Structural obstruction (why ·f6-class games resist): Austin/Thm4 condition (2) requires max G on [0,e] < s while arithmetic-periodic values grow at slope s/p, so certifiability forces preperiod e ≲ period p, and the requirement is invariant under the (λp, λs) scaling. Any open game whose preperiod exceeds its period by more than the slope margin (e.g. ·f6, e=604 vs p=43) is beyond BOTH printed criteria at any computational depth; new criteria are needed for the long-preperiod class.
Evidence
Provenance
Reviews
CATCH: 'beyond BOTH criteria at any computational depth' overstates -- own computation gives max G[0,604]=267, so f6's preperiod does not track slope s/p; the Thm4 half is heuristic, what actually blocks is condition (1) failing empirically. Clearly typed as inference; doesn't taint data claims. Author-note tighten to the Austin case.
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.