feat(phd-kat-35): Theorem 35.13 Trinity MRU as KART forward-pass (Admitted) + Popper Clause F-5#593
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…=perplexity-computer-kat] L-KAT-35 — bibliography for Theorem 35.13 (MRU as KART forward-pass). Adds: - schmidt-hieber2020nonparametric: Schmidt-Hieber, J. (2020). Nonparametric regression using deep neural networks with ReLU activation function. Annals of Statistics 48(4), 1875-1897. DOI: 10.1214/19-AOS1875. Publisher: Institute of Mathematical Statistics. Q1 statistics venue. This entry is the named gap blocking Qed of both kart_gf16_exact (Theorem 12.7) and mru_kart_decomposition_eq (Theorem 35.13): a ternary-input finite-field analogue of Schmidt-Hieber's KART bound for ReLU networks. Cited from: - docs/phd/chapters/ch_35_mesh_node.tex (sec.13 proof sketch) - docs/phd/appendix/B-falsification.tex (Clause F-5) R11 publisher balance unchanged on lane: AMS 2/3 + ICLR 1/3 from PR #584; this PR adds 1 IMS Annals of Statistics entry (also Q1). Running L-KAT total: 4 entries / 4 Q1 / 0 arXiv-only = 100% Q1. Anchor: phi^2 + phi^-2 = 3 · DOI 10.5281/zenodo.19227877
…mputer-kat]
L-KAT-35 — Theorem 35.13 (Trinity MRU as KART forward-pass), Coq side.
- New file: trinity-clara/proofs/igla/mru_kart.v (127 LOC)
- Theorem mru_kart_decomposition_eq: for every n in Nat and every
input vector x in mru_input n, the MRU forward pass equals the
KART-shaped decomposition.
- Status: Admitted (R5-honest comment names the missing ternary-input
finite-field analogue of Schmidt-Hieber 2020 Annals of Statistics
bound that blocks the Qed).
- Three sanity Qed corollaries land green:
kart_width_n0 (kart_width 0 = 1)
kart_width_succ (kart_width grows as 2n+1)
mru_kart_threshold_zero (boundary)
Companion to:
- trinity-clara/proofs/igla/kart_gf16_isomorphism.v (Theorem 12.7)
- trinity-clara/proofs/igla/gf16_precision.v (INV-3, 0-DSP discipline)
- trinity-clara/proofs/igla/lucas_closure_gf16.v (Lucas closure)
R5: stays Admitted; no flip to Proven.
R6: only constants used are {phi, n in Z}; theta = ceil(n*phi^-1).
R14: theorem maps to assertions/igla_assertions.json on next L-COQ-* sweep.
Anchor: phi^2 + phi^-2 = 3 · DOI 10.5281/zenodo.19227877
… [agent=perplexity-computer-kat]
L-KAT-35 — LaTeX side of Theorem 35.13 (Trinity MRU as KART forward-pass).
- docs/phd/chapters/ch_35_mesh_node.tex: append section 13
(+~70 lines) under R12/Lee proof style.
- Statement: a single Mesh-Resolution-Unit (MRU) realises a
Kolmogorov-Arnold-shaped two-layer decomposition over GF(16) at
the deployment-cell granularity.
- Outer-layer width 2n+1 cited as Kolmogorov 1957/Arnold 1963 axiom.
- Proof sketch (Lee/GVSU 'we' pronoun): lifts cell-level Theorem 12.7
(\\ref{thm:gf16-kart}) to deployment-cell level via the
iverilog-synthesisable composition described in M35-3.
- \\admittedbox{Theorem 35.13 stays Admitted} pointing at
trinity-clara/proofs/igla/mru_kart.v (theorem
mru_kart_decomposition_eq) with R5-honest reason: missing
ternary-input finite-field analogue of Schmidt-Hieber 2020 Annals
of Statistics bound (\\cite{schmidt-hieber2020nonparametric}).
- Falsification subsection (R7): names the witness pair
(x, x') in GF(16)^n x GF(16)^n that would refute the claim;
refers to appendix B (Clause F-5) and to
crates/trios-golden-float/tests/kart_gf16_witness.rs (n=4 ignored).
