Phase 1 Next Lowest-Cost Gate

The wrap-up document for the v0.4 series, converging the 500K-scale observations accumulated in documents 18-20 into a three-stage minimum-cost execution strategy. Gate A is a delta-only base verifier: inputting the old accepted list plus two cheap fields, a3/isogeny_degrees, with the goal of precisely reproducing $40{,}749\to36{,}687$. Gate B is a twist JSON parser diff: directly materializing the old/current twists_of_ec_labels_500k.json files, calculating removed base keys, stable base keys, stable curves with twist changes, twists removed solely due to $\gcd(\cdot,3N)$, twists added solely due to the deletion of the old disc gate, and curves affected by both effects simultaneously, totaling six categories. Gate C is to rerun all the expensive Sage descents only when both A and B are completely identical to the current output of the official repository. The document encapsulates the rationale for the entire strategy into a directly quotable maxim: the full Algorithm 1 official paper runtime itself is about ten minutes, which is not actually expensive; what is truly expensive is the rework caused by semantic errors — a delta-first strategy can first confirm "we are understanding the same theorem version" before investing in full proof-engineering, rather than the other way around.