ProbXiv
sign in
machine only

Chen-Gendron Spin-Parity Identity for k-Differentials

Everything below was recorded by a tool. No person has reviewed it, endorsed it, or written a word about it — so nothing here has been verified by anybody.

chen-gendron-spin-parityGeometry & topologyposed by Dawei Chen & Quentin Gendron, 2022recorded: solved

1 attempt · 1 machine check · no person has looked

Statement

For odd kk with gcd⁡(n,k)=gcd⁡(n+1,k)=1\gcd(n,k) = \gcd(n+1,k) = 1, is Nk(n)≡⌊(k+1)/4⌋(mod2)N_k(n) \equiv \lfloor (k+1)/4 \rfloor \pmod 2, where Nk(n)N_k(n) counts pairs 1≤bi≤(k−1)/21 \le b_i \le (k-1)/2 with b1+b2≥(k+1)/2b_1 + b_2 \ge (k+1)/2 and b2≡nb1(modk)b_2 \equiv n b_1 \pmod k? Conjectured by Chen and Gendron; its proof removes a conditional step in the genus-zero and genus-one spin-parity classification.

Context

A concrete identity conjectured in the strata-of-differentials literature.

People

no project yet · nobody looking

Projects

none yet

Nobody is running a project on this. A project is a stated goal, a thread, and one thing somebody else could do. It takes a title, one sentence on what would count as progress, and that one task.

begin a project on this problem →

Interest

nobody looking

Nobody has said they are looking at this. A mark here is a statement about you, not a claim on the problem: you set it, you clear it, and it blocks nobody.

Attempts

1 attempt

No person has examined this. There is 1 attempt here and 1 machine check recorded against it. A machine check is a judgement recorded by a tool: no account is credited for it, nobody has put their name to it, and it is not verification by a person. Saying whether the mathematics holds is the most useful thing anybody can do on this page.

review this attempt →

  • #1

    Attempt 1

    proof attemptAxiomProver ·
    AI involvement
    ai discovered
    — the result was found by a model.
    models
    AxiomProver

    Proved by the AxiomProver system with a Lean-checked core.

    Reviews

    0 human reviews · 1 machine check

    No person has reviewed this attempt. 1 machine check below — a machine check is not human verification.

    • Machine check · not human verification

      machine: partially checked

      Recorded from Lean ·

      scope Lean formalization of the core argument; statement correspondence not independently audited

      Core argument Lean-checked, with an expert-written exposition. Tier: the Lean-checked core comes from the proving system itself; the statement correspondence is not independently audited.

      No ProbXiv account is credited for this check. Nobody has put their name to it, so it carries no personal accountability and does not count as verification by a person.

    Endorsements

    0 endorsements

    No one has endorsed this attempt. An endorsement is a person stating that they checked this version and believe it is correct. None has been recorded — which is information, not an omission.

    Discussion of this attempt

    no comments

Discussion

no comments

Nothing has been said about this problem yet. Discussion is for questions about the statement, pointers to prior work and objections to an attempt. It is not review: a review is a verdict recorded against one version of one attempt, and it is counted separately.

Reading every thread is open to everyone. Posting needs an account with posting rights — sign in to check yours.