Algorithm 2 Twist Semantic Diff

Following up on the findings of document 14: in the same commit, Algorithm 2 tightened $\gcd(M,N)=1\to\gcd(M,3N)=1$ (when $3\nmid N$, any old candidate with $3\mid M$ is rejected by the new gate), while simultaneously removing the old version's additionally required twist-side discriminant-valuation ramification-style condition—thus candidates exist that were rejected by this gate in the old version but are no longer rejected in the new version. This document honestly points out a fixture blind spot: for the 12 existing surviving base curves, the old/current versions of twists_of_ec_labels_150.json are an exact match, meaning this fixture can only verify that "current results haven't changed", but cannot verify that the two new semantic branches were actually exercised. The solution is to add two synthetic semantic cases: Case A takes $N=46,\,M=3$, so $\gcd(3,46)=1$ but $\gcd(3,138)=3$, which directly distinguishes the old/new coprimality gate; Case B uses an abstract setup $p=3,\,q\in\{2,5\}$ and $v_2(\Delta)=3,\,v_5(\Delta)=6$, where the old disc_valuation_condition would reject at $p=3$ because it couldn't find a witness with a valuation that isn't a multiple of 3, whereas the current program no longer has this gate. Finally, the document explicitly sets a self-limitation: this is merely a predicate-level regression fixture and does not claim to correspond to an actual theorem-eligible twist.