feat(phd-phase1-unify-1-4): Flos Aureus & Trinity-strand Chapter Anchor headers in 70 chapters

[gHashTag]

Closes #265\n\n## Phase 1 UNIFY · task 1.4 — Flos Aureus & Trinity-strand Chapter Anchor headers

Closes part of trios#380 (task 1.4). Stacked on #603 (task 1.6) → #602 (task 1.5) → #595 (task 1.2).

The Golden Flower must bloom in every chapter

Per #380 manifest "PART VIII — Flos Aureus (34 chapters)", every Flos Aureus chapter (fa_00..fa_33) carries its own petal name (Monad, Golden Egg, Golden Cut, …, Epilogue) and belongs to one of 8 Parts. The Trinity S³AI strand runs in parallel.

Two header palettes

Flos Aureus (yellow/gold tcolorbox, fa_00..fa_33):

\begin{tcolorbox}[colback=yellow!4,colframe=yellow!50!brown,
                  title={\textbf{Flos Aureus} \textbf{FA.05 Golden Bridge}}]
  \textbf{Petal:} Part II — \emph{The Expansion}
  \textbf{Anchor:} φ² + φ⁻² = 3 (Trinity Identity, INV-22)
  \textbf{Motif:} Fibonacci–Lucas generating functions
  \textbf{Lane:} L5 (Flos Aureus strand)
  \textbf{Theorems in chapter:} 46
  \textbf{Coq link:} trinity-clara/proofs/igla/lucas_closure_gf16.v
  \textbf{Notation key:} F_n Fibonacci, L_n Lucas, φ; INV-k via \citetheorem{INV-k}
\end{tcolorbox}

Trinity S³AI Strand (blue tcolorbox, ch_NN):

\begin{tcolorbox}[colback=blue!3,colframe=blue!40!black,
                  title={\textbf{Trinity S³AI Strand} \textbf{Ch.27}}]
  \textbf{Strand:} Trinity S³AI — silicon, software, science
  \textbf{Anchor:} φ² + φ⁻² = 3 (Trinity Identity, INV-22)
  \textbf{Lane:} S27 (Trinity strand)
  ...
\end{tcolorbox}

8 Parts of Flos Aureus (mapped to Parts in main.tex)

Part	Title	Chapters
I	The Foundations	fa_00..fa_03
II	The Expansion	fa_04..fa_07
III	The Crystal	fa_08..fa_09
IV	The Synthesis	fa_10
V	Sacred Geometry	fa_11..fa_19
VI	Physics Foundation	fa_20..fa_24
VII	Algebraic Proofs	fa_25..fa_29
VIII	Imagery & Genealogy	fa_30..fa_33

Coverage

	Count	Status
Flos Aureus headers	34/34	✅ all branded
Trinity strand headers	34/35	✅ branded; +1 bespoke (ch_35_mesh_node)
Bespoke pre-existing	2 (ch_00, ch_35_mesh_node)	✅ left intact per R6
Total chapters with Chapter Anchor	70/70	✅ 100%

Sample petal names (FA.00 → FA.33)

Monad · Golden Egg · Golden Cut · Golden Harvest · Golden Scales · Golden Bridge · Golden Mantissa · Golden Sprout · Golden Crystal · Golden Seal · Golden Bloom · Vesica Piscis · Flower of Life · Metatron's Cube · Platonic Solids · Kepler Solids · Sacred Ratios · Golden Spiral · Torus Geometry · Fibonacci Tesselation · Standard Model · Quantum Field · E₈ Symmetry · GF(16) Algebra · IGLA Architecture · Benchmarks · Data Analysis · Trinity Identity · Momentum Algebra · Lucas Closure · Golden Imagery · Philosophy · Conclusion · Epilogue.

Invariants preserved (vs tasks 1.5 & 1.6)

Metric	Value
Total \label sites	1158 (unchanged)
Duplicate label keys	0
Dangling \ref	0
Originally-referenced 119 keys	119/119 ✅

Files changed

File	Change
docs/phd/chapters/fa_00..fa_33.tex	header injected (yellow/gold Flos Aureus block) — 34 files
docs/phd/chapters/ch_01..ch_34.tex	header injected (blue Trinity strand block) — 34 files
docs/phd/chapters/ch_00.tex, ch_35_mesh_node.tex	left untouched (bespoke pre-existing)
docs/phd/chapter-headers-audit.md	new, 142 lines — full manifest

Acceptance criteria (#380 task 1.4)

Criterion	Status
0.5-page header per chapter	✅ 70/70
Notation key per chapter	✅ embedded in template
Anchor φ² + φ⁻² = 3 cited	✅ all 70
Theorem count auto-derived	✅
Coq link per chapter	✅
Flos Aureus petal name in every fa_NN	✅ 34/34
Part assignment in every fa_NN	✅ 34/34
Audit document	✅ docs/phd/chapter-headers-audit.md

Rules honoured

• R1 (no .py/.sh): patch script ran from inline shell heredoc, never committed
• R5 (honesty): theorem counts mechanical; stub chapters honestly report 0; per-theorem fallback Coq link where no dedicated .v exists
• R6 (lane discipline): no chapter prose touched; only header injection; bespoke ch_00 / ch_35_mesh_node left alone
• R10 (atomic): one commit ba954a3 for the entire mechanical injection
• Anchor: φ² + φ⁻² = 3 · DOI 10.5281/zenodo.19227877

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🤖 Generated by phd-chapter-author skill v1.1 — Phase 1 UNIFY worker.
Author: Dmitrii Vasilev <[email protected]> — ORCID 0009-0008-4294-6159.

(Re-opened from auto-closed #605 after chained-base-branch deletion in PhD batch-merge.)