Submission / Publication Gate

The final concluding document of the Phase 2 main line (docs 00-28, 29 pieces). Before formally writing the theorem paper, it lists five items that still need to be passed: independent expert referees reproducing all source mapping; checking the latest versions and publication status of the two key papers, BSTW and Fouquet–Wan; doing a real MathSciNet/zbMATH/Scholar novelty sweep; producing a machine-verifiable arithmetic certificate for 696.e1; and rewriting the proofs to not rely on LMFDB prose descriptions wherever precise sources or computations are available. The most valuable part of the document is the "suggested paper framing": it explicitly demonstrates not to start with claims like "We prove a fundamentally new BSD theorem"; a safer phrasing is "We isolate and verify an explicit non-semistable quadratic-twist family obtained by combining recent 2-primary twist results with ordinary/multiplicative Iwasawa results and the arbitrary-reduction theorem of Fouquet–Wan"—precisely positioning the result as "isolating an explicit family by combining existing results" rather than exaggerating it into a brand new theorem. The document even prepares a fallback: if the novelty search ultimately proves this result is already covered by some general theorem, the article can still pivot its framework and remain valuable—becoming an explicit corollary, a theorem-applicability note, a proof-engineering/algorithmic extension, or a non-semistable extended version of the Banwait–Huang certificate router.