{"paper":{"title":"Excluded minors are almost fragile","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Ben Clark, Charles Semple, Geoff Whittle, James Oxley, Nick Brettell","submitted_at":"2016-03-31T18:47:37Z","abstract_excerpt":"Let $M$ be an excluded minor for the class of $\\mathbb{P}$-representable matroids for some partial field $\\mathbb P$, and let $N$ be a $3$-connected strong $\\mathbb{P}$-stabilizer that is non-binary. We prove that either $M$ is bounded relative to $N$, or, up to replacing $M$ by a $\\Delta$-$Y$-equivalent excluded minor, we can choose a pair of elements $\\{a,b\\}$ such that either $M\\backslash \\{a,b\\}$ is $N$-fragile, or $M^* \\backslash \\{a,b\\}$ is $N^*$-fragile."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.09713","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1603.09713/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}