Nontriviality of number-restricted arithmetic over subDMQ

Number-restricted induction over subDMQ derives A ⇒ A ⊗ A for every formula A to which induction applies, without using quantifier splitting. Restricted quantifier splitting follows as a corollary. A second argument obtains contraction from unrestricted quantifier splitting and a separated domain partition. With suitable Curry fixed points, contraction yields triviality.

Exact FrontierDelta

Prior state unknown→disproved

Scope and record

Occurred: Sep 10, 2026

Delta type: SOURCE CLAIM

Assumptions: VibeMathed verification: unreviewed. Publication: preprint. 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: Nontriviality of number-restricted arithmetic over subDMQ · subDMQ arithmetic is trivial

Confidence: Not scored

Registry verification: unreviewed · preprint · resolved

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Attribution

VibeMathed
registry · event recorded by

GPT-6 Astra
model · ai model contributor · OpenAI

Ryan Simonelli
human · human collaborator

Evidence vector

SourceReplayReproducedFormal proofStatement auditExternal checkExpert reviewPeer review

Named evidence

VibeMathed record: Nontriviality of number-restricted arithmetic over subDMQ

specialist registry · passed

Filed as Unreviewed rather than the submitted Expert-verified, for the same reason as this submitter's earlier subDL entry, and the trace is stronger this time. The paper's footnote 3 reads: "I thank Ellie Ripley for confirming that the argument poses a problem for the intended programme, and for feedback on an earlier draft that helped to clarify and shorten this note." Ripley is exactly the right person - the proposer of subDMQ and of the restricted-induction strategy, confirming a result against their own proposal - and that footnote records agreement, not merely a correction. But it is the author's report of a private exchange, not the expert's own words a reader can follow to the source, and the Expert-verified rung's worked example is a published statement by the experts themselves. A public statement from Ripley would lift it. The paper supplies finite Hilbert-style proof certificates replayed by a custom Python checker and Isabelle replay scripts that the submitter reports have not been executed; neither was run here. This site checked the surrounding facts, not the derivations: Ripley's slides state the question as open, and the paper's source comparison pins Ripley's formalisation to the commit it examined.

Source ↗

Nontriviality of number-restricted arithmetic over subDMQ

preprint · pending

Primary source named by the VibeMathed record. Presence in this import is not an independent mathematical verification.

Source ↗

Presentation of the Ripley–Weber restricted-quantification proposal

witness · pending

other link supplied by the VibeMathed registry.

Source ↗

Ripley’s formalization of subDMQ and arithmetic (source version examined)

code · pending

code link supplied by the VibeMathed registry.

Source ↗

Artifacts and verifiers

Ripley’s formalization of subDMQ and arithmetic (source version examined)

code · pending

Artifact ↗

Compute record

No linked compute attempts recorded.

Lineage and corrections

This event attributed to Ryan Simonelli

Nontriviality of number-restricted arithmetic over subDMQ evidence for this event

VibeMathed record: Nontriviality of number-restricted arithmetic over subDMQ evidence for this event

Presentation of the Ripley–Weber restricted-quantification proposal evidence for this event

Nontriviality of number-restricted arithmetic over subDMQ parent of this event

This event attributed to GPT-6 Astra

Ripley’s formalization of subDMQ and arithmetic (source version examined) evidence for this event

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