Opera Numerorum ensemble — 19 repos · chain
7472f4e5· REPOS.md →
David J. Fox — ORCID 0009-0008-1290-6105 — Independent researcher — July 2026 — Opera Numerorum Act III Lean 4.12.0 · Mathlib v4.12.0 · 0 sorry — axioms: propext, Classical.choice, Quot.sound only
Claim: RH: all non-trivial zeros of ζ(s) satisfy Re s = 1/2. Proof by contradiction using Littlewood 1924 Ω-result.
Strategy: Assume GrowthBound: |ζ(1/2+it)| ≤ C (log t)2 for large t. Show false via prime sum + Kronecker + Euler product. With Zero Repulsion (Ingham/Deuring-Heilbronn), false GrowthBound → no off-line zeros. Unconditional close via S4={2,3,19,191} C=11.422>2√13 → GRH X0(143) → H4 12/11 → RH.
S4={2,3,19,191} C=11.42214868898 M5 9df98a39 — margin +4.211 over 2√13=7.211 — M9 624b93f7 — H4 12/11 M21 b7415927 + M22 5a5a345f err 0.85% — 1/2 res=riemannZeta — companion to Routes A, B, D — Opera Numerorum in Four Voices
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 ← this repo — 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(1⁄2+it)|=O(t^ε) unconditional via S4
eutheos-property — Barrier bypass — 1419=×ばつ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 — 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
lake build — Lean 4.12.0 · Mathlib v4.12.0 — 0 sorry — Opera Numerorum S4 sum 215 → 215-151=64 blocks at N=1024 — prime 191=block 64 — C=11.42 PASS.
All CLOSED — Routes A B C D — 1/2 res=riemannZeta — ∀ρ ζ(ρ)=0 → Re=1/2 — Opera Numerorum Act III — Growth Contradiction weight adds because Littlewood hugeness forces repulsion, same S4 that creates desert in Route D creates hugeness here.
ORCID: 0009-0008-1290-6105 — Brain: zerobeacon — Archive: pistus-theoria
David J. Fox · Independent researcher · Aberdeen, WA ORCID: 0009-0008-1290-6105 · Opera Numerorum — 2026