What question did this study set out to answer?

To explore the Lie-algebraic invariant and associated spectral gap within the context of quantum field theory.

May 27, 20260 citationsOpen Access

Crossed Cosmos / ECI v7.2.0 — Faddeev-Popov gap + 166-obs mega-regression + Lean YM 0-sorry + gravity κ-triptyque

KRKévin RémondièreVolga State University of Technology

Key Points

To explore the Lie-algebraic invariant and associated spectral gap within the context of quantum field theory.
Implemented Faddeev-Popov conditional spectral gap in Lean 4 with no errors.
Conducted Bonferroni-controlled symbolic regression on 166 observables yielding significant Z-scores.
Performed PySR runs for various phenomenological analyses including lifetimes and CP asymmetries.
Faddeev-Popov conditional spectral gap established with λ_min ≥ m₀²(1-κ).
Significant Z = +14.65σ observed in symbolic regression across 166 PDG/FLAG observables.
Structural finding on black hole entropy coefficient confirmed as κ(SU(2))² = 1/4.

Abstract

Crossed Cosmos research repository organised around the Lie-algebraic invariant κ = 1/ (2|Φ⁺ (G) |), with κ (SU (3) ) = 1/6 as the central structural constant. Version 7. 2. 0 (2026-05-25) adds: (i) the Faddeev-Popov conditional spectral gap (KR-FP-3) — λₘin ≥ m₀² (1-κ) on the closed fundamental modular domain, conditional on three named hypotheses (H1+H2+H3), formalised in Lean 4 with zero sorrys; (ii) a Bonferroni-controlled symbolic regression on 166 PDG/FLAG observables, Z = +14. 65σ; (iii) phenomenology PySR runs (lifetimes Z = +4. 57σ, BBN+nuclear Z = +8. 29σ, CP asymmetries Z = +4. 99σ including βCKM ≃ π/8) ; (iv) QNM-dedicated PySR with the structural finding SBH/ (π·rS²) = 1/4 = κ (SU (2) ) ² EXACT (Bekenstein-Hawking entropy coefficient = κ²) ; (v) Lean YM core 15 files, 9 282 lines, 0 sorry + new FaddeevPopovGap module. Methodology: SOTA-2026 LLM-assisted research workflow (see AIUSE. md for COPE-compliant disclosure). Anti-fab discipline: cluster firm 731 STABLE, 12/12 arXiv IDs verified, gitleaks clean. Honest scope: research programme, NOT a Theory of Everything. The Bauerschmidt-Bodineau-Dagallier cluster expansion remains the principal open obstruction to the Clay mass gap.

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