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Math-3029-A1 · revision r1 · on Math-3029

OpenAI claim summary for Math-3029

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.

Manuscript 1 (family 309, 2026-09-24): The problem selects the mathematical statement summarized here, including its stated hypotheses and parameter range. The cited theorem gives a claimed proof of that assertion in full.

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

Manuscript

Contents
  1. Kervaire detection at the prime three
  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

Kervaire detection at the prime three

OpenAI's claim

The standard mod-three Adams Kervaire classes are claimed to survive exactly at indices zero, two, and three, each with an order-three representative; the new index-three element lies in stem 322. The cited manuscript argues for that result; its relation to this problem is specified below.

Mathematical statement of the claimed result

Mathematical claim 1.
In the mod-three Adams spectral sequence $\operatorname{Ext}_{\mathcal A_3}^{s,t}(\mathbb F_3,\mathbb F_3)\Rightarrow(\pi^S_{t-s})_3^\wedge$, let $b_j$ be the standard Kervaire family in bidegree $(2,4\cdot3^{j+1})$, $j\ge0$. OpenAI claims \[ \{j:b_j\text{ survives nontrivially}\} =\{j:\text{an order-three class is detected by }b_j\} =\{0,2,3\}. \] The surviving stems are $10,106,322$; $b_1$ and all $b_j$, $j\ge4$, fail to survive. Order-three existence is within each detection coset, without asserting that every representative has the same order.

Outline of the argument

Manuscript 1 (family 309, 2026-09-24): A height-six Morava detector with C_9 action imposes finite Euler deadlines and outgoing differentials on all higher candidate classes. Independently, a truncated extended cube of the known stem-106 Moore map carries the required primary operation. Finite obstruction corrections lift it back through the Moore sequence, preserving detection and producing an actual sphere element killed by three.

Formal verification

Family 309 has no Lean scope page in this snapshot; no formalization of these manuscript results is listed.

This site has not executed the Lean files or checked their dependencies. These descriptions report the scope of the linked declarations, rather than a new verification of the proofs.

Status caveat

OpenAI attributes these results to an internal model. Its release notice cautions that results lacking full formalization can contain mistakes. This site has not independently assessed the proofs; a solved label records the scope of the reported claim.

Sources