feat(phd): Lane E — GF16 + IGLA + benchmarks (Ch.22–25, Ch.32, App.C, App.D)

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🎯 Goal

Write computational, ML, and GF16 chapters with benchmark data.

Parent epic: #30
Lane: E — GF16 + IGLA + Benchmarks
Depends on: #41 (Lane A scaffold)

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📂 Chapters

Ch.22 — Golden Bridge (Trinity ⊆ Pellis)

• Trinity monomials form: n · 3ᵏ · φᵖ · πᵐ · eᶠ
• Pellis polynomial formulations review
• Main theorem: Trinity ⊆ Pellis as subalgebra (formal inclusion proof)
• Hybrid Conjecture H1: “Pellis polynomials are UV completions of Trinity monomials”
• Comparative table: Trinity vs Pellis vs Sherbon vs El Naschie vs RI 2024
• CLI evidence: tri math compare --pellis → output → Appendix D
• Trade-off: monomial simplicity vs polynomial expressiveness
• AdS/CFT Maldacena parallel (bridge between formulations)
• Source: paste.txt §5, Stergios Pellis papers

Ch.23 — Golden Mantissa (GF16 Format)

• GF16 bit layout: [sign:1][exp:6][mant:9] = 16 bits total
• Theorem 2 connection: φ − 3/2 = 0.118034 ≈ α_s(mZ), Δ < 0.03σ
• Derivation of 6:9 split: 9/6 = 1.5, φ − 1.5 = α_φ (bit-level golden cut)
• Scale invariance: same φ-principle at bit-level and particle-level
• VSA operations: bind/unbind/bundle (trinity-clara/specs/vsa/core.t27)
• Comparison table: GF16 vs FP16 vs BF16 (accuracy, range, cost)
• Claims: 65,000× wider dynamic range, 1.8× accuracy
• IEEE 754-2019 compliance
• Coq-verified float arithmetic
• Sources: crates/trios-golden-float/docs/whitepaper.md, Rashid Coq universal numbers

Ch.24 — Golden Logic (Ternary K3)

• Trit {-1, 0, +1} ≅ Kleene {F, U, T}
• Three as logical primitive (Trinity cuts deeper than binary)
• Łukasiewicz three-valued logic 1920
• Intuitionistic logic Heyting, Curry-Howard isomorphism
• Martin-Löf type theory, Lean prover
• Voevodsky HoTT (univalence axiom)
• Source: trinity-clara/specs/ar/, crates/trios-sacred/src/sacred/CHARTER.md

Ch.25 — Golden Sprout (IGLA-GF16 Empirical)

• Pre-registered protocol (H0, H1, N, seed, compute budget — all fixed before run)
• H0: BPB(φ-init) ≥ BPB(Xavier)
• H1: BPB(φ-init) < BPB(Xavier)
• IGLA architecture: 7 layers, 15.5MB, φ-scaled dimensions
• Theorem 5 (Empirical Validation): BPB(IGLA-GF16) < BPB(baseline_16MB) on FineWeb
• φ-init formula: all weights μ=0, σ=φ⁻²/√n
• φ-learning rate schedule: LR(t) = α_φ · φ^(-t/τ)
• Parameter Golf: 27+ experiments table (source: .parameter-golf/records/)
• Convergence curves: φ-init vs Xavier vs Random
• BPB benchmark tables
• Red Team results: 100% robustness on 50 adversarial cases
• Statistical significance tests
• Sources: trinity-clara/evidence/CLARA-RED-TEAM.md, phi_init.t27, benchmarks/

Ch.32 — Golden Telescope (Falsification Tests 2026–2030)

• JUNO 2026–2027: sin²θ₁₂ measurement → tests φ-PMNS prediction
• Lattice QCD 2028: α_s high-precision → tests α_φ = 0.118034
• DUNE, Hyper-Kamiokande: CP phase δ_CP
• LISA 2035: gravitational waves → cosmological sector
• For each: exact prediction made by Trinity, measurement protocol, pass/fail criterion
• Hilbert 23 problems template: explicit falsifiable predictions
• Clay Millennium prizes analogy

Appendix C — Golden Benchmark

• IGLA full BPB tables (all 27+ parameter golf runs)
• VSA performance results
• Red Team adversarial 50-case table
• Statistical significance full output
• Source: trinity-clara/benchmarks/, .parameter-golf/records/

Appendix D — Golden Mirror

• Full tri math compare --pellis CLI output
• All Trinity vs Pellis formula comparisons
• Subset proof evidence

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✅ Acceptance criteria

• Ch.22 has formal Trinity ⊆ Pellis proof
• Ch.23 has 6:9 bit derivation with Theorem 2 connection
• Ch.25 pre-registered protocol section present
• Ch.25 has Theorem 5 with statistical significance
• Ch.32 has ≥4 explicit falsifiable predictions with pass/fail criteria
• App.C has full benchmark tables
• NO .sh files
• Branch: feat/phd-gf16-igla
• Commit: feat(phd): Lane E GF16+IGLA refs #30 closes #47

📊 Sync

Before starting, post in #30:
🔒 AGENT [name] CLAIMING: Lane E GF16+IGLA | Branch: feat/phd-gf16-igla | Status: IN PROGRESS

refs #30

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🌸 BRIDGE DIRECTIVE — Lane E: GF16 + IGLA + Benchmarks

From: #143 Bridge Directive (2026-04-25)
Critical dependency: IGLA RACE (Track A) feeds Ch.24 empirical data

Bridge Update — What changed

Lane E is now the gating lane for the entire PhD. Ch.24 (IGLA-GF16 evidence) is the ONLY chapter requiring running code as evidence. Without BPB < 1.50 on 3 seeds, Ch.24 stays theoretical.

Chapter ↔ Bridge Links

Chapter	Key content	Bridge to
Ch.22 Golden Bridge	Trinity ⊂ Pellis proof + counterexample	NEW: add embedding lemma subsection
Ch.23 GF16 Format	GoldenFloat 1:6:9 specification	INV-3 gf16_safe_domain.v
Ch.24 IGLA-GF16	EMPIRICAL: BPB results, trial table, TikZ plot	Track A data from #143
Ch.25 Benchmarks	Performance comparison, convergence	IGLA RACE metrics
Ch.32 Conclusion	Integration of all results	all tracks
App.C	DARPA CLARA evidence (49× efficiency, Red Team)	trinity-clara repo
App.D	Pellis comparison tables	tri math compare --pellis output

Ch.24 Specific Requirements (Track A data)

• docs/phd/data/igla_trials.csv — exported from IGLA RACE (pure Rust)
• docs/phd/figures/fig-24-igla-bpb.tex — TikZ: BPB vs trial, 3-seed median ± IQR
• Falsification appendix: champion lr=0.004, threshold=3.5 NOT pruned
• Honest «Limitations» subsection: INV-3 e2e and INV-1 alpha_phi remain Admitted
• \admittedbox{} for each incomplete proof
• «Falsifiable predictions» subsection

Ch.22 Addition

• «Pellis ⊃ Trinity proof» subsection with formal embedding lemma
• Counterexample: Pellis polynomial with no Trinity preimage

App.C — DARPA CLARA

• Extract from trinity-clara: 100% Red Team success, 49× energy efficiency
• Format as industrial validation appendix

Merge dependency

Wait for Track C (pipeline macros) before writing chapters.

cc #143 #30 #109 #62

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Lane content exists in corresponding flos_XX.tex chapter and appendix files. Chapters expanded in commits 3a99bb9..988a80c.