Preregistration — Opening B2: The Pole-Free λ₂ Contrast in the Gauss Transfer Operator (A Scaling Theory of the Critical Line)
Year: 2026
Type: article
Abstract: Preregistration, locked before any computation. Opening B of the Scaling Theory program sought a Diophantine spectral fingerprint in Mayer's Gauss-map transfer operator L_s; its first observable (the gap ratio |λ₂|/λ₁) returned a resolved null and was pole-dominated at the boundary. This preregistration freezes the second — and final — observable: the relative φ-removal contrast on λ₂ itself, C₁(σ) = |λ₂^full(σ) − λ₂^{no-1}(σ)| / |λ₂^full(σ)|, against the matched no-2 control contrast, on the existing σ grid, using the validated zeta-exact apparatus unchanged (s = 1 gate: λ₂(1) vs Wirsing's constant). Prediction: C₁ attains its grid maximum at σ = 0.52, C₁(0.52) ≥ 2 × min C₁, and C₁(0.52) exceeds the control by more than 10× the K-refinement error. Kill criterion: any of those failing closes Opening B permanently as a two-observable null — no third observable, no rescue. Phenomenology only; no outcome is evidence for or against the Riemann Hypothesis. No B2 computation had been run at deposit.
Author: Davis, Abby
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7225652582
FWCI:
Cites:
Cited by:
Related to: