Algorithm 1's Execution Environment and Missing Items

Fully re-running Algorithm 1 requires SageMath, a local LMFDB PostgreSQL database, the lmfdb Python package, pandas/numpy, PARI 2-descent, mwrank, Sage native 2-isogeny descent, as well as sufficient memory and local data — the current environment does not possess these conditions. The document directly lists the items "not done" in this round: no connection to a local LMFDB PostgreSQL, no execution of Sage, no execution of 2-descent, no re-scanning of conductor<500000, and no independent proof of the official 36,687 curve count. Therefore, it explicitly states that "Full Algorithm 1 independently reproduced" cannot be written. Instead, what was completed in this round are six alternative tasks: item-by-item deconstruction of theorem conditions, reading the current official implementation, auditing certificate strength, obtaining official small-sample fixtures, independent reproduction of Algorithm 2, and establishing the Sage execution plan for the next round. The document provides the minimum environment test plan for Phase 1 v0.2: first run Algorithm1.py on conductor<150, expecting an output of 12 base curves, then run Algorithm2.py with this batch of curves, and compare whether the curve labels, source branches, twists, file SHAs, and pass/fail metadata are completely identical to the official ones — only after this small sample matches perfectly is it permitted to enter the 500K full-scale rerun.