The BSD Conjecture as a Positivity Normal-Form Theorem

We reformulate the Birch and Swinnerton-Dyer conjecture as a positivity normal-form characterisation. Four axioms (finite capacity, height positivity, controlled Iwasawa growth, Euler-system coherence) identify BSD as the expected canonical product form once explicit bridge hypotheses are supplied. For rank ≤ 1, this is a normal-form reading of the Gross–Zagier/Kolyvagin theorem package. For rank ≥ 2, Height Saturation is conditional: it names the missing higher Gross–Zagier height/cycle coupling and higher-rank Selmer/Kolyvagin/Sha control, but does not prove them. Note: This is an advanced draft. Major revisions are not excluded. CHANGELOG Changes in Version 1.1 (March 2026) No substantive changes.…