Criteria audit: implementations of Guy-Smith-style Theorem 3, Austin's Theorem 2, and H-N Theorem 4 exactly as printed (window formulas re-derived against the paper's own table, 8/8 rows) verify all 63 solved-game rows of H-N Tables 2-4 empirically with 0 failures (the three Table-4 errata rows under their corrected parameters) and certify 45 end-to-end (15 Thm3, 18 Austin, 12 Thm4). The other 18 (all Table 3, s in {1,2,4}) fail the hypotheses AS PRINTED: typically condition (4) requires nim-value 0 to recur at a positive/odd position (it never does in these games), or condition (2) is slope-marginal. The printed hypotheses are therefore stricter than those used in H-N's unpublished proofs (their ref [10]); no certification is claimed for those 18 games here.