A high-arity counterexample to Pixton completeness in Chow

Comments and discussion

• Marcus Bintz (@spurious-bows.bsky.social), post on Bluesky (2026-10-12). Pairs this paper with the release paper "Bloch's conjecture for surfaces with p_g=0", matching that paper's Lemmas 3.3 and 5.1 with Lemmas 5.3 and 5.5 here, and broadly its sections 5.1–5.4 with sections 5.5–5.7 here.

Formalization

• OpenAI, Exterior monomials, color counts and finite stable-graph bounds (release Lean source, accessed 2026-10-21). Formalizes numerical parameters, color counts, permutation multiplicities, exterior-monomial nonvanishing and finite graph bounds; its scope statement explicitly excludes the class Y, its realizations, the Pixton span, detector pairing and geometric vanishing.

Related prior literature mentioned by others

• Samir Canning, Hannah Larson and Johannes Schmitt, The Gorenstein property and Pixton's conjecture for compact type moduli (arXiv:2607.02249, 2026-07-02; revised 2026-08-07). The AI Proved What? exposition highlights this work's completeness results for the compact-type spaces of genera and marking counts (6,0), (5,2) and (7,0), providing context for the manuscript's claimed failure on the full stable compactification.
• Aaron Pixton, The tautological ring of M₂₅ is not Gorenstein (arXiv:2609.15949, 2026-09-14). The AI Proved What? exposition cites this simultaneous non-Gorenstein result and Faber–Zagier completeness result on the smooth unpointed space to distinguish the Gorenstein question from the manuscript's completeness claim.

Possibly relevant literature (found by the agent, not checked)

• D. Genlik, F. Janda, From 3-spin to negative r-spin: limits of cohomological field theories and tautological relations (arXiv:2609.36509, 29 September 2026). Shows that the negative r-spin relations, and for r = 2 the Kazarian–Norbury K-relations, follow from Pixton's 3-spin relations. This is relevant to the paper's comparison of other known relation systems with the fixed span $\mathcal P_{g,n}$.
• Q. Yin, Cycles on curves and Jacobians: a tale of two tautological rings (arXiv:1407.2216, July 2014). Derives tautological relations from the motivic Lefschetz decomposition on the Jacobian side and asks whether all tautological relations are motivic. This may bear on the paper's route to Chow vanishing through O'Sullivan's tensor reconstruction for the correspondences of a curve.
• B. Moonen, Q. Yin, Some remarks on modified diagonals (arXiv:1405.1646, May 2014). Proves vanishing results for modified diagonal classes, with sharp results for curves. This may relate to the paper's extra nilpotence identity for the Gross–Schoen-type cubic $\varphi$.
• D. Petersen, M. Tavakol, Q. Yin, Tautological classes with twisted coefficients (arXiv:1705.08875, May 2017; Ann. Sci. ENS 2021). Studies tautological rings of all fibered powers $C_g^n$ through Chow groups with $Sp(2g)$-twisted coefficients. This may relate to the paper's odd symplectic summand and its color-preserving alternation; the paper cites Tavakol's $C_g^n$/rational-tails comparison but not this work.
• D. Petersen, O. Tommasi, The Gorenstein conjecture fails for the tautological ring of $\overline{M}_{2,n}$ (arXiv:1210.5761, October 2012). Gives the first Gorenstein failure on the full compactification, as context for the paper's distinction between completeness and the Gorenstein property, which it discusses using Canning, Pixton and Canning–Larson–Schmitt.

Digests and expositions

• AI Proved What?, A relation Pixton missed? A counterexample to Pixton completeness in Chow (episode 053, October 2026; status updated 2026-10-19). This AI-assisted video and written exposition outline the claimed formal detection and Chow-vanishing arguments, explain the enormous parameters and distinguish the limited Lean checks from verification of the main theorem. [AI-generated per source]