Remark: Family 138. Subset Sum in O(2 (0.49n)) time

Gives a uniform randomized classical algorithm for worst-case Subset Sum in ordinary $O(2^{0.49n})$ word-RAM time on polynomial-bit inputs, where $n$ counts the integers. The time bound holds on every execution and success probability is at least $2/3$ on every input. Inputs may repeat positive integers; words have $O(n+b)$ bits for maximum input bit length $b$.

The authors are OpenAI. This companion does not verify the proof. The claim is not a theorem of the Enter series and not a premise of any registered sheet. It does not close O.1. O.1 stays NOT_CLOSED. It is not a de Sitter state and not the QdS external-leg scheme. No quantum coefficient is admitted. No compilation is asserted.