Discoveries / algorithms-optimization

Source authenticated

Zak's modified integer round-down conjecture for the skiving stock problem

Theorem 1: for every integer $c\ge0$ there is a rational instance with $5B$ items, sizes in $(53/270,11/54)$ for threshold $1$ , $LP_{\mathrm{SSP}}=LP_{\mathrm{SSP,prop}}=B$ and $OPT_{\mathrm{SSP}}\le B-c-1$ ; $c=1$ refutes MIRDP with no rounding ambiguity. Theorem 2 and Corollary 3: fixed additive approximation is NP-hard. The result is conditional on OpenAI's bin-packing theorem (itself a Candidate here). Not shown: any growth rate of the gap in terms of instance size.

Exact FrontierDelta

Prior state unknown→disproved

Scope and record

Occurred: Oct 7, 2026

Delta type: SOURCE CLAIM

Assumptions: VibeMathed verification: unreviewed. Publication: announcement. AI contribution: ai-co-developed. 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: Zak's modified integer round-down conjecture for the skiving stock problem · MIRDP

Confidence: Not scored

Registry verification: unreviewed · announcement · candidate

Open the source record ↗

Attribution

VibeMathed
registry · event recorded by

Anthropic Fable 5.1
model · ai model contributor · Anthropic / OpenAI

OpenAI GPT-5.6 Sol Pro
model · ai model contributor · Anthropic / OpenAI

Eric Winnington
human · human collaborator

Evidence vector

SourceReplayReproducedFormal proofStatement auditExternal checkExpert reviewPeer review

Named evidence

VibeMathed record: Zak's modified integer round-down conjecture for the skiving stock problem

specialist registry · passed

No independent mathematician has checked this yet. Checked here on 7 October 2026: the manuscript's TeX source was read in full. The transfer itself (Proposition 9, Theorems 6 and 7, Corollary 11 and the proof of Theorem 1) was checked by hand and is elementary: four items below $7/30$ always pack and six complemented items always cover, so a covering deficit $d$ gives a packing excess at most $\lceil 3d/2\rceil$ ; even without the $7/30$ bound, singletons give $24d$ , so the conclusion follows from the exported Lean statement of OpenAI's theorem alone. A brute-force computation written here on 60 random 10-item instances (sizes near $1/5$ , matching deficiency $0$ to $2$ ) confirmed the exact formulas $OPT_{\mathrm{BP}}-B=\lceil h/4\rceil$ and $B-OPT_{\mathrm{SSP}}=\lceil h/6\rceil$ in every case. The result depends on OpenAI's unbounded configuration-gap theorem, which is Lean-checked but not independently verified; the transfer is not formalised and nothing was rebuilt here.

Source ↗

Zak's modified integer round-down conjecture for the skiving stock problem

witness · pending

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

Source ↗

OpenAI, Additive hardness and unbounded configuration gaps in bin packing (source theorem)

paper · pending

paper link supplied by the VibeMathed registry.

Source ↗

Martinovic and Scheithauer, New theoretical investigations on the gap of the skiving stock problem (2019)

specialist registry · pending

problem-record link supplied by the VibeMathed registry.

Source ↗

Manuscript TeX source

code · pending

code link supplied by the VibeMathed registry.

Source ↗

The modified integer round-up conjecture, whose counterexample this adapts (OpenAI math release)

witness · pending

other link supplied by the VibeMathed registry.

Source ↗

Artifacts and verifiers

Manuscript TeX source

code · pending

Artifact ↗

Compute record

No linked compute attempts recorded.

Lineage and corrections

This event attributed to OpenAI GPT-5.6 Sol Pro

This event attributed to Anthropic Fable 5.1

The modified integer round-up conjecture, whose counterexample this adapts (OpenAI math release) evidence for this event

Martinovic and Scheithauer, New theoretical investigations on the gap of the skiving stock problem (2019) evidence for this event

Zak's modified integer round-down conjecture for the skiving stock problem evidence for this event

Manuscript TeX source evidence for this event

VibeMathed record: Zak's modified integer round-down conjecture for the skiving stock problem evidence for this event

This event attributed to Eric Winnington

Zak's modified integer round-down conjecture for the skiving stock problem parent of this event

OpenAI, Additive hardness and unbounded configuration gaps in bin packing (source theorem) evidence for this event

Act on this frontier

Verify, challenge, or extend the result.

Help verify Open canonical problem Explore evidence graph