{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:A2DTNQSP3QRH766IHRUB3YJER4","short_pith_number":"pith:A2DTNQSP","canonical_record":{"source":{"id":"1310.0185","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2013-10-01T08:35:14Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"dd513ae3e1ce3997eba04acb7aa8d32c40899dc2e04ec429ef6b30d2c9c9f41a","abstract_canon_sha256":"56b3d50e56b0ca8c0c1762634890d0a684dc9e165b618fcf6dbdbddba975da7d"},"schema_version":"1.0"},"canonical_sha256":"068736c24fdc227ffbc83c681de1248f21be402e153fd8c585feda271cc97ed7","source":{"kind":"arxiv","id":"1310.0185","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.0185","created_at":"2026-05-18T03:11:45Z"},{"alias_kind":"arxiv_version","alias_value":"1310.0185v1","created_at":"2026-05-18T03:11:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.0185","created_at":"2026-05-18T03:11:45Z"},{"alias_kind":"pith_short_12","alias_value":"A2DTNQSP3QRH","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_16","alias_value":"A2DTNQSP3QRH766I","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_8","alias_value":"A2DTNQSP","created_at":"2026-05-18T12:27:38Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:A2DTNQSP3QRH766IHRUB3YJER4","target":"record","payload":{"canonical_record":{"source":{"id":"1310.0185","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2013-10-01T08:35:14Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"dd513ae3e1ce3997eba04acb7aa8d32c40899dc2e04ec429ef6b30d2c9c9f41a","abstract_canon_sha256":"56b3d50e56b0ca8c0c1762634890d0a684dc9e165b618fcf6dbdbddba975da7d"},"schema_version":"1.0"},"canonical_sha256":"068736c24fdc227ffbc83c681de1248f21be402e153fd8c585feda271cc97ed7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:11:45.237197Z","signature_b64":"mwGzDubh3xuP3WF9zVP1xkNaZi1lcplfPqur3DlfpOBhH8ofyI+eidTfzoXha4hz//J7m68ZRur9ojjm62fHAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"068736c24fdc227ffbc83c681de1248f21be402e153fd8c585feda271cc97ed7","last_reissued_at":"2026-05-18T03:11:45.236599Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:11:45.236599Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1310.0185","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":"2026-05-18T03:11:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qYGnJKHj7NI1MpP2QP5ZCZqnByzdeMkNz2qxc0+TQIjqpc2/Olge7HXdfNKj4wpLjFhq8n5wxCarsEXoSzFDCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T09:08:24.261087Z"},"content_sha256":"c6176bdfbcf9646f0bb7e909b0fbf76c29a83d3f99452e5b0eaeac0d7c18d4c4","schema_version":"1.0","event_id":"sha256:c6176bdfbcf9646f0bb7e909b0fbf76c29a83d3f99452e5b0eaeac0d7c18d4c4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:A2DTNQSP3QRH766IHRUB3YJER4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Exact counting of Euler Tours for Graphs of Bounded Treewidth","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"cs.DM","authors_text":"Mary Cryan, Prasad Chebolu, Russell Martin","submitted_at":"2013-10-01T08:35:14Z","abstract_excerpt":"In this paper we give a simple polynomial-time algorithm to exactly count the number of Euler Tours (ETs) of any Eulerian graph of bounded treewidth. The problems of counting ETs are known to be #P-complete for general graphs (Brightwell and Winkler, (Brightwell and Winkler, 2005). To date, no polynomial-time algorithm for counting Euler tours of any class of graphs is known except for the very special case of series-parallel graphs (which have treewidth 2)."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.0185","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":"2026-05-18T03:11:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iIf3Xdukn9AnxbJnwBikIG96gv7CX0gJAd7muF1kQwaKgEQHbTrv9yTDEATyOvWhq+GqQyuqSIxLbFaJOx8xDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T09:08:24.261450Z"},"content_sha256":"e4efc20ee8a6e30e67a91db7a2b8d6eef20c7736f81ff638312609b5f16b0880","schema_version":"1.0","event_id":"sha256:e4efc20ee8a6e30e67a91db7a2b8d6eef20c7736f81ff638312609b5f16b0880"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/A2DTNQSP3QRH766IHRUB3YJER4/bundle.json","state_url":