geometry-topology / Algebraic geometry; moduli of curves; tautological rings

Pixton's conjecture: do Pixton's relations give all tautological relations on the moduli of stable curves?

Claims that Pixton's original relations are not complete in rational Chow or rational cohomology: on M‾g,n\overline{\mathcal M}_{g,n} with g=1060g=10^{60} and n=3(10603)n=3\binom{10^{60}}3 an alternating product of corrected small diagonals vanishes but lies outside the span. It does NOT give a small counterexample (the parameters are not claimed minimal), does NOT address enlarged relation systems, and is distinct from the Gorenstein question already settled negatively (Petersen-Tommasi, Canning).

38Significance / 100
1Frontier events
0Verification tasks
0Recorded attempts

Temporal state

Current frontier

No reconciled state yet.

Append-only history

Frontier timeline

geometry-topologySep 24, 2026Significance 38/100Registry: unreviewed

Pixton's conjecture: do Pixton's relations give all tautological relations on the moduli of stable curves?

Prior state unknown→disproved

Claims that Pixton's original relations are not complete in rational Chow or rational cohomology: on M‾g,n\overline{\mathcal M}_{g,n} with g=1060g=10^{60} and n=3(10603)n=3\binom{10^{60}}3 an alternating product of corrected small diagonals vanishes but lies outside the span. It does NOT give a small counterexample (the parameters are not claimed minimal), does NOT address enlarged relation systems, and is distinct from the Gorens…

SourceReplayReproducedFormal proofStatement auditExternal checkExpert reviewPeer review

Research memory

Claims and attempts

Scoped claims

Source authenticated

Claims that Pixton's original relations are not complete in rational Chow or rational cohomology: on M‾g,n\overline{\mathcal M}_{g,n} with g=1060g=10^{60} and n=3(10603)n=3\binom{10^{60}}3 an alternating product of corrected small diagonals vanishes but lies outside the span. It does NOT give a small counterexample (the parameters are not claimed minimal), does NOT address enlarged relation systems, and is distinct from the Gorenstein question already settled negatively (Petersen-Tommasi, Canning).

Claims that Pixton's original relations are not complete in rational Chow or rational cohomology: on M‾g,n\overline{\mathcal M}_{g,n} with g=1060g=10^{60} and n=3(10603)n=3\binom{10^{60}}3 an alternating product of corrected small diagonals vanishes but lies outside the span. It does NOT give a small counterexample (the parameters are not claimed minimal), does NOT address enlarged relation systems, and is distinct from the Gorenstein question already settled negatively (Petersen-Tommasi, Canning).

Recorded attempts

Evidence graph

Connected research record