What was already known
The standard generic dynamic program takes O(n2^n) time. A sub-2^n algorithm had previously been known for two-dimensional posets, not arbitrary posets.
AI involvement
Oka credits Claude Opus 5 with the new first-upper-element pattern representation, multiplicity decoding, deadline dynamic program and state count. ChatGPT 5.6 Sol generated the research prompt; Oka checked the results.
Oka credits Claude Opus 5 with the pattern representation, profile decoding, deadline dynamic program and state counting. Another model generated the research prompt; Oka checked the results.
Importance
The result gives a sub-2^n exact algorithm for general posets.
Limitations
The paper includes executable finite-poset verification for n≤7. That computation checks examples and parts of the construction, not the full asymptotic theorem.
Technical verification
Oka says he independently checked the statements and proofs, including the asymptotic theorem. Exact computational audits compare finite cases through n=7 and sampled families; those computations do not prove the runtime bound.
Human understanding
Oka explains the pattern representation, decoding, deadline dynamic program and two-branch state count.
Correction and publication history
Claim-level primary-source review for non-notifying local inclusion.
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