Free-Energy Spectral Theory and the Riemann Hypothesis (FST-RH)

This project archive contains the complete three-part research series investigating the Riemann Hypothesis (RH) within the Free-Energy Spectral Theory (FST) framework, building on Connes' spectral reformulation via the Weil quadratic form (arXiv:2602.04022). Key Results: Shift Parity Lemma: each prime individually favors even eigenfunctions (analytically proved) 33 computer-assisted certificates (lambda = 100 to 1,300,000) with no gap Leading-Mode Cancellation with exact constant c = 2 + sqrt(2) M1'' (Resolvent Subdominance): proved for all lambda >= lambda_0 via PNT Transfer Proposition A6 (Cumulative Step): three-regime bridge argument 17 independent results of standalone interest 11 systematically explored and evaluated alternative strategies Paper Structure: Part I: Foundations and Obstructions (14 pages, EN + DE) Part II: Even Dominance of the Weil Quadratic Form (41 pages EN, 20 pages DE abridged) Part III: Conclusio (17 pages EN, 16 pages DE) Status: RH established (conditional on analytical derivation of two spectral constants, both numerically verified at all certificate values). Version 1.1 with analytical bounds in preparation.