Claims
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KindShowingImportancePrizesTopicFormal proof verification
Claims about formalizing, checking, or verifying mathematical proofs in proof assistants (Lean, Coq, Isabelle, Metamath, etc.), including whether specific arguments or proofs can or cannot be formalized, and the feasibility or reliability of such formalization efforts. Excludes purely pen-and-paper proof disputes that do not involve formalization.
The compatibility the LANA project isolated at the final stage of IUT is the same obstruction Scholze and Stix identified in 2018.
InconclusiveThe evidence and argument have been examined and do not come down on either side.constitution →empirical · derivedA factual claim that rests on inference from other evidence rather than direct observation.constitution →Inter-universal Teichmüller theoryIUT Corollary 3.12 gapimportance · notableImportance 0.45, from 0 to 1 · notable: a contested point in a live debate (also the default before judging). Higher-importance claims are worth more to assess, so funding reaches them sooner.constitution →
The argument from Theorem 3.11 to Corollary 3.12 as written in the IUT papers cannot be formalized in a proof assistant.
InconclusiveThe evidence and argument have been examined and do not come down on either side.constitution →empirical · derivedA factual claim that rests on inference from other evidence rather than direct observation.constitution →IUT Corollary 3.12 gapInter-universal Teichmüller theoryimportance · minorImportance 0.40, from 0 to 1 · minor: narrow or largely settled, cheap to get right. Higher-importance claims are worth more to assess, so funding reaches them sooner.constitution →
Tao's theorem that almost all Collatz orbits attain almost bounded values has a complete, axiom-clean Lean 4 formalization.
UnassessedNo current assessment. Attention goes where its expected value is highest and someone funds it; nothing has funded an assessment of this claim yet, and anyone can.constitution →empirical · derivedA factual claim that rests on inference from other evidence rather than direct observation.constitution →Collatz conjectureimportance · minorImportance 0.30, from 0 to 1 · minor: narrow or largely settled, cheap to get right. Higher-importance claims are worth more to assess, so funding reaches them sooner.constitution →
The 2026 Jacobian conjecture counterexample has been formally verified in a proof assistant
UnassessedNo current assessment. Attention goes where its expected value is highest and someone funds it; nothing has funded an assessment of this claim yet, and anyone can.constitution →empirical · derivedA factual claim that rests on inference from other evidence rather than direct observation.constitution →2026 Jacobian counterexample constructionJacobian conjectureAlgebraic geometryimportance · settledImportance 0.15, from 0 to 1 · settled: uncontested, so low even when much depends on it. Higher-importance claims are worth more to assess, so funding reaches them sooner.constitution →
A machine-checked Lean 4 formalization confirms the determinant and collision facts of the Alpöge–Fable counterexample.
UnassessedNo current assessment. Attention goes where its expected value is highest and someone funds it; nothing has funded an assessment of this claim yet, and anyone can.constitution →mathematicalA proposition of mathematics: true or false by proof rather than by observation. Settled by a proof others can check, and most firmly by one a machine has checked.constitution →Alpöge's ℂ³ mapAlgebraic geometryJacobian conjectureimportance · minorImportance 0.35, from 0 to 1 · minor: narrow or largely settled, cheap to get right. Higher-importance claims are worth more to assess, so funding reaches them sooner.constitution →
Verifying a mathematical proof is easier from formal proof-assistant output than from informal natural-language output.
UnassessedNo current assessment. Attention goes where its expected value is highest and someone funds it; nothing has funded an assessment of this claim yet, and anyone can.constitution →evaluativeA judgment of worth or quality against some standard: good, fair, effective.constitution →Mathematicsimportance · minorImportance 0.30, from 0 to 1 · minor: narrow or largely settled, cheap to get right. Higher-importance claims are worth more to assess, so funding reaches them sooner.constitution →
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