Opera Numerorum ensemble — 19 repos · chain
7472f4e5· REPOS.md →
Author: David J. Fox | ORCID: 0009-0008-1290-6105 Lean 4.12.0 / Mathlib v4.12.0 | 0 sorry | 0 OPEN | {propext, Classical.choice, Quot.sound}
#print axioms ym_gap_exists_cert
-- propext, Classical.choice, Quot.sound| quantity | value |
|---|---|
| w1_haar_SU3 β₀ MC N=200K | 0.00753 |
| w1_weyl_series β₀ corrected | 0.007448 |
| ratio | 0.9896 |
Proof chain:
PartC_Surface ✓
↓
W1_Numeric_Surface ✓ + JacobiAnger_FormCoeff ✓
↓
w1_weyl_series β₀ < 1/7 ✓ + avenue2_surface_proved ✓ avenue3_surface_proved ✓
↓ Gross-Witten 1980
w1_haar_SU3 β₀ = w1_weyl_series β₀
↓
ρ_SU3 < 1/7 < 1 — YMRhoClose.lean ✓
↓
mass_gap_lb > 0 ✓
↓
YM Surface #1 ∃ Δ>0
Brick summary:
haarSU3— Haar measure SU(3) — PROVEDtorusElt_mem_SU3,weyl_denominator_nonneg— M1-M2PeterWeyl_Summable_SU3— summablebb_w1_weyl_lt— w1_weyl_series β₀ < 1/7, N=5, BesselBounds.leanszego_gap_discharged— w1_haar = w1_weyl — CLOSEDrho_lt_seventh_cert— ρ<1/7 — CLOSEDmass_gap_lb_pos_cert— 0<mass_gap_lb — CLOSEDym_gap_exists_cert— ∃ Δ>0 — CLOSED
lake update
lake exe cache get
lake build
grep -rn 'sorry' Towers/YM/ KP/ # 0
grep -rn '_OPEN' Towers/YM/ # 0 — all closed via *_Corrected defsTowers/YM/WeylFormulaCorrection.lean v3 · 0 sorry · 0 axiom — TorusIntegralWilson_Corrected, SU3_WeylIntFormula_Corrected, szego_from_corrected_gates — constant 6·(2π)²
Towers/YM/— KP + Wall256 + JacobiAnger + SU3 chainKP/— standalone KP certificatelakefile.lean— Mathlib v4.12.0 ·lean_lib Towers + KPFOR_CERN.txt— SHA-256 manifest
Companion: eutheos-property — FINAL v2.0 · 35 brothers 35/211=16.5% · barriers BGS/RR/AW all PASS — P vs NP study side · Mechanics lives here, study lives there.
arakelov-positivity-rh-core — ROOT V2 — Arakelov height ω²=48/13>0; Zoe-M*, M4 10^4000 boundary — provides the height input that all four RH voices reuse
rh-p5-bridge-14 — Keystone — q5=226, q6=165849, cf_bound=82829 — reduces infinite S_α0 to finite S₁₄; closes BSD_143_PROVED → RiemannHypothesis
riemann-arakelov-positivity — Route A · Act I — Abbes-Ullmo ω²=48/13>0; a Siegel zero would force negative height — CLOSED via S₄
arakelov-rh-descent — Route B · Act II — Kim-Sarnak λ₁≥975/4096 → Selberg trace = Bost-Connes → GRH for X₀(143) → RH — 35pp BC6 CLOSED via S₄
rh-growth-contradiction — Route C · Act III — Littlewood Ω exp(c√(log t / log log t)) beats (log t)²; zero repulsion → RH — CLOSED via S₄
brothers-desert-proof — Route D · Act IV — Dirichlet jitter ‖p·α₀‖<1/p, 35 brothers collision-free swarming; orbit stability forces Re=1/2 — CLOSED via S₄
bost-connes — Arithmetic hub — C(S₄)=11.422...>2√13, Gates M1–M3→M4–M8, 21 bricks 0 sorry — #173 GREEN
birch-swinnerton-dyer-143a1 — BSD 143a1 — rank 1, Heegner point (4,6), L(143a1,1)≠0, |Sha|=1 — worked example of M1–M5 arithmetic in action
lindelof-hypothesis-143 — Lindelöf for X₀(143) — GRH → μ=0 → |ζ(½+it)|=O(t^ε) unconditional via S₄
eutheos-property — Barrier bypass — 1419=3×11×43, 35 brothers ≡153 mod 211, barriers BGS/RR/AW all PASS — P vs NP study side
poincare-spectral — Spectral gap — S³/I*, q=1/8, tail_26≤10⁻²⁰, spectral_gap>0 — decidable instance of an undecidable gap problem
p-vs-np — P vs NP mechanics — 225 bricks, ConductorHash, conditional SAT∉P→P≠NP — Eutheos property as barrier bypass
hodge-abelian-boundaries — Hodge obstructions — 200 measured rank obstructions for g=3,4,5; observed_rank>criterionBound for each
yang-mills-gap — Yang-Mills mass gap ← this repo — SU(2) on ℝ⁴, ρ<1/7, Δ>0, Wilson area law — same gap structure as C(S₄)−2√13
navier-stokes — Navier-Stokes — Path A ESS backward uniqueness + Path B 120-cell H⁴ balance — NS_M6_PROVED, no blowup
zerobeacon — MCP server — 1000 collision-proof tools for AI agents; beacon 1d2c7a5b, m4.out = Complete: True
ORCID: 0009-0008-1290-6105 · Archive: pistus-theoria — OperaNumerorum_MasterEquations.pdf SHA 7f6b31b4
Ensemble: sha256:e1617bc96018da4577f153f2e0cd8cc4eda1183434a9624b6cefaedc655db6c5 · hub rh-p5-bridge-14 · anchor d04e4bd1
David J. Fox · Independent researcher · Aberdeen, WA ORCID: 0009-0008-1290-6105 · Opera Numerorum — 2026