Kurkov's Fubini-Number Sum Conjecture

For the Fubini numbers $a(n)$ , is $a(n) = \sum_{k=0}^{2^{n-1}-1} A284005(k)$ for every $n > 0$ , as conjectured on the OEIS in 2018?

Result: Proved
Status: Resolved
AI contribution: AI-discovered
Method: Argument
Field: Enumerative combinatorics
Posed by: —
Year posed: 2018
Years open: 8y
Solved: 2026-07-08
Model: Demonstrandum multi-agent pipeline
Vendor: —
Collaborators: —
Verification: Unreviewed
Publication: Announced
Significance: 5 / 100
Disclosed cost: —
Wikipedia: No dedicated article

What the AI did

Found by the Demonstrandum multi-agent pipeline; every refutation ships a finite certificate, a mutation-tested checker, and an independent clean-room recomputation.

Verification

Refined ordered-set-partition proof, audited, with an exhaustive checker; not externally refereed.

Source

Demonstrandum artifacts repository (RESULTS.md)

Kurkov's Fubini-Number Sum Conjecture

What the AI did

Verification

Source

Discussion