# Elliptic-curve BSD evidence ledger

Family 002: The full BSD formula from low Selmer corank. First application triage, 9 October 2026 Australia/Brisbane.

## Problem and potential new use

Number-theory researchers can connect a proven low Selmer-corank condition to the stated full leading-term formula.

## Applicability and commercial boundary

The low-corank condition and Tate–Shafarevich information are not automatically cheap to compute. This gives no blanket cryptographic security or fast point-counting improvement.

## Initial business decision

Research infrastructure or conditional engineering until a computable implementation, effective bounds and a recurring buyer need are demonstrated. No commercial novelty or profitability is established.

## Next verification action

Inspect computability of the inputs and compare a known exact curve calculation.

## Evidence scope

The catalog statement was individually reviewed. Manuscript proof and selected formal scope comparison remain queued. No independent Lean verification was run. Source revision `fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb`. See [source metadata](source.json).

[Exact Birch–Swinnerton-Dyer Formula from Low Selmer Corank](https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Exact-Birch-Swinnerton-Dyer-Formula-from-Low-Selmer-Corank-October-7-2026/exact-bsd-low-selmer-corank.pdf).