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The Iyengar-Ma-Walker Dutta multiplicity conjecture for complete local domains of positive characteristic

Corollary of the uniform complex estimate: for a complete Noetherian local domain $R$ of characteristic $p>0$ and every short complex $F$ over $R$ , the Dutta multiplicity exists and $\chi_\infty(F)\ge e(R)$ . This is the complete-domain, positive-characteristic case of IMW Conjecture 8.1; the general conjecture for all complete local rings (and mixed characteristic) is not claimed. The paper notes it is a consequence of, not an input to, its proof of Lech's conjecture.

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Prior state unknown→proved

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Occurred: Sep 23, 2026

Delta type: SOURCE CLAIM

Assumptions: VibeMathed verification: lean-checked. Publication: announcement. AI contribution: ai-discovered. VibeMathed editorial classifications, scores, notes, relations, and dataset structure are CC BY 4.0. Source statements and linked content retain their own rights.

Canonical aliases: The Iyengar-Ma-Walker Dutta multiplicity conjecture for complete local domains of positive characteristic · IMW conjecture, char p domains

Confidence: Not scored

Registry verification: lean checked · announcement · partial

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VibeMathed record: The Iyengar-Ma-Walker Dutta multiplicity conjecture for complete local domains of positive characteristic

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No independent mathematician has checked this yet. Checked here: Corollary (Dutta domain case) of the Lech manuscript was read against IMW Conjecture 8.1 as the paper cites it; it is the complete-domain, positive-characteristic case only. The challenge is not in the formalization catalogue (lean/formalization.yaml); it is found through lean/docs/194.md, and its solution module OAI.RingTheory.Multiplicity.Main (importing DuttaDomain) exists at the pinned commit. ComparatorChallenges/DuttaDomain.lean was read here: for every complete Noetherian local domain $D$ of characteristic $p$ and every short complex $F$ (free, finite, bounded in degrees $-d..0$ , finite-length homology, nonzero $H^0$ ) it asserts finite-length homology of all Frobenius iterates, convergence of the Dutta sequence, and $e(D)\le\chi_\infty(F)$ . This states the corollary. Not rebuilt here.