Signed depth relevance in subDL
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For every theorem A→B of subDL, must A and B share a variable with the same sign at the same relevant-arrow depth? Signed variable sharing and unsigned depth relevance separately do not require one variable to satisfy both.
Why it matters and what counts as progress
Why it matters: The combined property would sharpen the connection between subDL derivability and syntactic relevance.
What counts as progress: A proof producing the same variable with both matching sign and depth, or a derivable implication for which no such common witness exists.
How the problem developed
- February 2026 · Partial result [1]
Tore Fjetland Øgaard Established signed variable sharing and unsigned depth relevance as separate subDL results; the conjunction called signed depth relevance remained a distinct question.
- August 2026 · Reported claim [2]
Ryan Simonelli and GPT-5.6 Sol An author-hosted manuscript reports an AI-generated solution to signed depth relevance; its account notes a notation correction from Øgaard.
AI contribution
Signed Depth Relevance for subDL
For every subDL theorem A → B, GPT-5.6 Sol’s terminal-hierarchy argument claims that A and B share a variable with the same sign at the same relevant-arrow depth.
Sources
Website timeline
Publication dates and editorial changes.