"https://pith.science/pith/A2DTNQSP3QRH766IHRUB3YJER4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/A2DTNQSP3QRH766IHRUB3YJER4/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":"2026-06-24T09:08:24Z","links":{"resolver":"https://pith.science/pith/A2DTNQSP3QRH766IHRUB3YJER4","bundle":"https://pith.science/pith/A2DTNQSP3QRH766IHRUB3YJER4/bundle.json","state":"https://pith.science/pith/A2DTNQSP3QRH766IHRUB3YJER4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/A2DTNQSP3QRH766IHRUB3YJER4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:A2DTNQSP3QRH766IHRUB3YJER4","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":"56b3d50e56b0ca8c0c1762634890d0a684dc9e165b618fcf6dbdbddba975da7d","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2013-10-01T08:35:14Z","title_canon_sha256":"dd513ae3e1ce3997eba04acb7aa8d32c40899dc2e04ec429ef6b30d2c9c9f41a"},"schema_version":"1.0","source":{"id":"1310.0185","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.0185","created_at":"2026-05-18T03:11:45Z"},{"alias_kind":"arxiv_version","alias_value":"1310.0185v1","created_at":"2026-05-18T03:11:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.0185","created_at":"2026-05-18T03:11:45Z"},{"alias_kind":"pith_short_12","alias_value":"A2DTNQSP3QRH","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_16","alias_value":"A2DTNQSP3QRH766I","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_8","alias_value":"A2DTNQSP","created_at":"2026-05-18T12:27:38Z"}],"graph_snapshots":[{"event_id":"sha256:e4efc20ee8a6e30e67a91db7a2b8d6eef20c7736f81ff638312609b5f16b0880","target":"graph","created_at":"2026-05-18T03:11:45Z","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 this paper we give a simple polynomial-time algorithm to exactly count the number of Euler Tours (ETs) of any Eulerian graph of bounded treewidth. The problems of counting ETs are known to be #P-complete for general graphs (Brightwell and Winkler, (Brightwell and Winkler, 2005). To date, no polynomial-time algorithm for counting Euler tours of any class of graphs is known except for the very special case of series-parallel graphs (which have treewidth 2).","authors_text":"Mary Cryan, Prasad Chebolu, Russell Martin","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2013-10-01T08:35:14Z","title":"Exact counting of Euler Tours for Graphs of Bounded Treewidth"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.0185","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:c6176bdfbcf9646f0bb7e909b0fbf76c29a83d3f99452e5b0eaeac0d7c18d4c4","target":"record","created_at":"2026-05-18T03:11:45Z","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":"56b3d50e56b0ca8c0c1762634890d0a684dc9e165b618fcf6dbdbddba975da7d","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2013-10-01T08:35:14Z","title_canon_sha256":"dd513ae3e1ce3997eba04acb7aa8d32c40899dc2e04ec429ef6b30d2c9c9f41a"},"schema_version":"1.0","source":{"id":"1310.0185","kind":"arxiv","version":1}},"canonical_sha256":"068736c24fdc227ffbc83c681de1248f21be402e153fd8c585feda271cc97ed7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"068736c24fdc227ffbc83c681de1248f21be402e153fd8c585feda271cc97ed7","first_computed_at":"2026-05-18T03:11:45.236599Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:11:45.236599Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mwGzDubh3xuP3WF9zVP1xkNaZi1lcplfPqur3DlfpOBhH8ofyI+eidTfzoXha4hz//J7m68ZRur9ojjm62fHAA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:11:45.237197Z","signed_message":"canonical_sha256_bytes"},"source_id":"1310.0185","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c6176bdfbcf9646f0bb7e909b0fbf76c29a83d3f99452e5b0eaeac0d7c18d4c4","sha256:e4efc20ee8a6e30e67a91db7a2b8d6eef20c7736f81ff638312609b5f16b0880"],"state_sha256":"c3dc2512fab939808cf4213559c7fe38566ff373f6327d3fbbb6fc5540722564"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XtjxFEpL0Y6yFe33kn7Kxgc4AY1yNabzEYEJYCUMwvBpvH2vsFZ63vkW59pqUdJEnfaQrWzQD8/jMYuf6QC6CQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T09:08:24.263448Z","bundle_sha256":"95b842b17d8fd194390c41101d34d7dbebf00209c30d94ccfb409da75aa67adc"}}