{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:G5KARXNVBE3GIIL23IDM7GFW4M","short_pith_number":"pith:G5KARXNV","schema_version":"1.0","canonical_sha256":"375408ddb5093664217ada06cf98b6e317099e710ca9373b9e6a1da881d9e6a5","source":{"kind":"arxiv","id":"2412.18558","version":1},"attestation_state":"computed","paper":{"title":"A new way to prove configuration reducibility using gauge theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.CO","authors_text":"Ben McCarty, Scott Baldridge","submitted_at":"2024-12-24T17:21:07Z","abstract_excerpt":"We show how ideas coming out of gauge theory can be used to prove configurations in the list of ``633 unavoidable configurations\" are reducible. In this paper, we prove the smallest nontrivial example, the Birkhoff diamond, is reducible using our filtered $3$- and $4$-color homology. This is a new proof of a 111-year-old result that is a direct consequence of a special (2+1)-dimensional topological quantum field theory. As part of the proof, we introduce the idea of a state-reducible configuration. Because state-reducibility does not involve Kempe switches, this leads to an independent way to "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2412.18558","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2024-12-24T17:21:07Z","cross_cats_sorted":["math.GT"],"title_canon_sha256":"875325dd1290557dbdf1fab0714ca80633fba2009b237a439db6e476c263ca7a","abstract_canon_sha256":"3319b6c5a1f9c502b90f05213892b52483c97b1b0ba975cd3180f72b018ba54c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:53:57.514582Z","signature_b64":"qqC52bfsNmvvAJiHUL/dWx448F9XrJxFASn7sbrC9RfcHzcSN/L3nLc8PMmFYbhGby3lTb08/OyYaYtaw7DAAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"375408ddb5093664217ada06cf98b6e317099e710ca9373b9e6a1da881d9e6a5","last_reissued_at":"2026-07-05T09:53:57.514109Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:53:57.514109Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A new way to prove configuration reducibility using gauge theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.CO","authors_text":"Ben McCarty, Scott Baldridge","submitted_at":"2024-12-24T17:21:07Z","abstract_excerpt":"We show how ideas coming out of gauge theory can be used to prove configurations in the list of ``633 unavoidable configurations\" are reducible. In this paper, we prove the smallest nontrivial example, the Birkhoff diamond, is reducible using our filtered $3$- and $4$-color homology. This is a new proof of a 111-year-old result that is a direct consequence of a special (2+1)-dimensional topological quantum field theory. As part of the proof, we introduce the idea of a state-reducible configuration. Because state-reducibility does not involve Kempe switches, this leads to an independent way to "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.18558","kind":"arxiv","version":1},"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/2412.18558/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2412.18558","created_at":"2026-07-05T09:53:57.514165+00:00"},{"alias_kind":"arxiv_version","alias_value":"2412.18558v1","created_at":"2026-07-05T09:53:57.514165+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2412.18558","created_at":"2026-07-05T09:53:57.514165+00:00"},{"alias_kind":"pith_short_12","alias_value":"G5KARXNVBE3G","created_at":"2026-07-05T09:53:57.514165+00:00"},{"alias_kind":"pith_short_16","alias_value":"G5KARXNVBE3GIIL2","created_at":"2026-07-05T09:53:57.514165+00:00"},{"alias_kind":"pith_short_8","alias_value":"G5KARXNV","created_at":"2026-07-05T09:53:57.514165+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2606.06643","citing_title":"New relations for the Penrose polynomial","ref_index":6,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/G5KARXNVBE3GIIL23IDM7GFW4M","json":"https://pith.science/pith/G5KARXNVBE3GIIL23IDM7GFW4M.json","graph_json":"https://pith.science/api/pith-number/G5KARXNVBE3GIIL23IDM7GFW4M/graph.json","events_json":"https://pith.science/api/pith-number/G5KARXNVBE3GIIL23IDM7GFW4M/events.json","paper":"https://pith.science/paper/G5KARXNV"},"agent_actions":{"view_html":"https://pith.science/pith/G5KARXNVBE3GIIL23IDM7GFW4M","download_json":"https://pith.science/pith/G5KARXNVBE3GIIL23IDM7GFW4M.json","view_paper":"https://pith.science/paper/G5KARXNV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2412.18558&json=true","fetch_graph":"https://pith.science/api/pith-number/G5KARXNVBE3GIIL23IDM7GFW4M/graph.json","fetch_events":"https://pith.science/api/pith-number/G5KARXNVBE3GIIL23IDM7GFW4M/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/G5KARXNVBE3GIIL23IDM7GFW4M/action/timestamp_anchor","attest_storage":"https://pith.science/pith/G5KARXNVBE3GIIL23IDM7GFW4M/action/storage_attestation","attest_author":"https://pith.science/pith/G5KARXNVBE3GIIL23IDM7GFW4M/action/author_attestation","sign_citation":"https://pith.science/pith/G5KARXNVBE3GIIL23IDM7GFW4M/action/citation_signature","submit_replication":"https://pith.science/pith/G5KARXNVBE3GIIL23IDM7GFW4M/action/replication_record"}},"created_at":"2026-07-05T09:53:57.514165+00:00","updated_at":"2026-07-05T09:53:57.514165+00:00"}