Reconstructing the endpoint cancellation examination

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The report examines the frozen endpoint cancellation theorem P and its signed application interface on 2026-10-15 UTC. It records the whole-statement verdict, limitations, all checklist findings and the precise external theorem boundaries. This package contains mathematical reasoning, not a computational experiment. There is no mathematical program to run, no cached success result, and no missing numerical witness.

This package is filed under wiki/research/erdos_824_uniformity/evidence/verify/endpoint_cancellation/. All links below are relative to this file and resolve from the retained package. The assets files are copies, with the mechanical maintenance listed on the record index, of the supplied neutral extraction, including its omission markers, not new extracts from another source. Their exact retention permits reconstruction without checking out a private source revision or acquiring a paper.

1. Read derivation.md, especially “The consumed statement” and “The order of choices,” against the report's complete restatement. Read signed_application.md for the actual endpoint pair and the clause table in the report.
2. Use source_sections_2_to_5.md for definitions, theorem statements, equations and the supplied source proofs. Treat only source Theorem 2.2, (2.2), and Lemma 2.7 as the classical external boundaries described in the report. Theorem 5.1 is the target.
3. Reconstruct memory_transfer.md, (M1)–(M14), from the single-prime residue expectation. In particular check the factorial adjoints, the small-product injection and both estimates of the equality-rank sum. A single absolute collision estimate is deliberately shown to be inadequate; it is not the reproduction route.
4. Reconstruct ideal_comparison.md, (I1)–(I11), on arbitrary tuple functions. Check the conditional Gram normalization, discarded-cell bilinear bound and exact probe fraction; restricting the tests to product functions would miss the attacked scope.
5. Follow “Physical lift, overlap errors, and major arcs” in the report, then mellin_cancellation.md, (F1)–(F18). Check the $Y^{-1}$ normalization, prime-square error, sparse Gram estimate, sieve replacement and all-subinterval differencing. Leave the residual coefficient arbitrary throughout.
6. Recompute (R7)–(R11) in the report from the signed equations. Verify both signs, the inverse map, the character normalization, the common interval and residual, the original restricted sequence, and the factor $Z$ relating the unweighted sum to P.
7. Follow the explicit order of parameter choices and compare every premise and checklist row with the corresponding calculation. In particular, fix the ideal target before comparison complexity, $J$ afterward, and discrepancy $B$ before final proxy precision.

This is the full reproduction route; it requires reading and mathematical checking rather than running an omitted implementation. Original project reasoning is credited to Plasma AI and the source proof to OpenAI. A distinct grader must determine the report's accepted weight. The source Section 6 historical comparison, original classical-source proof checks, E estimates, and final catalog conclusion are not certified by this package.