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feat(phd): Wave-14c Round 3 — expand 5 thinnest chapters to ≥1000 LoC each#812

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Closes #808

Wave-14c PhD Chapter Expansion Round 3

Expands the 5 thinnest Flos Aureus chapters (excluding already-fattened: 00, 34, 59, 62, 63, 64, 65, 66, 67, 68) to ≥1000 LoC each.

Before / After LoC

Chapter Title Before After
flos_41 Vogel Phyllotaxis 197 1001
flos_45 Pre-registration H₁ 199 1005
flos_47 STROBE Sealed Seeds 195 1005
flos_53 Statistical Analysis (Welch-t) 186 1017
flos_57 MCP Integration 187 1001

R-rule Compliance

  • R3: ≥1000 LoC, ≥2 citations, ≥1 theorem — all 5 chapters ✓
  • R7: Falsification witness in each chapter (F-41a/b, F-45a/b/c, F-47a/b/c, F-53a/b/c, F-57a/b/c) ✓
  • R12: Lee/GVSU numbered-step proof style throughout ✓
  • R14: assertions/coq_map.json updated with 10 new invariant entries ✓

New Theorems Added

flos_53 (Ch.19 Statistical Analysis)

  1. Welch Consistency (Admitted — CLT library pending)
  2. Satterthwaite Lower Bound (Admitted)
  3. Gate-2 Statistical Sufficiency (Admitted)
  4. φ-Quantisation Variance Reduction (Admitted)
  5. Loss Normalisation via Trinity Identity (Qed)

flos_57 (Ch.23 MCP Integration)

  1. Seed Preservation (Admitted — Weyl library pending)
  2. MCP-INV7 Consistency (Admitted)
  3. Fibonacci Gap Upper Bound (Qed)
  4. MCP Throughput Lower Bound (Admitted)
  5. Snap Composition (from §18, Qed)

flos_47 (Ch.13 STROBE Sealed Seeds)

  1. ASHA Threshold Derivation (Qed)
  2. Forbidden Seed Gradient Spike (Admitted)
  3. Cross-Platform Reproducibility (Admitted)
  4. Admissibility Completeness (Admitted)
  5. ASHA Champion Invariant (Qed, via INV2)
  6. Old Threshold Kills Champion (Qed, via INV2)

flos_41 (Ch.7 Vogel Phyllotaxis)

  1. Golden Angle Packing Optimality (Admitted — three-distance library)
  2. Exact Golden Angle in ℤ[φ] (Qed)
  3. Fibonacci Lattice Init Efficiency (Admitted)
  4. E8 Contact Graph Approximation (Admitted)
  5. Three-Distance Theorem for Golden Angle (Admitted)
    6–8. H4/E8 Coq certificates (4 Qed, 2 Abort — KER-3)

flos_45 (Ch.11 Pre-registration H₁)

  1. Ternary BPB Lower Bound (Admitted)
  2. Seed Statistical Independence (Admitted)
  3. Gate-3 Implies Gate-2 (Qed)
  4. Pre-registration Integrity (Admitted)
  5. Three-Seed Minimum Necessity (Admitted)

Author

Dmitrii Vasilev admin@t27.ai

License

Apache-2.0

Closes #808

Expanded chapters (baseline → final LoC):
- flos_41 (Ch.7  Vogel Phyllotaxis):          197 → 1001 LoC
- flos_45 (Ch.11 Pre-registration H₁):         199 → 1005 LoC
- flos_47 (Ch.13 STROBE Sealed Seeds):          195 → 1005 LoC
- flos_53 (Ch.19 Statistical Analysis Welch-t): 186 → 1017 LoC
- flos_57 (Ch.23 MCP Integration):              187 → 1001 LoC

Per-chapter R-rule compliance:
- R3: ≥1000 LoC, ≥2 citations, ≥1 theorem ✓
- R7: falsification witness in each chapter ✓
- R12: Lee/GVSU numbered-step proof style ✓
- R14: assertions/coq_map.json updated with 10 new invariant entries ✓

New theorems added:
- flos_53: Welch Consistency, Satterthwaite LB, Gate-2 Sufficiency,
           phi-Quantisation Variance Reduction, Loss Normalisation (5 thms)
- flos_57: Seed Preservation, MCP-INV7 Consistency, Fibonacci Gap UB,
           Throughput LB, Snap Composition (5 thms)
- flos_47: ASHA Threshold Derivation, Forbidden Seed Spike, Cross-Platform
           Reproducibility, Admissibility Completeness, ASHA Champion Inv,
           Old Threshold Kills Champion (6 thms)
- flos_41: Packing Optimality, Exact Golden Angle, Lattice Init Efficiency,
           E8 Approx, Three-Distance Theorem, +H4/E8 Coq certs (8 thms)
- flos_45: Ternary BPB LB, Seed Independence, Gate-3 Implies Gate-2,
           Pre-registration Integrity, Three-Seed Minimum (5 thms)

Author: Dmitrii Vasilev <admin@t27.ai>
License: Apache-2.0
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Wave-14c PhD Chapter Expansion Round 3: flos_53, flos_57, flos_47, flos_41, flos_45 (≥1000 LoC each)

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