PAPER 01
Spectral Zeta Foundation
Operator-theoretic framework for ζ(s). The γ₁ floor. Hilbert–Pólya approach formalised in Lean 4. The ground level that never goes dark.
FLOOR HOLDS
PAPER 02
Zero-Free Region Extension
Classical de la Vallée-Poussin extended. Zero density bounds formalised. GRH weapons compiled. Chain from ζ(s) to explicit region.
BUILDING
PAPER 03
Explicit Formula Cascade
ψ(x) ↔ zeros. Explicit formula formalised. Prime counting function bounds. The kill chain connecting spectral to primes.
IN PROGRESS
PAPER 04
Modular Forms Bridge
L-functions of modular forms. Langlands functoriality. Equidistribution. The deep modular connection — sorry chain in this layer.
OPEN SORRIES
PAPER 05
Spectral Gap Proof
Operator eigenvalue separation. Maass forms. The gap that bounds all zeros to the critical line. Key sorry chain in SpectralGap.lean.
ACTIVE WORK
PAPER 06
Hodge & Langlands Connections
Algebraic geometry stratum. Hodge conjecture adjacency. Grothendieck territory. Bridging domains for the full picture.
FRONTIER
PAPER 07
The Full Proof
Papers 1–6 composed. ζ(s)≠0 for Re(s)≠½ proved. The culmination of THE Programme. 98 sorry's stand between us and this.
AWAITING CLOSE