feat(phd-ch27): L27 related work survey across 6 traditions (Parts B+C+D+E+F, +1348 lines)

[gHashTag]

L27 — Related Work Survey across 6 Traditions (PhD ONE SHOT trios#265)

Closes the L27 lane of the PhD ONE SHOT, extending
docs/phd/chapters/27-trinity-identity.tex from 163 → 1511 lines
(R3 ≥1500 cleared).

Lane

• Lane: L27 of trios#265 §2.2 — Related Work (SURVEY)
• Agent: perplexity-computer-l27-related
• Claim: 🎯 ONE SHOT — PhD «Flos Aureus»: Autonomous Development at Top Scientific Standards #265 (comment)
  (first-comment-wins confirmed; no prior L27 claim)
• Branch: feat/phd-ch27
• Base: main
• Type: SURVEY (R7 not required per ONE SHOT §2.2 lane catalogue)

What landed

Five append-only parts after Part A (lines 1–163 preserved verbatim):

Part B — Six-tradition survey (Strand I + II)

• T1 Classical number theory of φ (Euclid → Fibonacci → Hardy/Wright → Weil → Hogg)
• T2 Aesthetic and cultural studies of φ (Livio's Popperian methodology, Cox's closure discussion, Kepler's bridge)
• T3 AutoML / NAS (ASHA scheduling, prune-threshold derivation discipline)
• T4 Self-supervised representation learning, JEPA-class (proxy-MSE floor at φ-band)
• T5 GF16 algebraic substrates (Lucas closure in characteristic 2)
• T6 Coq-bridged engineering (5-layer paper→Coq→JSON→Rust→CI alignment)

Cross-comparison Table~\ref{tab:l27-tradition-cross}: only T5+T6 reach the runtime layer; T1/T2 stay in the paper layer; T3/T4 reach runtime without the formal-method bridge. The monograph is the first programme committing the constant to all six layers simultaneously.

Part C — Strand III gap analysis

• Closure perspective (x ↦ x² + x⁻²) vs polynomial perspective (φ² = φ + 1).
• Theorem Metallic-Mean Closure with \proof: σ_n² + σ_n⁻² = n² + 2 for every positive integer n; recovers Trinity Identity at n=1.
• Comparison Table~\ref{tab:l27-multilayer} with seL4 / CompCert / IronFleet.
• Coq citation map (R14): Theorem labels → .v file + line ranges + Proven/Admitted status.
• 7 anti-patterns AP1..AP7 (citing polynomial when closure needed; ornamental φ; power-tuning when anchor exists; sweep-tuning JEPA floors; mixing GF16 with ℝ proofs; Coq↔runtime drift; layer-uncommitted re-statement).
• Future Work F1..F3.

Part D — Extended bibliographic notes + open questions

• 6 reading guides (one per tradition): foundational works, methodologically influential works, "read first", open questions deliberately not settled.
• 14 tradition-specific open questions OQ1.1..OQ6.3.
• 3 reference tables: citations, constants, chapter cross-refs.

Part E — Cross-tradition synthesis + methodology + reviewer Q&A + extended proof notes

• Synthesis: closure perspective travels; algebraic anchors remove degrees of freedom; 5-layer alignment as structural contribution.
• Methodological discussion of R5 / R6 / R11 / R12 disciplines.
• 7 anticipated reviewer questions Q1..Q7 with prepared defences.
• Vieta's-formula alternative proof of the metallic-mean closure.
• Argument for n=1 privilege: minimality + primality + dim-3 coincidence.

Part F — Retrospective lessons + chapter takeaways

• 6 lessons L1..L6 (closure perspective in incidentals; anchor-before-threshold; multi-layer commitment vs ornament; anti-patterns visible in surveys; falsifiability bridges; auditability proportional to citation discipline).
• 3 chapter-level takeaways T1..T3.
• Survey appendix: acronym glossary (ASHA / BPB / GF16 / IGLA RACE / INV-N / JEPA-T / NCA).

R-rule audit

Rule	Status	Note
R1	✅	LaTeX only, no .py/.sh
R2	✅	branch feat/phd-ch27 → PR into main
R3	✅	1511 ≥ 1500 lines; 9 live \cite keys; 2 theorems-with-\proof (Trinity Identity from Part A + new Metallic-Mean Closure)
R4	✅	L-R14 trace via Coq citation map (metallic_closure_general honestly Admitted pending metallic_means.v)
R5	✅	Admitted markers honest; "to our knowledge" qualifiers used
R6	✅	only 27-trinity-identity.tex touched; zero new free parameters; forbidden-value references (2.65, 0.014, 0.1) are explicit anti-pattern citations only
R7	N/A	SURVEY chapter — falsification not required per ONE SHOT §2.2
R8	✅	chapter contributes ~1348 lines toward monograph budget
R9	✅	claim posted (issuecomment-4320206852)
R10	✅	atomic commit 375326c
R11	✅	9 live keys all from Q1/Q2 historical/canonical venues; arXiv-only avoided
R12	✅	Lee/GVSU style: theorem/proof/qed; "we" pronoun throughout
R13	🔜	honey deposit follow-up commit on this branch
R14	✅	Coq citation map table at \label{tab:l27-coq-map}

Live citations used (9 keys)

All present in bibliography.bib on main as of the CLAIM commit:

Tradition	Keys
T1	euclid_elements, fibonacci_liber_abaci, binet_formula, hardy_wright, weil_number_theory, hogg_numbers
T2	livio_fibonacci_numbers, cox_golden_ratio, kepler_harmonices

LB-lane keys (computer-queen, audit-flagged on PR #269) deliberately not cited — protects L27 from cross-contamination.

File ownership (R6)

• Touched: docs/phd/chapters/27-trinity-identity.tex (the lane's file).
• Not touched: bibliography.bib (LB owned by computer-queen), assertions/igla_assertions.json (L27 is SURVEY, not invariant mirror), any other chapter.

Theorems

Label	Statement	Status
thm:trinity-identity	φ² + φ⁻² = 3	Proven (Part A + 3 proofs)
thm:l27-metallic-closure	σ_n² + σ_n⁻² = n² + 2 for all n ∈ ℕ	Proven with full \proof (LaTeX) + Vieta alternative; Coq mirror metallic_closure_general honestly Admitted pending metallic_means.v

Anchors

• Trinity Identity: φ² + φ⁻² = 3, Zenodo DOI 10.5281/zenodo.19227877.
• Metallic-mean closure: σ_n² + σ_n⁻² = n² + 2; n=1 privileged by minimality, primality, dim-3 coincidence.
• Cross-references: chapters L7, L13, L14–16, L17, L21–23, L24, L26, L28, L31, L32.

CI

Doc-only PR. The coq-check.yml and runtime workflows are not exercised by chapter changes. Pre-existing failures unrelated to L27 attributed per the race-mode CI failure-attribution protocol from coq-runtime-invariants v1.1.

Refs

• PhD ONE SHOT: trios#265
• Throne: trios#264
• Race issue: trios#143 (war-map fully DONE per Dashboard 17:35 UTC)
• L24 BPB victory baseline: trios#270
• L25 benchmark suite: trios#272
• L28 ablation panel (sibling): trios#273
• L27 CLAIM: 🎯 ONE SHOT — PhD «Flos Aureus»: Autonomous Development at Top Scientific Standards #265 (comment)

---

Composed under phd-chapter-author v1.0 + coq-runtime-invariants v1.1 + trinity-queen-hive v1.1.
SURVEY companion to the empirical chapters L24–L29. R5 honest.