← Phase 1 / 23 · Fresh Algorithm2 Semantic Replay
Pushing the timeline one step further back, we trace to three semantic nodes: generator commit 7286794 ($G$), OLD commit 1a0489 ($O$), and CURRENT commit 31fae2 ($C$). $G\to O$ added the disc-valuation condition $D(E,d)$; $O\to C$ removed $D(E,d)$ and tightened $\gcd(d,N)=1$ to $\gcd(d,3N)=1$. Because the generator archived twist JSON is itself the output of generator Algorithm 2 on real curves, we only need to apply $D(E,d)$ to it to precisely reconstruct OLD, without recomputing unchanged gates like $a_p$, 2-division fields, or Kronecker conditions. Applying $D$ pair-by-pair to all $39{,}394$ generator curves and $293{,}482$ twist pairs yielded $0$ failures, proving that $T_O(E)=T_G(E)$ holds in this data domain. For the $36{,}687$ stable curves, an exact $2\times2$ gate contingency table was built: $D{=}1,G_3{=}1$ has $247{,}391$ pairs (common), $D{=}1,G_3{=}0$ has $21{,}306$ pairs (removed by the new gcd gate), and both $D{=}0,G_3{=}1$ and $D{=}0,G_3{=}0$ are $0$ — curve-by-curve mismatch is $0$. **This is the most critical correction in the entire document**: previously, documents 07/09/13 inferred from the source diff that Algorithm 2 might simultaneously have both tightening and relaxing directions. Now, exact replay with real data proves that the expand mechanism was never triggered in this actual data domain. The CURRENT semantic update is purely a monotonic reduction in the stable domain, and all observed deltas fall in the Zha16 branch (the CLZ20 branch's twist primes inherently exclude $p=3$, so its delta is always zero). The document honestly delineates the boundaries of knowledge: there are still 1,355 OLD-only curves that cannot be covered by this replay because they were added to the OLD base file after the generator twist JSON was generated. However, these curves have all been excluded by CURRENT's Algorithm 1 isogeny gate, so for the "current theorem-qualified universe," the replay is closed; completing those 1,355 only holds value for historical reconstruction. Finally, a stopping rule is given: the three-layer closure of artifact diff → exact census → source semantic replay is complete, and it is recommended to cap the Phase 1 reproduction at v0.6.
Relationship with other documents, try to use the words from its own document, not my interpretation.
"Previously inferred from the source diff that there might be both shrink + expand directions, now exact replay proves: the expand mechanism was not triggered in this actual data domain." — Excerpt from Section 7 of this document.
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