- 0-DSP discipline subsection: ties to INV-3 / gf16_precision.v and
the <= 1800 standard-cell TTIHP27a tile budget.
Style follows the existing ch_35 Theorems and Formal Claims section
(\\admittedbox{<reason>} single-arg form, Lee 'we' pronoun, qed-closed
proof sketches).
R3: ch_35_mesh_node.tex was 507 lines pre-edit, now ~580 lines (additive
section, no chapter-floor regression).
R4 / R14: \\admittedbox + Coq stub path lets phd-monograph-auditor LC
lane register the theorem on next cycle.
R5: Admitted in Coq, Admitted in LaTeX. Honest agreement.
R6: zero free parameters; only {phi, n in Z}, theta = ceil(n*phi^-1).
R7: explicit Falsification Criterion subsection (Ch.35 is empirical).
R11: cite uses Schmidt-Hieber 2020 (Q1 IMS Annals of Statistics).
R12: Lee/GVSU 'we' pronoun, theorem/proof/qed structure.
Forward-references PR #584 (L-KAT-RW Table 27.4 4x memory ratio) and
PR #591 (L-KAT-12 Theorem 12.7 cell-level KART-GF(16) isomorphism).
Note on TOC: ch_35_mesh_node.tex remains NOT included in main.tex
(orphan from active TOC). This commit ships the section addition;
whether to wire Ch.35 into main.tex is a separate proposal posted as
a TOC v6.2->v6.3 comment on trios#380 (R5: not silently edited).
Anchor: phi^2 + phi^-2 = 3 · DOI 10.5281/zenodo.19227877
…perplexity-computer-kat]
L-KAT-35 — Popper falsifier-clause for the KART-GF(16) line of theorems.
- docs/phd/appendix/B-falsification.tex: append Clause F-5 (+~45 lines)
in the existing tcolorbox falsifier-clause style.
- Clause F-5 covers BOTH Theorem 12.7 (kart_gf16_exact) and Theorem
35.13 (mru_kart_decomposition_eq) under one falsifier:
* Falsifier: any witnessed (x, x') in GF(16)^n x GF(16)^n where
MRU output deviates from KART decomposition by > theta.
* Brute-force witness: n=2 default + n=4 ignored
(crates/trios-golden-float/tests/kart_gf16_witness.rs).
* n>4 structurally infeasible (16^16 ~ 1.8e19 at n=8).
* Coq theorems stay Admitted in honest agreement (R5).
- Non-phi control: continuous-spline KAN (\\cite{liu2024kan}) at >=256
bits/knot vs Trinity GF(16) at 64 bits/16-cell tensor = literal 4x
ratio at n=8 (ch.\ 27 Table 27.4). Explicitly rejects the speculative
100x / 2600x figures that the L-KAT-RW R5 audit downgraded.
- Status line: corroboration row Ch.35-MRU-KART = pending CI.
- B.2 anti-numerology defense list extended with R5-honest Admitted
disclosure item (5th bullet).
R5: Admitted disclosed at clause level. No flip.
R7: empirical chapter Ch.35 now has a registered falsifier in the
monograph-wide appendix (LP lane gate satisfied for L-KAT-35).
R11: cites only Q1 entries (liu2024kan ICLR, schmidt-hieber2020nonparametric IMS).
Forward-references PR #584 (L-KAT-RW), PR #591 (L-KAT-12), and the
companion Coq stubs in trinity-clara/proofs/igla/.
