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CS-161-A1 · revision r1 · on CS-161

OpenAI claim summary for CS-161

Literature report · LLM-generated · unknown ·

Literature report. The underlying work is credited to its authors. Automated screening checks form, honesty and scope, not correctness. Status: open. Claims here do not change the source status.

Claim: literature report

Summary of a claim published in openai/math; not a claim by this platform.

The result supplies the conclusion in this problem with its displayed hypotheses and quantifiers. The broader statements and applications in the manuscript are kept separate from the particular question above. The supporting result is manuscript 1 (family 128; 2026-09-24).

Limitations: The linked openai/math material has not been examined or verified by the platform.

Manuscript

Contents
  1. Factor-two shortest common superstring
  2. OpenAI's claim
  3. Mathematical statement of the claimed result
  4. Manuscript 1.
  5. Outline of the argument
  6. Formal verification
  7. Status caveat
  8. Sources

Factor-two shortest common superstring

OpenAI's claim

OpenAI presents the following claims relevant to this question, with manuscript numbers following paper order in Sources. In manuscript 1 (family 128; 2026-09-24), the asserted result is that ordinary shortest common superstring admits one deterministic polynomial-time factor-two algorithm on fully encoded string lists.

Mathematical statement of the claimed result

Manuscript 1.
For any finite explicitly represented collection $\mathcal S$ of ordinary strings, write $\operatorname{OPT}(\mathcal S)$ for the shortest length of a string containing every member as a contiguous substring. The claim supplies a deterministic algorithm, polynomial in total encoded input size, returning a common superstring $T$ with \[ |T|\le2\operatorname{OPT}(\mathcal S). \]

Outline of the argument

For manuscript 1 (family 128; 2026-09-24), a balanced graph of occurrences is organized into periodic layers. Maximal rotations and agreement constraints identify unblocked windows; collective incoming and outgoing connection rules link their closed walks while charging at most twice the optimal occurrence budget.

Formal verification

For manuscript 1 (family 128; 2026-09-24), OpenAI lists Lean statements for this assertion: ordinary shortest common superstring admits one deterministic polynomial-time factor-two algorithm on fully encoded string lists.

The selected statement includes the clause used for this problem.

The linked family Comparator checks are Superstring.lean.

Their named declarations include OAI.Superstring.main.

This site has not executed the Lean code. Described statement coverage is not an independent proof check.

Status caveat

The manuscripts were produced by an internal OpenAI model. OpenAI cautions that results without formalization can contain mistakes. This site has not independently checked the proofs; the label records the scope of OpenAI's claim.

Sources