Maximum vertex number of a (3,5)-zonoboxtope

Determine the largest possible number of vertices of a (3,5)-zonoboxtope, equivalently a maxout polytope of type (3,5,1). A published preprint gave the upper bound 44, asserted tightness, and conjectured the value 44 as part of its odd-n formula.

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74Significance / 100

1Frontier events

1Verification tasks

1Recorded attempts

Temporal state

Current frontier

Replayed

Exact certificate replay supports a reported maximum of 42 vertices under stated reductions

Acceptance criteria: Independently audit the geometric row model and reductions, replay the complete exact certificate library, verify an exact attaining witness, and obtain expert or peer-reviewed scrutiny.

Append-only history

Frontier timeline

geometry-topologyAug 30, 2026Significance 82/100

Exact maxout (3,5) certificate suite replay passed

Prior state unknown→Exact certificate replay supports a reported maximum of 42 vertices under stated reductions

The pinned public repository passed 132,869 checks with zero failures in its generation-independent upper-bound audit. Certificate transport passed 2,220 exact group-item checks, and the rational 42-vertex witness passed. The record remains scoped to artifact replay pending an independent audit of the geometric reductions.

ReplayedMaximum vertex number of a (3,5)-zonoboxtope →

SourceReplayReproducedFormal proofStatement auditExternal checkExpert reviewPeer review

Research memory

Claims and attempts

Scoped claims

Replayed

At pinned commit d047359e7892106021022b0401554f56eb4e4d8a, the exact certificate suite passes its complete replay: 132,560 cell-wide Gordan certificates establish the source's upper-bound computation, and an exact rational witness has 42 vertices. Under the source's stated row model and reduction arguments, the maximum number of vertices is 42 rather than the conjectured 44.

The replay takes the source's 25-by-8 row model, valid-side-pattern definition, and reduction to four split representatives as stated. Those prose reductions were not independently derived in this audit.

Recorded attempts

Replay the pinned maxout (3,5) exact certificate suite

success · MFN independent verifier

The upper-bound audit passed 132,869 checks with zero failures. Transport passed 2,220 exact group-item pairs. The rational witness certified exactly 42 vertices and 22 non-vertices.

Evidence graph

Connected research record

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At pinned commit d047359e7892106021022b0401554f56eb4e4d8a, the exact certificate suite passes its complete replay: 132,560 cell-wide Gordan certificates establish the source's upper-bound computation, and an exact ration
parent of · claim · theorem
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Exact maxout (3,5) certificate suite replay passed
parent of · event · reproduction