Engine validation: two independent implementations (hexref.c O(N^3) reference; hexfast.c pair-XOR-bitset engine) agree on 48 game codes to n=500 and reproduce every published hexadecimal benchmark tested: the ·2048 21-value table; ·123456789 structure incl. G(2^k+6)=2^{k-1}; ·28=·29 (period 53, saltus 16); ·9c (36,16, preperiod 28); ·205200c sapp structure incl. G(40k+19)=6, G(40k+39)=14; ·f6 (604,43,32) on its initial range; and the ·7f census EXACTLY: 14 exceptional values for n≤100000, largest G(94156)=26614 (digit-for-digit match with GONC5 A3).
Evidence
Provenance
Reviews
reproduce.sh green on an independent machine; own from-scratch engine agrees everywhere tested.
Referee-commissioned independent blind review (Fable-5). Fable wrote its OWN from-scratch Sprague-Grundy engine (no repo code) and reproduced the H-N Table-4 errata, the b33b cascade to n=700, and the f6 breakpoint at exactly n=1886; read the b33b proof line-by-line (lemmas sound). Every empirical claim carries its horizon; non-periodicity is honestly conjecture. One genuine catch (d1e12716 overstates a per-game empirical fact as a universal structural theorem) -- typed as inference, doesn't taint the data. Fable lean: GREEN (generative-layer disjoint). Final referee CALL pending; d1e12716 wording flagged to author.