cftsecnumwidth}{3.4em} +\setlength{\cftsubsecnumwidth}{4.4em} +\setlength{\cftsubsubsecnumwidth}{5.4em} +\setlength{\cftsecindent}{2.6em} +\setlength{\cftsubsecindent}{6.0em} +\setlength{\cftsubsubsecindent}{10.4em} \usepackage{fancyhdr} \usepackage{xcolor} @@ -164,6 +199,22 @@ \newtheorem{example}[theorem]{Пример} \theoremstyle{remark} \newtheorem{remark}[theorem]{Замечание} +\newtheorem{claim}[theorem]{Утверждение} +\newtheorem{fact}[theorem]{Факт} +\newtheorem{observation}[theorem]{Наблюдение} +\newtheorem{hypothesis}[theorem]{Гипотеза} +\newtheorem{assumption}[theorem]{Предположение} +\newtheorem{question}[theorem]{Вопрос} +\newtheorem{principle}[theorem]{Принцип} +\newtheorem{invariant}[theorem]{Инвариант} +\newtheorem{guarantee}[theorem]{Гарантия} +\newtheorem{convention}[theorem]{Конвенция} +\newtheorem{terminology}[theorem]{Термин} +\newtheorem{property}[theorem]{Свойство} +\newtheorem{protocol}[theorem]{Протокол} +\newtheorem{notation}[theorem]{Обозначение} +\newtheorem{conjecture}[theorem]{Гипотеза~(Открытая)} +\newtheorem{axiom}[theorem]{Аксиома} \renewcommand{\proofname}{Доказательство} \renewcommand{\qedsymbol}{} \providecommand{\admittedbox}[1]{\fcolorbox{red}{red!10}{\parbox{\dimexpr\linewidth-2\fboxsep}{\textbf{[Допущено]:} #1}}} @@ -191,10 +242,22 @@ \begin{document} -% ===== ТИТУЛ ===== +% ===== ОБЛОЖКА (true full-bleed) ===== \frontmatter \begin{titlepage} \thispagestyle{empty} +\AddToShipoutPictureBG*{% + \AtPageLowerLeft{% + \includegraphics[width=\paperwidth,height=\paperheight,keepaspectratio=false]% + {cover_chalkboard.png}% + }% +} +\null +\end{titlepage} + +% ===== ТИТУЛ ===== +\begin{titlepage} +\thispagestyle{empty} \begin{center} \vspace*{0.5cm} {\LARGE\bfseries Цветок Золотой (Flos Aureus)}\\[0.3cm] diff --git a/scripts/wrap_tabulars_oneshot.py b/scripts/wrap_tabulars_oneshot.py new file mode 100644 index 0000000000..57cbf2d583 --- /dev/null +++ b/scripts/wrap_tabulars_oneshot.py @@ -0,0 +1,76 @@ +#!/usr/bin/env python3 +""" +ONE-SHOT bridge for `mechanical_latex_fixes::wrap_wide_tabulars`. + +Implements the EXACT same algorithm as the Rust function in +`crates/trios-phd/src/main.rs::wrap_wide_tabulars`. Used only when +the operator cannot run `trios-phd compile-resilient` directly +(e.g. cargo unavailable in the current environment) but still +needs the canonical fix applied to docs/phd/ before tectonic. + +Idempotent. Skips tables already wrapped, and `tabular*` / `tabularx`. +""" +import os, sys + +ROOTS = ['docs/phd/chapters', 'docs/phd/appendix', 'docs/phd/frontmatter'] +BEGIN = r'\begin{tabular}' +END = r'\end{tabular}' +OPEN = '\\resizebox{\\linewidth}{!}{%\n' +CLOSE = '\n}' + +def wrap(s: str) -> str: + out = [] + cursor = 0 + while True: + rel = s.find(BEGIN, cursor) + if rel < 0: + out.append(s[cursor:]) + return ''.join(out) + after = rel + len(BEGIN) + # tabular* / tabularx → не наша таблица, идём дальше + if after < len(s) and s[after] in ('*', 'x'): + out.append(s[cursor:after]) + cursor = after + continue + end_rel = s.find(END, after) + if end_rel < 0: + out.append(s[cursor:]) + return ''.join(out) + end_abs = end_rel + len(END) + head = s[max(0, rel - 120):rel] + already_resized = '\\resizebox{\\linewidth}{!}{' in head and head.count('{') > head.count('}') + already_adjust = '\\adjustbox{' in head and head.count('{') > head.count('}') + out.append(s[cursor:rel]) + if already_resized or already_adjust: + out.append(s[rel:end_abs]) + else: + out.append(OPEN) + out.append(s[rel:end_abs]) + out.append(CLOSE) + cursor = end_abs + +def main(): + total = 0 + files_changed = 0 + for root in ROOTS: + if not os.path.isdir(root): + continue + for dirpath, _, files in os.walk(root): + for f in files: + if not f.endswith('.tex'): + continue + p = os.path.join(dirpath, f) + with open(p, encoding='utf-8') as fh: + src = fh.read() + new = wrap(src) + if new != src: + with open(p, 'w', encoding='utf-8') as fh: + fh.write(new) + delta = new.count(OPEN) - src.count(OPEN) + total += delta + files_changed += 1 + print(f"{p}: +{delta} wraps") + print(f"TOTAL: {total} tabulars wrapped across {files_changed} files") + +if __name__ == '__main__': + main()