Signed Depth Relevance of subDL

subDL satisfies the signed depth relevance property, answering an open question posed by Øgaard (2026). More precisely, every valid inference in subDL contains a propositional variable that occurs in both the premises and conclusion with matching sign and at matching implicational depth.

Exact FrontierDelta

Prior state unknown→proved

Scope and record

Occurred: Aug 4, 2026

Delta type: SOURCE CLAIM

Assumptions: VibeMathed verification: unreviewed. Publication: preprint. AI contribution: ai-discovered. Editorial metadata: CC BY 4.0; linked content retains its own rights.

Canonical aliases: Signed Depth Relevance of subDL

Confidence: Not scored

Registry verification: unreviewed · preprint · resolved

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Attribution

VibeMathed
registry · event recorded by

Ryan Simonelli
human · human collaborator

ChatGPT 5.6-Sol
model · ai model contributor · OpenAI

Evidence vector

SourceReplayReproducedFormal proofStatement auditExternal checkExpert reviewPeer review

Named evidence

VibeMathed record: Signed Depth Relevance of subDL

specialist registry · passed

Filed as Unreviewed rather than the submitted Expert-verified, and the distinction is narrow enough to spell out. The paper's acknowledgments thank Tore Fjetland Øgaard - who posed the question, and so is both a named domain expert and a person with no stake in this proof - "for identifying the notational error concerning $\Rightarrow_m$ and $\to$ in an earlier draft and for pointing out the relation between the terminal clause and Brady's $\omega$ -rule". That is genuine engagement by the right person: he read it closely enough to catch an error. It is not an endorsement of the final proof, and it is the only publicly checkable trace of his involvement. The submission states that he has verified the proof correct; that may well be so, but it rests on a private communication a reader cannot follow, and the Expert-verified rung on this site requires a checkable endorsement (its worked example is a published essay stating outright that named experts checked a proof and believe it correct). This site checked the surrounding facts, not the mathematics: Øgaard's paper exists as cited and leaves exactly this question open, and the proof itself - five pages over the Anderson-Belnap matrix $M_0$ - was read but not audited.