Worst-case Subset Sum in time 2^((1/2 - c)n)

Theorem 1.1: a uniform randomized word-RAM algorithm decides Subset Sum with error at most 1/3 on every input and runs in worst-case time $O(2^{0.49n})$ for every fixed polynomial bound on input bit length, the time bound holding on every random execution. The method combines isolation, a random prime modulus, a filtered Fourier checksum and alias extraction. It is not deterministic, it does not treat super-polynomial bit lengths, and it does not improve the space bound. The companion manuscript separately gives one-sided error, time $\mathrm{poly}(n)2^{n/2}$ and space $O(2^{n/5})$ .

Exact FrontierDelta

Prior state unknown→proved

Scope and record

Occurred: Oct 4, 2026

Delta type: SOURCE CLAIM

Assumptions: VibeMathed verification: unreviewed. Publication: announcement. AI contribution: ai-discovered. VibeMathed editorial classifications, scores, notes, relations, and dataset structure are CC BY 4.0. Source statements and linked content retain their own rights.

Canonical aliases: Worst-case Subset Sum in time 2^((1/2 - c)n) · Subset Sum below 2^(n/2)

Confidence: Not scored

Registry verification: unreviewed · announcement · candidate

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Unreleased internal OpenAI model
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VibeMathed record: Worst-case Subset Sum in time 2^((1/2 - c)n)

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No independent mathematician has checked this yet. Checked here: Theorem 1.1 of the principal manuscript was read against the posed question. It gives a single uniform randomized algorithm, correct with probability at least 2/3 on every input, whose running time is at most $C_c 2^{0.49n}$ on every execution for inputs with bit length $b\le n^c$ , on a word RAM with $O(n+b)$ -bit words; the intermediate bound is $2^{0.489995n}\mathrm{poly}(n+b)$ . The model is stated precisely (no advice, no random oracle, randomness charged). Scope limits stated by the paper: randomized two-sided error (not deterministic), polynomial-bit inputs, word-RAM model. No Lean formalization exists for this family. The proof was not refereed.

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Chen, Jin, Randolph, Servedio, Subset Sum in time 2^(n/2)/poly(n) (2023)

specialist registry · pending

problem-record link supplied by the VibeMathed registry.

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Worst-case Subset Sum in time 2^((1/2 - c)n)

witness · pending

Primary source named by the VibeMathed record. Presence in this import is not an independent mathematical verification.

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Companion: A Low-Space Algorithm for Worst-Case Subset Sum (time 2^(n/2), space 2^(n/5))

paper · pending

paper link supplied by the VibeMathed registry.

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This event attributed to Unreleased internal OpenAI model

VibeMathed record: Worst-case Subset Sum in time 2^((1/2 - c)n) evidence for this event

Worst-case Subset Sum in time 2^((1/2 - c)n) parent of this event

Worst-case Subset Sum in time 2^((1/2 - c)n) evidence for this event

Chen, Jin, Randolph, Servedio, Subset Sum in time 2^(n/2)/poly(n) (2023) evidence for this event

Companion: A Low-Space Algorithm for Worst-Case Subset Sum (time 2^(n/2), space 2^(n/5)) evidence for this event

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