📖 Ch.5 — Conjecture C1 (exp/mant equals 1/phi) (700w · 🟢 P2)

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Ch.5 — Conjecture C1 (exp/mant equals 1/phi)

Master: trios#380 GOLDEN SUNFLOWERS Book
Priority: 🟢 P2 · Word target: 700 · Owner: GoldenSunWeaver

🎯 Scope (FROZEN)

Statement of C1: exp/mant ≈ 1/φ minimizes KL divergence to log-normal weight distribution. Weber-fraction argument + range/precision Pareto. Ablation table: GF16(6/9 vs 5/10 vs 7/8 vs shuffled). Open question: does this hold beyond log-normal?

🔑 Key claims / formulas

• C1: argmin_{e+m=N-1} KL(W_target || gfN_quantize(W_target)) ≈ exp/mant ratio satisfying e/m = 1/φ
• Pareto identity: range × precision = constant (info budget)
• Weber fraction: relative perceptual precision
• Ablation: 6/9 baseline vs 5/10 (less mantissa) vs 7/8 (more) vs shuffled (control)

📦 Deliverables

• paper/sections/5_conjecture_c1_expmant_equals_1phi.tex
• Coq: T6 Golden Corridor (PR-2 deliverable, t27#319 cited)
• KL ablation figure: figures/kl_ablation.pdf (10K log-normal samples)
• Honest: C1 stated as conjecture, not theorem

🔗 Dependencies

• Ch.4 GoldenFloat

📝 Draft (Markdown — paste here when ready)

Operator types наполни Ch.5 → General fills this section with research-backed Markdown.

✅ Definition of Done (NeurIPS checklist aligned)

• Word count 700 ±10%
• All claims cited (primary literature, not just our repos)
• No AI as author (Acknowledgments only)
• Compiles in main.tex via tectonic, no warnings
• Limitations stated (where applicable)
• Reproducibility info present (where applicable)
• PR with Closes #<this> + green CI
• L1 (no .sh) · L3 (clippy zero) · L4 (tests pass) · L8 (PUSH FIRST)

🤖 ONE-SHOT directive (когда operator typed ONE SHOT Ch.5)

A CHAPTER-AGENT: take Markdown draft from this issue body §"Draft", convert to LaTeX,
place in paper/sections/5_<slug>.tex, ensure compile via tectonic with main.tex,
open PR linked to #, run cargo clippy/test, push, request review.
Hard deadline per priority (P0 → T-3h, P1 → T-1h, P2 → defer).

phi^2 + phi^-2 = 3 · TRINITY · NEVER STOP