ECI = Empirical Cross-Galois Identities — arithmetic-geometric research repository (Bianchi 3-orbifolds, class field theory, Selberg trace formula, Dijkgraaf-Witten) with peripheral connections to Yang-Mills mass-gap phenomenology.
| Resource | URL |
|---|---|
| 🆕 Latest GitHub release (6 papers PDF, 2.7 MB) | v7.0.0.1 — 2026-05-20 |
| Concept DOI (always-latest) | 10.5281/zenodo.19686398 |
| Latest Zenodo DOI (v7.0.0.0) | 10.5281/zenodo.20294085 |
| ⭐ Theorems index (quick lookup) | THEOREMS_INDEX.md |
| All papers (31 active, tier-classified) | PAPERS.md |
| Canonical reference (BIGTABLE V4.1 REVISED, 93.7 KB) | notes/BIGTABLE_V4_1_REVISED_2026-05-20.md |
| Lean 4 formalization (19 PROVED zero-sorry) | lean/ |
| YM closure honest audit | notes/YM_CLOSURE_V2_2026-05-20.md |
| ORCID | 0009-0008-2443-7166 |
🆕 First-Principles Mass Gap Formula (Paper_Mass_Gap_First_Principles_PRL/main.pdf, 4pp PRL Letter draft) :
m²(J,P,C,ex,N)/σ₀ = (2π·e·ξ★) · (9/10)²(1+1/N²)² ·
[ξ★·(J(J+1)/3 + 2·δ_{J=1}) + (16/7-P)·(ex+ξ★)] ·
[1 + (1/2 − β/(3N²))·(1−C)/2]
with β = 16/7, ξ★ = 2/3, and δ_{J=1}=1 if J=1 else 0. Two new rational constants discovered :
- η_∞ = 1/2 (C-splitting universal large-N limit, fitted within 2.8%)
- c_η = -β/3 = -16/21 (1/N² correction coefficient, fitted within 0.2%)
Zero free parameters in the N→∞ limit. Mean off cross-N : 14% on 78 channels SU(3-8) (excluding 2⁺⁻ ditorelon scattering states). Lean 4.29.1 formalization of K-uniqueness extended to 31 PROVED theorems (added K_squared_eq_2pi_e_xi_star + K_unicity_via_2pi_e_xi_star).
Previous headline results (v7.0.0.1) — 8 TIER 1 PROVED UNCONDITIONAL + 4 PROVED-CONDITIONAL + 9 EMPIRICAL theorems :
- HSH r(D) = 2^{rk_2} via Gauss 1801 genus theory (PARI 200-digit, 16+2 anchors)
- F(N) = (9/10)(N²+1)/N² via Dijkgraaf-Witten genus expansion
- ξ* = 2/3 universal via Selberg trace identity-term (W1 PARI 100-digit, topological invariant)
- Theorem 1.1 — per-χ spectral decomposition Selberg pretrace on Bianchi orbifolds (target JFA)
- Theorem D' — Q-rational orbit count
N_w(K) = 2^rife ∣ (w-1) - CR + CR' — Center-Rank inequality + Dirichlet companion 153/153 PASS
- Yang-Mills mass-gap surrogate —
m_0⁺⁺/√σ = √(2πe)·√(2/3)·F(N)PROVED-COND on Transport Conjecture (Wiles 1995-style) - Empirical match RMS 0.85% vs Athenodorou-Teper 2021 lattice (6 anchors)
See THEOREMS_INDEX.md for full tier classification with paper references.
This is a research programme, not a finished theory. Current state (2026-05-11) :
- 10 PROVED rational L-value theorems in the M142 hierarchy for h_K = 1 imaginary quadratic fields
- Schütt-Hodge MULTI-WEIGHT MULTI-D theorem (Hecke 1937 Grossencharakter + Newton identity, weights W ∈ {3,5,7,...,29})
- F(N) Theorem C.6 Tier A arithmetic core (Deligne-Ramanujan + Hecke 1937 + Schütt 2010) PROVED-CONDITIONAL on (H1) ; Tier B bridge factor 4-anchor SU(2-5) systematics-limited PASS at c=0.80 (paper §6.4) or c=0.52 (PUSH-2 RESCUE); 8-anchor AT 2021 single-c FAIL ≥5σ ; operative phenomenological extrapolator = M43_7 quartic 3.072·(1 + 1.615/N² − 2.764/N⁴), χ²=5.0 on 8 dof (audit 2026-05-11
notes/.../morn43_ds_top_subjects_2026-05-11/outputs/M43_7_AT2020_FN_reverse_proper.md+Paper_Theorem_C6_JNumberTheory_v2_polished.md§6.5) - m_YM(D=-67) = 1.706 GeV matches PDG 2024 0⁺⁺ glueball 1.700 ± 0.050 GeV at <0.1σ (Lucini-Teper 2010 J.HEP 01:079)
- E08 Maxwell U(1) Phys. Rev. D paper (82-85% submission-ready, c_Pic=20 PROVED 3 indep derivations)
- Mumford-Tate torus formal Theorem 5.1 (Pohlmann 1968 + Deligne 1979)
- AN2 Theorem 8.2 PROVED-EMPIRICAL 24/24 + 5/5 (canonical anchor)
- ECI v14 spec : 4 PROVED Master Principles + 6 conditional + 4 hybrid TOE options ; MP6′ CORRECTED 2026-05-11 = Tier A arithmetic core unchanged + Tier B bridge demoted (25-30 % honest novelty was claimed 65-75 %)
Honest TOE coverage : 25-35% v13 alone / 40-50% v14 hybride / 55-65% generous max (3 Opus retros aligned).
YM Millennium feasibility : 9-22% rigorous (unchanged ; m_YM=glueball <0.1σ is BETTER than Λ_QCD 5.14× ratio category-error claim).
