One Property, Two Readings — A Pre-Registered Attempt to Separate BSD and Riemann
Year: 2026
Type: preprint
Abstract: A claim-and-evidence record. Conjecture: for an elliptic curve E over the rationals, the Riemann hypothesis for L(E,s) and the Birch and Swinnerton-Dyer leading-coefficient identity are two readings of a single property of L(E,s) — synchronization at its symmetry center, in the family of Weil's and Li's positivity criteria. The record reports a pre-registered failure hunt across a 17-curve panel (ranks 0–5): the BSD quotient equals 1 by two independent L-value routes at 50-digit precision on every curve; 535 zeros recorded on the critical line; Schoenfeld-envelope test extended to 10^9; all 85 Li-family lambda coefficients positive. No separation was found, and no proof is claimed. The deposit includes the verification scripts that recompute every stated number from public inputs (LMFDB data, PARI/GP). Other working code — test construction and exploratory apparatus — is held pending independent verification and will be released after it; none of it is needed to check any number in the record. Correspondence: [email protected]
Authors: Carroll, Joseph, Willow, Pip
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7225596118