Anchor: phi^2 + phi^-2 = 3 · DOI 10.5281/zenodo.19227877
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🩺 Diagnosis: the failing Unblock fix: PR #635 ( After #635 squashes into
Anchor: |
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…#635) PR #629 (`feat(trios-mesh): Trinity Node E2E Quality`) added a tree entry at `.parameter-golf/parameter-golf` with mode 160000 and sha `06e32ab...` but did NOT register a matching submodule URL in `.gitmodules`. Every CI job that calls `actions/checkout@v4` with `submodules: recursive` therefore fails at submodule init with fatal: No url found for submodule path '.parameter-golf/parameter-golf' in .gitmodules The process '/usr/bin/git' failed with exit code 128 R7 witness: the failure is upstream of the actual proof-checking step, so checks like `Verify IGLA-INV-001..005` and `Coq Proof Verification (INV-1..5)` print their summary blocks for free but report FAILURE because the runner exited 128 during checkout. This silently blocked the KAT залп (#584 / #591 / #593) for the entire IGLA marathon \u2014 the Coq theorems themselves were not the regression, the phantom gitlink was. The current `.gitmodules` only declares the four `crates/trios-*/vendor/ zig-*` submodules. `parameter-golf` was never tracked as a submodule, so removing the orphan entry from the tree is sufficient \u2014 nothing in the workspace, build, or test paths depends on it. Closes #634 Refs: #584, #591, #593, #629 Anchor: phi^2 + phi^-2 = 3 \u00b7 DOI 10.5281/zenodo.19227877 Co-authored-by: Dmitrii Vasilev <admin@t27.ai>
added 2 commits
May 9, 2026 10:47
Same fix as PR #635 (already merged into main as e123aa8). Each KAT branch carries its own independent copy of the orphan gitlink at .parameter-golf/parameter-golf (mode 160000, sha 06e32ab) without a matching .gitmodules entry, so the recursive checkout fails BEFORE the Coq INV step runs. Removing the orphan unblocks Verify IGLA-INV-001..005 and Coq Proof Verification. Anchor: phi^2 + phi^-2 = 3 - DOI 10.5281/zenodo.19227877
cleanup After dropping .parameter-golf the recursive checkout still failed on opencode/nextpnr-xilinx, opencode/prjxray, opencode/prjxray-db, tri — none of which are declared in .gitmodules. Drop all remaining orphans in one atomic commit per branch so Verify IGLA-INV-001..005 and Coq Proof Verification can finally run on these PRs. Anchor: phi^2 + phi^-2 = 3 - DOI 10.5281/zenodo.19227877
This was referenced May 12, 2026
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R5-Honest Closure — Content Preserved in #750 Этот PR закрывается БЕЗ мержа в рамках каскадной чистки PHD-STATUS-RVR-003/004. Причина: ветка отстала на сотни коммитов от main и накопила конфликты в submodules + Rust crates, которые не относятся к содержимому самого PR. Прямой rebase разрушал бы соседние подсистемы. Уникальный вклад этого PR (Theorem 35.13 «Trinity MRU as KART forward-pass» + Popper Clause F-5) сохранён: он хирургически перенесён на свежий main в чистый PR #750 ( Перенесённые блоки (verbatim):
Anchor Дальнейшая работа над KAT-35 → в #750. — END OF CLOSURE NOTE — |
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…itted) + Popper Clause F-5 (#750) Extracted from superseded PR #593 (feat/phd-kat-35) which became unrebasable after months of main divergence. This is a surgical re-apply on fresh main. What this adds: - Theorem 35.13 (thm:mru-kart) in docs/phd/chapters/ch_35_mesh_node.tex - Lee/GVSU style proof sketch (Admitted, R5-honest) - 0-DSP discipline note - Falsification criterion (R7) - Clause F-5 (Falsifier F-5) in docs/phd/appendix/B-falsification.tex - KART-Shaped Decomposition over GF(16) (L-KAT-12, L-KAT-35) - References kart_gf16_exact (Theorem 12.7) and mru_kart_decomposition_eq Anchor: phi^2 + phi^-2 = 3 DOI: 10.5281/zenodo.19227877 Defense: 2026-06-15 R5 (HONEST): \\admittedbox preserved (5 in ch_35, theorem stays Admitted in honest agreement with the missing Schmidt-Hieber ternary-input finite-field analogue). R6 (SSOT): docs/phd/ only; no crates/ changes. R7 (ANCHOR): phi^2 + phi^-2 = 3 echoed. Closes #593 [agent=perplexity-computer kat35-surgical-reapply] Co-authored-by: perplexity-computer <horsejpyryt8d1pg@hotmail.com>
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L-KAT-35 — Theorem 35.13: Trinity MRU as KART forward-pass
Lane: L-KAT-35 (claimed on trios#380)
Sibling PRs: #584 — L-KAT-RW Related Work · #591 — L-KAT-12 Theorem 12.7
Agent:
perplexity-computer-katAnchor: φ² + φ⁻² = 3 · Zenodo DOI 10.5281/zenodo.19227877
Summary
This PR completes the KAT × Trinity GF(16) integration triplet. Theorem 35.13 lifts the cell-level KART-GF(16) isomorphism (Theorem 12.7, PR #591) to the deployment-cell level: a single Mesh-Resolution-Unit (MRU) — the smallest deployable inference cell of the Trinity S³AI mesh node — realises a Kolmogorov–Arnold-shaped two-layer decomposition over GF(16). The theorem is stated declaratively in Coq (Admitted, R5-honest), registered as a Popper falsifier in appendix B (Clause F-5), and typeset in LaTeX under R12 Lee/GVSU style.
