Source authenticated

Can an infinite self-dual uniform matroid be constructed in ZFC?

The manuscript constructs, in ZFC, a self-dual uniform matroid $Q$ on a countable set with every basis and its complement infinite, answering the Bowler-Geschke question and the Gollin-Joo existence question affirmatively. Its bases satisfy an extra ordinal inequality used to build the packing/covering counterexample. It does not address uncountable ground sets or classify such matroids.

Exact FrontierDelta

Prior state unknown→proved

Scope and record

Occurred: Sep 24, 2026

Delta type: SOURCE CLAIM

Assumptions: VibeMathed verification: unreviewed. 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: Can an infinite self-dual uniform matroid be constructed in ZFC? · Self-dual uniform matroid in ZFC

Confidence: Not scored

Registry verification: unreviewed · announcement · candidate

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Attribution

VibeMathed
registry · event recorded by

Unreleased internal OpenAI model
model · ai model contributor · OpenAI

Evidence vector

SourceReplayReproducedFormal proofStatement auditExternal checkExpert reviewPeer review

Named evidence

VibeMathed record: Can an infinite self-dual uniform matroid be constructed in ZFC?

specialist registry · passed

No independent mathematician has checked this yet. Checked here: the introduction's claim and Remark (uniform local matroid) were read against the question as the paper quotes it from Bowler-Geschke and Gollin-Joo. The Lean challenge InfiniteMatroidCorollaries.json (theorem OAI.InfiniteMatroidCounterexample.partitional_intersection_counterexample, module OAI.Combinatorics.InfiniteMatroid.Corollaries, file exists at the pinned commit, not in the formalization catalogue) states the existence of a self-dual uniform Mathlib matroid Q on an infinite countable type. Left unreviewed under the strict tier rule: the question is about provability in ZFC, and the Lean statement expresses existence in Lean's own foundations, not ZFC, so it does not state the headline as posed. Not rebuilt here.

Source ↗

The unrestricted infinite matroid intersection and packing/covering conjectures

witness · pending

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

Source ↗

Lean corollaries (partitional intersection, covering, packing)

lean artifact · pending

lean-proof link supplied by the VibeMathed registry.

Source ↗

Bowler-Geschke, Self-dual uniform matroids on infinite sets

specialist registry · pending

problem-record link supplied by the VibeMathed registry.

Source ↗

Artifacts and verifiers

Lean corollaries (partitional intersection, covering, packing)

lean artifact · pending

Artifact ↗

Compute record

No linked compute attempts recorded.

Lineage and corrections

This event attributed to Unreleased internal OpenAI model

VibeMathed record: Can an infinite self-dual uniform matroid be constructed in ZFC? evidence for this event

The unrestricted infinite matroid intersection and packing/covering conjectures evidence for this event

Bowler-Geschke, Self-dual uniform matroids on infinite sets evidence for this event

Can an infinite self-dual uniform matroid be constructed in ZFC? parent of this event

Lean corollaries (partitional intersection, covering, packing) evidence for this event

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