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Math-2625-A1 · revision r1 · on Math-2625

OpenAI claim summary for Math-2625

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.

Random triangle-removal terminal constant: The manuscript’s result is exactly the terminal-edge-count mean-square limit E[(F_n/n^(3/2)-1/(2sqrt(2)))^2]->0 for uniform triangle selection until no triangles remain. It concerns the terminal leave rather than an intermediate-time spread estimate.

With the hypotheses and conventions above, the claimed result addresses the whole mathematical assertion on this page.

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

Manuscript

Contents
  1. Sharp terminal edge count in random triangle removal
  2. OpenAI's claim
  3. Mathematical statement of the claimed result
  4. Mathematical claim 1.
  5. Outline of the argument
  6. Formal verification
  7. Status caveat
  8. Sources

Sharp terminal edge count in random triangle removal

OpenAI's claim

Random triangle-removal terminal constant: The final edge count in uniform random triangle removal from $K_n$, divided by $n^{3/2}$, is claimed to approach $1/(2\sqrt2)$ in mean square. Convergence of expectation and in probability follow.

Mathematical statement of the claimed result

Mathematical claim 1.
Start from $K_n$ and repeatedly choose uniformly among the remaining triangles, deleting its three edges, until no triangle remains. If $F_n$ is the final edge count, the claim is \[\mathbb E\left[\left(F_n/n^{3/2}-1/(2\sqrt2)\right)^2\right]\longrightarrow0.\] Thus $F_n/n^{3/2}\to1/(2\sqrt2)$ in probability and $\mathbb EF_n/n^{3/2}\to1/(2\sqrt2)$ as well.

Outline of the argument

Random triangle-removal terminal constant: The process is stopped while subgraph counts remain controlled, then its continuation is represented by independent triangle priorities. Backward recursive survival queries are unfolded over the growing terminal time interval. Stability and paired-query estimates have errors smaller than the two-root survival scale, permitting first- and second-moment computations with the sharp constant.

Formal verification

Family 188 describes Lean coverage for the terminal triangle-removal mean-square limit with its sharp coefficient.

Random triangle-removal terminal constant: The manuscript links TriangleRemoval.lean.

The documented selection includes this manuscript’s main assertion; that assertion retains the restrictions stated above.

This site has not run the Lean development. These links describe OpenAI’s selected formal statements and should be read with their stated scope.

Status caveat

OpenAI reports that an internal model produced the manuscripts. Their arguments have not been independently verified as proofs by this site. Any portion outside the documented formal scope may contain mistakes, and the catalogue label reports the announced mathematical claim.

Sources