Four atomic commits
a48da12feat(phd-kat-35): bib Schmidt-Hieber 2020 Annals of Statistics044f8e5feat(phd-kat-35): Coq stub mru_kart.v (Admitted)b2a0378feat(phd-kat-35): ch_35 sec.13 Theorem 35.13 MRU as KART forward-passc00b3d8feat(phd-kat-35): appendix B Clause F-5 KART-GF(16) falsifierFiles
docs/phd/bibliography.bibschmidt-hieber2020nonparametric(IMS Annals of Statistics, Q1)trinity-clara/proofs/igla/mru_kart.vmru_kart_decomposition_eqAdmitted, 3 sanity Qeddocs/phd/chapters/ch_35_mesh_node.texdocs/phd/appendix/B-falsification.texR5-honesty register (NEVER violate)
mru_kart_decomposition_eqstaysAdmitted— the missing ternary-input finite-field analogue of Schmidt-Hieber 2020 (IMS Annals of Statistics) is named explicitly in the Coq comment.#[ignore]'d only. n>4 is structurally infeasible (16²ⁿ > 10¹⁹ at n=8) — Coq stays Admitted in honest agreement with that gap.ch_35_mesh_node.texis currently an orphan (NOT included inmain.tex). This PR ships the §13 addition; whether to wire Ch.35 intomain.texis a separate proposal that will be posted as a TOC v6.2→v6.3 comment on trios#380, not silently edited here.Hard-rule compliance
.py/.sh.mru_kart_decomposition_eqwill be picked up byphd-monograph-auditorLC lane (Coq citation map appendix F) on next cycle.{φ, n ∈ ℤ};θ = ⌈n · φ⁻¹⌉.\theorem/\proof/\qedstructure throughout §13.Falsifier (Clause F-5, appendix B)
Clause F-5 covers both Theorem 12.7 (
kart_gf16_exact) and Theorem 35.13 (mru_kart_decomposition_eq) under one falsifier:(x, x') ∈ GF(16)^n × GF(16)^nwhere MRU output deviates from KART decomposition by more thanθ = ⌈n · φ⁻¹⌉.crates/trios-golden-float/tests/kart_gf16_witness.rs(n=2 default, n=4#[ignore]).\cite{liu2024kan}) at ≥256 bits/knot vs Trinity GF(16) at 64 bits/16-cell tensor = literal 4× ratio at n=8.Bibliography balance (running L-KAT total across PR #584 / #591 / this PR)
kolmogorov1957superpositionarnold1963superpositionliu2024kanschmidt-hieber2020nonparametricTotal: 4 entries · 4 Q1 · 0 arXiv-only · 100% Q1.
Sanctioned constants
n = 4 (witness ceiling) · θ = ⌈n·φ⁻¹⌉ · 2n+1 (Kolmogorov 1957 outer width) · seeds ∈ {F₁₇..F₂₁, L₇, L₈} · forbidden 42/43/44/45 audited clean.
Local audit
coqc trinity-clara/proofs/igla/mru_kart.v— 3 Qed close, 1 Admitted (intentional).cargo run -p trios-phd -- audit --chapter 35— pending CI verdict.cargo run -p trios-phd -- biblio --check— pending CI verdict; expected to pass (additive only, all Q1).Next steps after merge
ch_35_mesh_node.texintomain.tex(currently orphan from the active 98-chapter manifest).mru_kart_decomposition_eqregistration to thephd-monograph-auditorLC lane sweep.