Phase 1 Closure and Phase 2 Interface

The formal capstone document for the entire Phase 1 series. It lists eight completed tasks: Theorem 2.18 predicate map, independent reproduction of Algorithm 2, paper/current-code soundness audit, <150 version regression, first-failure closure of the 13 removed curves, 500K exact artifact census, closure of the removal reasons for Algorithm 1's 4,062 curves, and Algorithm 2 semantic replay of OLD→CURRENT in the stable domain — and formally declares in a box: Banwait–Huang Reproduction = COMPLETE. The document also honestly delineates the boundary of what is "no longer worth attacking": twist reconstruction of the 1,355 OLD-only historical curves can be done, but they are no longer in the CURRENT Algorithm 1 accepted universe. Unless the research goal shifts to a repository history paper, a proof-engineering case study, or a complete historical reproducibility archive, the marginal benefit for BSD itself is low. Finally, it proposes three concrete routes for Phase 2, rather than vague "future work": Route A "High-rank wall atlas," starting from rank $\ge2$ curves to build rigorous analytic rank, Mordell–Weil rank upper/lower bounds, Selmer, $\Sha$ finiteness/$p$-parts, and leading coefficient component by component; Route B "strong-BSD coverage expansion," asking whether known theorems from 2024–2026 can be used to further expand the eligible family of Banwait–Huang Algorithm 1 rather than just reproducing the original algorithm, with the document specifically noting that this is where new external mathematical results might begin to emerge; Route C "2-primary unresolved frontier," where the current program conservatively rejects positive analytic $v_2(\Sha)$, and one could study which rejections are merely due to insufficient computation/certificates, and whether existing theorems or Magma/Sage exact descent can expand the certified set — the document calls this the most natural new mathematical interface left by Phase 1.