lean artifact · pending
Artifact ↗Source authenticated
Reciprocal-triple-free sets: finite maxima through 734
The Lean development proves f(732)=f(731), f(733)=f(732)+1 and f(734)=f(732)+2. The 732 step replaces an isolated five-vertex component without reducing an admissible set. Exact finite certificates show that neither 733 nor 734 belongs to a forbidden reciprocal triple with vertices at most 734, so each new vertex raises the maximum by one. Conditional on the published OEIS value f(731)=606, the resulting values are f(732)=606, f(733)=607 and f(734)=608. The historical asymptotic Erdős problem remains open. Priority is provisional; the elementary component argument may be folklore.
Exact FrontierDelta
Prior state unknown→proved
Scope and record
Occurred: Sep 7, 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: Reciprocal-triple-free sets: finite maxima through 734 · A390395: finite values through 734
Confidence: Not scored
Registry verification: lean checked · announcement · partial
Attribution
VibeMathed
registry · event recorded by
OpenAI ChatGPT/Codex (exact model identifier unavailable)
model · ai model contributor · OpenAI
Sodelin (project owner and research direction)
human · human collaborator
Artifacts and verifiers
lean artifact · pending
Artifact ↗Compute record
No linked compute attempts recorded.
Lineage and corrections
Reciprocal-triple-free sets: finite maxima through 734 evidence for this event
The Lean development proves f(732)=f(731), f(733)=f(732)+1 and f(734)=f(732)+2. The 732 step replaces an isolated five-vertex component without reducing an admissible set. Exact finite certificates show that neither 733 nor 734 belongs to a forbidden reciprocal triple with vertices at most 734, so each new vertex raises the maximum by one. Conditional on the published OEIS value f(731)=606, the resulting values are f(732)=606, f(733)=607 and f(734)=608. The historical asymptotic Erdős problem remains open. Priority is provisional; the elementary component argument may be folklore. parent of this event
Passing Lean build, axiom audit, and exact verifiers evidence for this event
This event attributed to Sodelin (project owner and research direction)
VibeMathed record: Reciprocal-triple-free sets: finite maxima through 734 evidence for this event
This event attributed to OpenAI ChatGPT/Codex (exact model identifier unavailable)
Reciprocal-triple-free sets: finite maxima through 734 parent of this event
Original 732 proof commit evidence for this event
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