{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:O2HATR22SICPUA4GI7ZKCGF4NO","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"44c6bd35f6b90d538ae35538a1064ea54524ddfd47f42616c2d5f3bb46ebc848","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2013-04-01T06:10:05Z","title_canon_sha256":"e3414a7de988805492b312a3bc0ad97915c2bdd8abc2f8ffaa87e0f29d1263d3"},"schema_version":"1.0","source":{"id":"1304.0299","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.0299","created_at":"2026-05-18T03:21:23Z"},{"alias_kind":"arxiv_version","alias_value":"1304.0299v2","created_at":"2026-05-18T03:21:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.0299","created_at":"2026-05-18T03:21:23Z"},{"alias_kind":"pith_short_12","alias_value":"O2HATR22SICP","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_16","alias_value":"O2HATR22SICPUA4G","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_8","alias_value":"O2HATR22","created_at":"2026-05-18T12:27:54Z"}],"graph_snapshots":[{"event_id":"sha256:0378bececd42842cc980b22b1a1a99aca66a14780950319615604afd834a877e","target":"graph","created_at":"2026-05-18T03:21:23Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We introduce a new matroid width parameter based on the operation of matroid amalgamation, which we call amalgam-width. The parameter is linearly related to branch-width on finitely representable matroids (which is not possible for branch-width). In particular, any property expressible in the monadic second order logic can be decided in linear time for matroids with bounded amalgam-width. We also prove that the Tutte polynomial can be computed in polynomial time for matroids with bounded amalgam width.","authors_text":"Lukas Mach, Tomas Toufar","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2013-04-01T06:10:05Z","title":"Amalgam width of matroids"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.0299","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:dbba328bf6d87b13716c74eaf862dfd7b07f709bb3434e8acce02c199c9391f9","target":"record","created_at":"2026-05-18T03:21:23Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"44c6bd35f6b90d538ae35538a1064ea54524ddfd47f42616c2d5f3bb46ebc848","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2013-04-01T06:10:05Z","title_canon_sha256":"e3414a7de988805492b312a3bc0ad97915c2bdd8abc2f8ffaa87e0f29d1263d3"},"schema_version":"1.0","source":{"id":"1304.0299","kind":"arxiv","version":2}},"canonical_sha256":"768e09c75a9204fa038647f2a118bc6bb2667161fc29e4ac5e0c0d8c6d9768c5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"768e09c75a9204fa038647f2a118bc6bb2667161fc29e4ac5e0c0d8c6d9768c5","first_computed_at":"2026-05-18T03:21:23.479614Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:21:23.479614Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bKfu+63MbBos204Wkul6u8pS7M2TVuQv6jd+ScsT0HCk5+UlIgYm9c5bshrzokKxp+KpBOODfGWYHVy/3UgBAA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:21:23.480148Z","signed_message":"canonical_sha256_bytes"},"source_id":"1304.0299","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dbba328bf6d87b13716c74eaf862dfd7b07f709bb3434e8acce02c199c9391f9","sha256:0378bececd42842cc980b22b1a1a99aca66a14780950319615604afd834a877e"],"state_sha256":"923152488a7a1a6eadaa436fb3c7350311c76ea3d0632abce09301680e52be89"}