{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:HQSNJNSYXZXGQWKHHL7EDHYSEN","short_pith_number":"pith:HQSNJNSY","canonical_record":{"source":{"id":"1403.2926","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2014-03-12T13:31:37Z","cross_cats_sorted":["cs.CC","cs.CG","math.CO"],"title_canon_sha256":"ca653e4777e058c0533d9810513c7f45c26005fbfc3ca1c41d1e5adb54b5d708","abstract_canon_sha256":"eb824ecb659fdc2195d9af9ef804b9deddf01c9b30fa8b58fa9bb534ff82720a"},"schema_version":"1.0"},"canonical_sha256":"3c24d4b658be6e6859473afe419f12235f158a01dead7ce313b1fd6cb95902e7","source":{"kind":"arxiv","id":"1403.2926","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.2926","created_at":"2026-05-18T02:56:33Z"},{"alias_kind":"arxiv_version","alias_value":"1403.2926v1","created_at":"2026-05-18T02:56:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.2926","created_at":"2026-05-18T02:56:33Z"},{"alias_kind":"pith_short_12","alias_value":"HQSNJNSYXZXG","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_16","alias_value":"HQSNJNSYXZXGQWKH","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_8","alias_value":"HQSNJNSY","created_at":"2026-05-18T12:28:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:HQSNJNSYXZXGQWKHHL7EDHYSEN","target":"record","payload":{"canonical_record":{"source":{"id":"1403.2926","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2014-03-12T13:31:37Z","cross_cats_sorted":["cs.CC","cs.CG","math.CO"],"title_canon_sha256":"ca653e4777e058c0533d9810513c7f45c26005fbfc3ca1c41d1e5adb54b5d708","abstract_canon_sha256":"eb824ecb659fdc2195d9af9ef804b9deddf01c9b30fa8b58fa9bb534ff82720a"},"schema_version":"1.0"},"canonical_sha256":"3c24d4b658be6e6859473afe419f12235f158a01dead7ce313b1fd6cb95902e7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:56:33.569111Z","signature_b64":"RhX7FJ7wuu1i0eNllI9/2T54rGtULx0hRQ4hy8h1hujyMOTkvq71Um4mOkI++HKHMgwSzWsIv+ol8rkcZHa/BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3c24d4b658be6e6859473afe419f12235f158a01dead7ce313b1fd6cb95902e7","last_reissued_at":"2026-05-18T02:56:33.568248Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:56:33.568248Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1403.2926","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:56:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OcZcTr3KmKckAyezyz4tec7NaYfenMxka3z7F87b595Rv8YkVvpEGWSf9rFx25kNtZhm6F5f9qC2/zR6HkvzBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T18:27:10.972425Z"},"content_sha256":"ef9737831fc7151a670909a6516569a3befeb4fa4d0f57695d884f5f328b91ba","schema_version":"1.0","event_id":"sha256:ef9737831fc7151a670909a6516569a3befeb4fa4d0f57695d884f5f328b91ba"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:HQSNJNSYXZXGQWKHHL7EDHYSEN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Courcelle's theorem for triangulations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","cs.CG","math.CO"],"primary_cat":"math.GT","authors_text":"Benjamin A. Burton, Rodney G. Downey","submitted_at":"2014-03-12T13:31:37Z","abstract_excerpt":"In graph theory, Courcelle's theorem essentially states that, if an algorithmic problem can be formulated in monadic second-order logic, then it can be solved in linear time for graphs of bounded treewidth. We prove such a metatheorem for a general class of triangulations of arbitrary fixed dimension d, including all triangulated d-manifolds: if an algorithmic problem can be expressed in monadic second-order logic, then it can be solved in linear time for triangulations whose dual graphs have bounded treewidth.\n  We apply our results to 3-manifold topology, a setting with many difficult comput"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.2926","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":""},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:56:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Bmlx06qhEIJGk8A9LzpLyCriJUnoTD1atPCKiSlqNt6Oyn5O0Ru2tSzp1lrOUvxKDeq+psKxEB4QgsKE6AUzAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T18:27:10.972978Z"},"content_sha256":"be773304240d300b86ab8404a89be242204dd71f20d056e4d29f64e8189ccade","schema_version":"1.0","event_id":"sha256:be773304240d300b86ab8404a89be242204dd71f20d056e4d29f64e8189ccade"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HQSNJNSYXZXGQWKHHL7EDHYSEN/bundle.json","state_url":"https://pith.science