The chain is: normalize a fixed-k CNF while retaining declared variables; partition its satisfying assignments into disjoint sparse leaves; construct initial support checks; select more parity rows by exact sparse-system counts; count the final system via integer parity lifting, shared truncation, checked replacement layouts and rational interpolation; add leaf counts. For fixed k>=2 the manuscript concludes (n+m)^{O_k(1)}2^{O_k(rho(n))} bit operations and polynomial space, with exhaustive fallbacks for finitely many failing sizes. This learning path exposes the contracts and reductions behind that conclusion. Model reviews and finite exact checks are not independent expert verification of the full theorem, a production SAT solver, or evidence of practical speedup.

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Normalize each fixed-width formula with at most O_k(n^k) possible clauses. Per node, enumerate each clause's at most 2^k literal subsets to select the branch and normalize its children in polynomial time for fixed k. Traverse the sparsification tree depth first: keep a polynomial-depth path and count one leaf at a time, not the whole tree. With sigma=1/s and s<=sqrt(ceil(log2 n)), the path, formulas and one sparse-counter workspace use polynomial space. Disjointness keeps the running sum between zero and 2^n, requiring at most n+1 bits. A polynomial-space bound does not make the exponentially many sequential leaf operations disappear.

Streaming disjoint SAT leaves and retaining the exact total

OpenAI. The Exponential Time Hypothesis is False. Manuscript dated October 17, 2026, revised October 25, 2026. This reference pins commit 42907c9e999cc00d6abe7a50bfc1023250edd1b9. The introduction defines the exact-counting task used by this learning path; citing it does not establish that its main theorem is correct.

https://github.com/openai/math/blob/42907c9e999cc00d6abe7a50bfc1023250edd1b9/preprints/The-Exponential-Time-Hypothesis-is-False-October-25-2026/paper.pdf

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