For the specified bounded-degree bipartite Boolean networks and uniformly computable entries, the manuscript argument combines exact reconstruction, shrinking children, controlled precision, and streamed evaluation. Its claimed conclusion is deterministic (s+description_length)^{O(1)} 2^{O(s/sqrt(log s))} bit time and polynomial space, with constants depending on the fixed input bounds. The original-ring output is preserved. This learning path now exposes the argument rather than treating contraction as a black box. Its model-assisted reviews and finite exact tests are not independent expert verification of the manuscript, a practical fast implementation, or evidence of improved human learning.

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The original tensor entries lie in B_(P0,ell), represented as the constant U coordinates of A_(P0). Their contraction is a finite sum of products of those entries, so it remains in that subring. After the recursive computation returns the correct residue, extract its constant U coordinate for every retained power of V; all nonconstant U coordinates are zero modulo 2^P0. Do not sum the V coefficients here: that is a separate operation required by particular counting encodings, not by tensor contraction itself. The extension enabled interpolation without changing the requested output ring.

Returning from the interpolation extension to the original coefficient ring

Each leaf has at most 2^H assignments and polynomially many entry evaluations per assignment. Original entries satisfy the theorem input contract; new entries cost exp(O(s^(9/10))) times polynomial work. Since H=O(s/sqrt(log s)) and s^(9/10)=o(s/sqrt(log s)), leaf work fits the claimed exponent. Multiply by the bound on all calls and include polynomial-delay tuple enumeration and exact local arithmetic. The total is (s+description_length)^{O(1)} times 2^{O(s/sqrt(log s))} bit operations. Immutable descriptions keep the description-length polynomial from acquiring a new exponent at each recursion depth.

Combining recursion branching, leaf work and entry-evaluation time

Traverse one child at a time, retaining one product over groups and one sum over beta. Keep only the current interpolation index, tuple counters, graph, new descriptions and the polynomially many local coefficients needed for recovery. Precision, field coordinates and rational common denominators have polynomial bit length. Immutable older descriptions are referenced rather than recursively copied. There are O_C(log lambda) stack levels, so their combined storage remains polynomial in s+description_length. Original entry routines must obey the input polynomial-space contract, and the new routines have the same property. Exponentially many calls do not require storing the recursion tree.

Depth-first evaluation keeps the exponential recursion polynomial in space

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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