L-PHASE1-R3: expand 5 thinnest chapters honestly (R3-partial allowed)

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Mission

Expand the 5 thinnest auto-generated chapters in docs/phd/chapters/ (ch_01 .. ch_05) toward R3 compliance (≥1500 lines each) without padding or LLM-slop.

Live dashboard: https://trios-production.up.railway.app/ — currently 0/48 chapters meet R3.

Chapter targets (current line count):

• ch_01 — Introduction: TRINITY S³AI Vision (147 lines)
• ch_02 — Background: Neuro-Symbolic AI (164 lines)
• ch_03 — Trinity Identity (φ²+φ⁻²=3) (231 lines)
• ch_04 — Sacred Formula: α_φ Derivation (182 lines)
• ch_05 — φ-distance and Fibonacci-Lucas seeds (211 lines)

Acceptance (per chapter)

• L1 Real LaTeX content. No Lorem ipsum, no repeated paragraphs, no "TODO expand" markers.
• L2 ≥2 citations resolvable in docs/phd/bibliography.bib (212 entries since PR docs(phd): L-KAT-BIB — KART + KAN bibliography (closes #573) #581).
• L3 ≥1 theorem with EITHER full proof OR runtime witness comment + Coq cross-ref OR explicit "structural analogy not isomorphism" framing (R5).
• L4 Compiles with tectonic without new errors. CI green: phd-build audit + tectonic compile gates.
• Anchor footer in chapter front matter.

R5-honest policy (overrides ≥1500 if conflict)

If existing repo material genuinely cannot source 1500 honest lines:

• Expand to maximum honest depth.
• Document in PR: Ch.N: BEFORE → AFTER lines (R3 ≥1500 NOT met; honest content cap; recommend merging fa-N with fa-M to reach R3)
• Mark such chapters with TODO comment block at top: % R3-PARTIAL: target 1500, achieved N, blocker = <reason>, defer to L-PHASE1-R3-PT2
• Honest 1100-line chapter > fake 1500.

Honesty rules (R5 / R7)

• No padded paragraphs.
• No empty proofs without runtime-witness reference.
• No fabricated citations.
• KAT bibliography (PR docs(phd): L-KAT-BIB — KART + KAN bibliography (closes #573) #581 — liu_kan_2024, liu_kan2_2025, finite_field_expressivity_2025, etc.) is available and may be cited honestly in Ch.2 (Background: Neuro-Symbolic AI).

Anchor

phi^2 + phi^-2 = 3 · DOI 10.5281/zenodo.19227877