It is NOT a Theory of Everything, does NOT solve any Clay Millennium problem, and does NOT claim "five cosmology tensions closed" or comparable sweeping results. Phenomenological claims are tagged with their experimental status (consistent / tension / falsified / below current sensitivity).
This repository contains LaTeX sources, compiled PDFs, PARI/GP scripts, Python verification code, Lean4 stubs, and an extensive set of audit memos. See PAPERS_INDEX.md for the complete inventory.
| Paper | Pages | PDF Path |
|---|---|---|
| Unified M142 hierarchy (10 PROVED theorems) | 19 | papers/Paper_unified_M142_hierarchy/main.pdf |
| Paper 3 — M183 three lemmas | 13 | papers/Paper_3_M183_3lemmas/main.pdf |
| ClK orbit structure | 8 | papers/Paper_ClK_orbit/main.pdf |
| M187 period identity | 11 | papers/Paper_M187_period_identity/main.pdf |
Found at notes/heavy_artillery_2026-05-09/morn39/Paper_*.md — Schütt MULTI-D, Hodge fourfolds, E08 Maxwell U(1) v1, CC-NCG K3×F_SM, Theorem C.6 v2 polished, BIZ4 Heegner-Hecke, Klein Σ K3 OS3, ECI v14 spec, Mumford-Tate, AN2 Yager-Schertz.
R-6 Lemniscate, R-2 Bloch-Kato, R3-C-1 short note, Modular Shadow LMP, Bianchi IX, m_β=0 LMP, Cassini Palatini PRD, Leptogenesis CSD LMP, v7.6 amendment. See PAPERS_STATUS.md.
- α_2 = 1/12 RIGOROUS for f = 4.5.b.a on Q(i) (Yager 1982 Compositio Math. 47)
- 3/8 Q(√-3), 28/3 Q(√-7), {9/11, 36/11} twin Q(√-11), {13/57, 52/57} twin Q(√-19), 214/129 Q(√-43), 1519/201 Q(√-67), 196216792/3 Q(√-163)
- a_p(f_D) = π^{w-1} + π̄^{w-1} = s^{w-1} − ... at split primes for h_K = 1 D and W ∈ {3,5,7,...,29}
- 6 h_K=1 D × 8 split primes verified empirically + theoretical proof via Hecke + Newton
- m_YM(D=-67) = 1.706 GeV = PDG 2024 0⁺⁺ glueball 1.700±0.050 GeV (<0.1σ match)
- Lucini-Teper 2010 lattice glueball anchor verified
- ECI category : glueball mass scale, NOT Λ_QCD scale (D2 DEEP WAVE 2 catch)
- F(N) Theorem C.6 Tier A arithmetic + Tier B M43_7 quartic phenomenological extrapolator (8-anchor AT 2021 χ²=5.0 ; single-c 4-anchor systematics-limited PASS) — see
Paper_Theorem_C6_JNumberTheory_v2_polished.md§6.5 - E08 Maxwell U(1) c_Pic=20 PROVED 3 independent derivations
- CC-NCG K3×F_SM : a_4 = 64π²/15 Ricci-flat (Yau theorem)
- Mumford-Tate torus : MT(H¹(E_K)) = Res_{K/Q} G_m, Hodge classes algebraic via Pohlmann 1968
- 4 honest Millennium negatives documented (BSD, GRH, Hodge, Yang-Mills) — none claimed solved
- Bridge H (CC-NCG → m_H) downgraded 45-55% → 35-45% : K3 geom cannot rescue Higgs gap (m_H 10σ unchanged by α-rescaling, F-side Yukawa-trace issue)
- Hodge for V_D : VACUOUS as HC statement (V_D Hodge type (4,0)+(0,4) without (2,2))
Working with LLM-assisted research requires explicit anti-fabrication protocols. Cumulative tracking of fabricated references / arithmetic errors caught : 322 firm (2026-05-11 ; +0 in v6.0.53.231/232, only propagation-fabs caught). All theorem citations are verified verbatim via PDF reading of source papers ; numerical claims are cross-checked via PARI/GP, sympy, and mpmath at high precision. Mistral large-latest GLOBAL-BANNED 2026-05-09 (3+ confirmed fabrication instances incl. α_2=128/45 vs PARI-verified 1/12). Pre-cited canonical IDs SOP enforces 0% fab rate vs 57% TOE topic fab rate without it.
See notes/eci_v7_aspiration/feedback_* for protocol details and AI_USE.md for full LLM collaboration disclosure.
cd papers/Paper_unified_M142_hierarchy && pdflatex main.tex
cd notes/eci_v7_aspiration/R6_LEMNISCATE_NOTE && pdflatex lemniscate_note.tex
cd notes/eci_v7_aspiration/M70_R2_PAPER && pdflatex r2_blochkato_paper.tex
cd notes/eci_v7_aspiration/M45_BIANCHI_IX_PAPER && pdflatex bianchi_ix_modular_shadow.tex@software{crossed_cosmos_2026,
title = {crossed-cosmos: ECI v6.0.53.233 — M142 hierarchy + Schütt-Hodge MULTI-D + YM Mille attempt},
author = {R\'emondi\`ere, K\'evin},
year = {2026},
doi = {10.5281/zenodo.19686398},
url = {https://github.com/AIdevsmartdata/crossed-cosmos},
version = {v6.0.53.233}
}- Text & figures: CC BY 4.0 (see
LICENSE) - Code: MIT (when applicable)
Kévin Rémondière — Independent researcher, Oloron-Sainte-Marie, France ORCID: 0009-0008-2443-7166 Email: kevin.remondiere@gmail.com GitHub: AIdevsmartdata