/pith/HQSNJNSYXZXGQWKHHL7EDHYSEN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HQSNJNSYXZXGQWKHHL7EDHYSEN/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-03T18:27:10Z","links":{"resolver":"https://pith.science/pith/HQSNJNSYXZXGQWKHHL7EDHYSEN","bundle":"https://pith.science/pith/HQSNJNSYXZXGQWKHHL7EDHYSEN/bundle.json","state":"https://pith.science/pith/HQSNJNSYXZXGQWKHHL7EDHYSEN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HQSNJNSYXZXGQWKHHL7EDHYSEN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:HQSNJNSYXZXGQWKHHL7EDHYSEN","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":"eb824ecb659fdc2195d9af9ef804b9deddf01c9b30fa8b58fa9bb534ff82720a","cross_cats_sorted":["cs.CC","cs.CG","math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2014-03-12T13:31:37Z","title_canon_sha256":"ca653e4777e058c0533d9810513c7f45c26005fbfc3ca1c41d1e5adb54b5d708"},"schema_version":"1.0","source":{"id":"1403.2926","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.2926","created_at":"2026-05-18T02:56:33Z"},{"alias_kind":"arxiv_version","alias_value":"1403.2926v1","created_at":"2026-05-18T02:56:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.2926","created_at":"2026-05-18T02:56:33Z"},{"alias_kind":"pith_short_12","alias_value":"HQSNJNSYXZXG","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_16","alias_value":"HQSNJNSYXZXGQWKH","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_8","alias_value":"HQSNJNSY","created_at":"2026-05-18T12:28:30Z"}],"graph_snapshots":[{"event_id":"sha256:be773304240d300b86ab8404a89be242204dd71f20d056e4d29f64e8189ccade","target":"graph","created_at":"2026-05-18T02:56:33Z","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":"In graph theory, Courcelle's theorem essentially states that, if an algorithmic problem can be formulated in monadic second-order logic, then it can be solved in linear time for graphs of bounded treewidth. We prove such a metatheorem for a general class of triangulations of arbitrary fixed dimension d, including all triangulated d-manifolds: if an algorithmic problem can be expressed in monadic second-order logic, then it can be solved in linear time for triangulations whose dual graphs have bounded treewidth.\n  We apply our results to 3-manifold topology, a setting with many difficult comput","authors_text":"Benjamin A. Burton, Rodney G. Downey","cross_cats":["cs.CC","cs.CG","math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2014-03-12T13:31:37Z","title":"Courcelle's theorem for triangulations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.2926","kind":"arxiv","version":1},"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:ef9737831fc7151a670909a6516569a3befeb4fa4d0f57695d884f5f328b91ba","target":"record","created_at":"2026-05-18T02:56:33Z","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":"eb824ecb659fdc2195d9af9ef804b9deddf01c9b30fa8b58fa9bb534ff82720a","cross_cats_sorted":["cs.CC","cs.CG","math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2014-03-12T13:31:37Z","title_canon_sha256":"ca653e4777e058c0533d9810513c7f45c26005fbfc3ca1c41d1e5adb54b5d708"},"schema_version":"1.0","source":{"id":"1403.2926","kind":"arxiv","version":1}},"canonical_sha256":"3c24d4b658be6e6859473afe419f12235f158a01dead7ce313b1fd6cb95902e7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3c24d4b658be6e6859473afe419f12235f158a01dead7ce313b1fd6cb95902e7","first_computed_at":"2026-05-18T02:56:33.568248Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:56:33.568248Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RhX7FJ7wuu1i0eNllI9/2T54rGtULx0hRQ4hy8h1hujyMOTkvq71Um4mOkI++HKHMgwSzWsIv+ol8rkcZHa/BQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:56:33.569111Z","signed_message":"canonical_sha256_bytes"},"source_id":"1403.2926","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ef9737831fc7151a670909a6516569a3befeb4fa4d0f57695d884f5f328b91ba","sha256:be773304240d300b86ab8404a89be242204dd71f20d056e4d29f64e8189ccade"],"state_sha256":"b0f70246c621ffdda9c984606358dc8ca6fad22315f5a4ee23af63943663b1c4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ah5nnZyZaI7A7gAS60+ENjCR3YbaTA+fK7YnDlQJAcU7RUsQhTdez9xbeDGqhPt4alWYDjW5HyHqSsIjkSjaCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T18:27:10.975560Z","bundle_sha256":"b43bd3cee29e6548d56852eebbb77114d92bb6b1ae55a635f568c9274de2b6c7"}}