01.zeta

frontier mathematics · 13 days

A candidate strengthening of the Montgomery–Taylor constant, the unconditional share of the zeros of ζ in a dyadic window that lie on the critical line: 0.6725007036 to 0.6725106958. One step of the chain is still open, so it is a candidate and not a theorem, and the gain is a statement about the limit rather than about any height that can be computed.

four theorems, verified by the Lean 4 kernel against Mathlib. zero sorries, standard axioms only

1. The census floor of the genuine Montgomery–Taylor kernel, c_u ≥ 5.021172019×10⁻⁶, by rational weak duality. FloorCert
2. The retention certificate's cover closes at its four depths, and cannot be vacuous. BandCert
3. The composition inequality behind the chain, which settles that the retention enters multiplicatively: exact arithmetic rather than analogy. t3_composition_skeleton
4. The grid-incidence law Σ φ̂(x−n)φ̂(y−n) = 2π·FT(φ²)(x−y) for even bounded measurable φ, shipped with a counterexample showing evenness is necessary. law_d_incidence

state of record → source →

Fulcrum directed the pursuit.