ECI (Entanglement, Complexity, Information) — research repository at the intersection of arithmetic CM modular forms, rational L-value hierarchies, Hodge & Mumford-Tate theory, Yang-Mills mass-gap, F-theory τ_p prediction, and Connes-Chamseddine non-commutative geometry.
Version: v6.0.53.233 (2026-05-11) Latest Zenodo DOI: 10.5281/zenodo.20115008 (v6.0.53.231 ; v6.0.53.233 webhook pending) Concept DOI (always-latest): 10.5281/zenodo.19686398
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 RESCUED with c=0.52 (4/4 SU(N) glueball lattice masses within 0.4σ)
- 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
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 c=0.52 (4/4 SU(N) glueball lattice within 0.4σ)
- 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 = {Remondière, Kevin},
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 Remondière — Independent researcher, Tarbes, France ORCID: 0009-0008-2443-7166 Email: kevin.remondiere@gmail.com GitHub: AIdevsmartdata