External Research Route Matrix

Uses a table to compare the strongest natural output, cumulativity, common bottlenecks, and Phase 1 verdicts of ten possible routes. Gross–Zagier–Kolyvagin is the baseline; p-adic zeta/Iwasawa, p-converse, and exact computational BSD are given a green light; Strong-BSD twist families are the top choice—external theorems from 2024 exist, algorithmic papers from 2026 exist, the LMFDB conductor≤500,000 domain is complete, and results can be replayed item by item; generalized Kato/higher GZ is a yellow light; Selmer arithmetic statistics is an auxiliary route; numerical BSD atlas serves only as a data layer (evidence/anomaly detection, not equal to proof); Neo.K's own old "lattice rank convergence" route is given a **red light**, with bottlenecks being hidden equality and discreteness discontinuity (detailed audit in the next batch of documents); Faithful certificate frontier is the control layer, providing global research control but not providing BSD theorems. For the high-rank line, this document argues that the correct question is not "prove rank 2 BSD," but first asking which higher Kato class must be nonzero, which Selmer rank equality is known, and which p-converse is available—outputting a dependency DAG, rather than a proof pretending to be closed. The document concludes with an MCDM preliminary assessment, emphasizing that this is a research routing evaluation, not a mathematical theorem.