{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:XDYMHYVZWDQHKOYM6NLXVQPF3B","short_pith_number":"pith:XDYMHYVZ","schema_version":"1.0","canonical_sha256":"b8f0c3e2b9b0e0753b0cf3577ac1e5d84610b73ff93484c7051fd30867de1ce4","source":{"kind":"arxiv","id":"1312.3537","version":2},"attestation_state":"computed","paper":{"title":"Computing the Tutte Polynomial of Lattice Path Matroids Using Determinantal Circuits","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC"],"primary_cat":"math.CO","authors_text":"Jacob Turner, Jason Morton","submitted_at":"2013-12-12T16:32:33Z","abstract_excerpt":"We give a quantum-inspired $O(n^4)$ algorithm computing the Tutte polynomial of a lattice path matroid, where $n$ is the size of the ground set of the matroid. Furthermore, this can be improved to $O(n^2)$ arithmetic operations if we evaluate the Tutte polynomial on a given input, fixing the values of the variables. The best existing algorithm, found in 2004, was $O(n^5)$, and the problem has only been known to be polynomial time since 2003. Conceptually, our algorithm embeds the computation in a determinant using a recently demonstrated equivalence of categories useful for counting problems s"},"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":"1312.3537","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-12-12T16:32:33Z","cross_cats_sorted":["cs.CC"],"title_canon_sha256":"055bde6d8a9f4c37a9fcdad937ee2226bb5920303439782ee3824d771f02db0b","abstract_canon_sha256":"5cbd949a8cc784be5aefea8e830be280b017768a476222a825b554cd2e9980f5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:30:55.613118Z","signature_b64":"k7K/9mnN3GC+Nb/s6yzurBsH/ya36wRX5Bq1+SjQNMnfbhSmGV2qW0rGa5NedAgPWznR4lajVdYowLh+rlGTBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b8f0c3e2b9b0e0753b0cf3577ac1e5d84610b73ff93484c7051fd30867de1ce4","last_reissued_at":"2026-05-18T01:30:55.612543Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:30:55.612543Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Computing the Tutte Polynomial of Lattice Path Matroids Using Determinantal Circuits","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC"],"primary_cat":"math.CO","authors_text":"Jacob Turner, Jason Morton","submitted_at":"2013-12-12T16:32:33Z","abstract_excerpt":"We give a quantum-inspired $O(n^4)$ algorithm computing the Tutte polynomial of a lattice path matroid, where $n$ is the size of the ground set of the matroid. Furthermore, this can be improved to $O(n^2)$ arithmetic operations if we evaluate the Tutte polynomial on a given input, fixing the values of the variables. The best existing algorithm, found in 2004, was $O(n^5)$, and the problem has only been known to be polynomial time since 2003. Conceptually, our algorithm embeds the computation in a determinant using a recently demonstrated equivalence of categories useful for counting problems s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.3537","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":""},"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":"1312.3537","created_at":"2026-05-18T01:30:55.612673+00:00"},{"alias_kind":"arxiv_version","alias_value":"1312.3537v2","created_at":"2026-05-18T01:30:55.612673+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.3537","created_at":"2026-05-18T01:30:55.612673+00:00"},{"alias_kind":"pith_short_12","alias_value":"XDYMHYVZWDQH","created_at":"2026-05-18T12:28:06.772260+00:00"},{"alias_kind":"pith_short_16","alias_value":"XDYMHYVZWDQHKOYM","created_at":"2026-05-18T12:28:06.772260+00:00"},{"alias_kind":"pith_short_8","alias_value":"XDYMHYVZ","created_at":"2026-05-18T12:28:06.772260+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/XDYMHYVZWDQHKOYM6NLXVQPF3B","json":"https://pith.science/pith/XDYMHYVZWDQHKOYM6NLXVQPF3B.json","graph_json":"https://pith.science/api/pith-number/XDYMHYVZWDQHKOYM6NLXVQPF3B/graph.json","events_json":"https://pith.science/api/pith-number/XDYMHYVZWDQHKOYM6NLXVQPF3B/events.json","paper":"https://pith.science/paper/XDYMHYVZ"},"agent_actions":{"view_html":"https://pith.science/pith/XDYMHYVZWDQHKOYM6NLXVQPF3B","download_json":"https://pith.science/pith/XDYMHYVZWDQHKOYM6NLXVQPF3B.json","view_paper":"https://pith.science/paper/XDYMHYVZ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1312.3537&json=true","fetch_graph":"https://pith.science/api/pith-number/XDYMHYVZWDQHKOYM6NLXVQPF3B/graph.json","fetch_events":"https://pith.science/api/pith-number/XDYMHYVZWDQHKOYM6NLXVQPF3B/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XDYMHYVZWDQHKOYM6NLXVQPF3B/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XDYMHYVZWDQHKOYM6NLXVQPF3B/action/storage_attestation","attest_author":"https://pith.science/pith/XDYMHYVZWDQHKOYM6NLXVQPF3B/action/author_attestation","sign_citation":"https://pith.science/pith/XDYMHYVZWDQHKOYM6NLXVQPF3B/action/citation_signature","submit_replication":"https://pith.science/pith/XDYMHYVZWDQHKOYM6NLXVQPF3B/action/replication_record"}},"created_at":"2026-05-18T01:30:55.612673+00:00","updated_at":"2026-05-18T01:30:55.612673+00:00"}