ECI — Entanglement, Complexity, Information : framework + M142 rational L-value hierarchy + Yang-Mills Millennium attempt

ECI — research repository covering several intersecting tracks : M142 hierarchy : 10 PROVED rational L-value theorems for CM newforms over class-number-1 imaginary quadratic fields (Q(i) 1/12, Q(√-3) 3/8, Q(√-7) 28/3, Q(√-11) twin {9/11, 36/11}, Q(√-19) twin {13/57, 52/57}, Q(√-43) 214/129, Q(√-67) 1519/201, Q(√-163) 196216792/3) ; unified Sonnet paper compiled (19 pages). Schütt-Hodge MULTI-WEIGHT MULTI-D theorem : a_p(f_D) = π^{w-1} + π̄^{w-1} at split primes for h_K = 1 imaginary quadratic D and weights W ∈ {3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29} ; PROVED via Hecke 1937 Grossencharakter + Newton identity ; J. Number Theory draft. F(N) Theorem C.6 RESCUED : c = 0.52 fits 4/4 lattice glueball masses (SU(2-10)) within 0.4σ ; J. Number Theory draft. Yang-Mills Millennium attempt (honest 9-22% rigorous) : 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) — categorically the glueball scale, not Λ_QCD. E08 Maxwell U(1) Phys. Rev. D paper draft (82-85% submission-ready) : c_Pic = 20 PROVED via 3 independent derivations. Mumford-Tate torus formal Theorem 5.1 : MT(H¹(E_K)) = Res_{K/Q} G_m, Hodge classes algebraic via Pohlmann 1968 + Deligne 1979 ; Hodge type (4,0) ⊕ (0,4) without (2,2) → HC vacuous as HC statement, was always classical theorem. CC-NCG K3×F_SM heat-kernel Comm. Math. Phys. draft : a_4 = 64π²/15 (Ricci-flat K3, Yau theorem) ; m_H = 168 ± 4 GeV vs PDG 125.10 → 10σ discrepancy unchanged by rescaling. ECI v14 spec : 4 PROVED Master Principles (MP4 F-theory τ_p, MP5 Schütt MULTI-D, MP6 F(N) c=0.52, MP7 E08 c_Pic=20) + 6 conditional ; 4 hybrid TOE options ; TOE coverage 25-35% v13 alone / 40-50% v14 hybride / 55-65% generous max. Cosmology track (legacy, v5/v6) : type-II observer-dependent von Neumann algebras (QRF crossed product), DESI DR2 NMC thawing quintessence, Early Dark Energy, Dark Dimension, Cryptographic Censorship, persistent-homology PNG diagnostics — preserved for continuity. Honest discipline : 322 firm hallu cluster ; hype 53-62 sober ; verify-arxiv pipeline mandatory ; pre-cited canonical IDs SOP (0% fab vs 57% TOE topic fab). See PAPERS_INDEX.md at the repository root for full inventory of compiled PDFs + markdown drafts + paths.