We introduce a Selmer-ratio ledger for prime-degree isogeny edges of elliptic curves over Q. The ledger separates the Sha residual from a mechanism term B = sigma + kappa + mu, where sigma is the local Selmer-ratio contribution, kappa is the kernel normalization, and mu is the Mordell-Weil quotient correction, with cancellation residual Delta = S + B. We audit this mechanism in two stages: a text-level sign-convention audit against classical identities (Cassels 1965, Dokchitser-Dokchitser 2015, Silverman 2009), and an independent Sage-only local BSD ledger computed on an 80-edge stratified sample drawn from the Paper12 prime-isogeny catalogue of 23,494 edges. In this audit, sigma is recomputed independently from Cremona database Tamagawa products and real-period ratios. Of the 80 sampled edges, 54 admit a unique C5-assisted source-target lock, while 26 are orientation-degenerate and are certified by evaluating all best candidates. The independent residual satisfies Delta = 0 on all 80/80 certified edges. This paper does not claim a direct computation of the cohomological Selmer groups; rather, it provides a mechanism-level and independent local-BSD-ledger audit of the Selmer-ratio cancellation law.
Tao Rui (Sun,) studied this question.
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