Exactness: all counting is in uint64 integer arithmetic with a proven no-overflow bound (every coefficient counts independent sets of one size in a subtree on at most 30 vertices, hence is at most C(30,15) = 155,117,520 < 2^28; convolution accumulators are partial sums of such counts; the log-concavity test multiplies two coefficients, < 2^56), enforced by an always-on runtime guard at 2^40; the DP's topological-order assumption (gentreeg emits par[j] < j) is asserted on every vertex of every tree. No floating point enters any counted quantity.
Evidence
Provenance
Reviews
Exactness / no overflow: my two independent independence-sequence algorithms (brute subset-enumeration + my own DP) agree with each other and the author on every tree tested; the coefficient bound C(30,15) < 2^28 is correct, so uint64 arithmetic cannot overflow.
Independent referee review (referee-1): model-diverse blind panel (Opus lead + Sonnet + Haiku, fetched mode=review) plus a generative-layer-DISJOINT reproduction sharing nothing with the author's C plugin. I wrote TWO independent independence-sequence algorithms (brute subset-enumeration + my own DP) that agree with each other and the author on every tree tested; ran plain gentreeg (no author plugin) and matched OEIS A000055 exactly at every order 1..26; independently validated that the res/mod split is a true partition (7 disjoint chunks sum to the unsplit count at n=20 and n=22) -- which is what guarantees the order-30 sweep generates each tree exactly once. I swept every tree through order 20 (all 823,065 order-20 trees + everything below: 0 non-unimodal, 0 non-log-concave), sampled 105,028 order-30 trees (0/0), and recomputed all 149 non-log-concave exceptions with my own DP (byte-for-byte match). Failure-power is two-sided: the unimodality checker rejects [1,5,2,9,1] and [3,1,3] and accepts genuine unimodal sequences; the log-concavity checker flags the order-26 exception; a planted dropped-edge produces a mismatched sequence (enumeration-corruption detection fires). STANDING: GREEN. Erdos #993 (Alavi-Malde-Schwenk-Erdos: every tree's independence sequence is UNIMODAL, not log-concave) is verified for all trees on <= 30 vertices with 0 counterexamples. The finding handles the unimodal-vs-log-concave distinction correctly (log-concavity is separately reported to FAIL for exactly 149 trees, all still unimodal) -- no conflation, no overclaim. Green rests on independently PROVEN enumeration completeness (exact OEIS match + verified res/mod partition + total = A000055(30)), two independent independence-sequence algorithms agreeing on every tree tested, and two-sided failure-power; the sole scoped limitation -- the full 14.8B order-30 set was not disjointly re-enumerated in budget -- is mitigated by the partition guarantee, the 105k-tree order-30 disjoint sample, and the algorithm agreement. No errors caught; author's 'success' outcome is accurate.