{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:TJC74CKMA5BDASDQKHHWEUJG4K","short_pith_number":"pith:TJC74CKM","canonical_record":{"source":{"id":"1205.2766","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2012-05-12T11:12:10Z","cross_cats_sorted":[],"title_canon_sha256":"13bd6568bd3f901b98911e127345d4388e1f4bd5d33a9e88d17cc64b905a1a0d","abstract_canon_sha256":"a7e199e4d9a4341b0ad86b98a7fd50650cf9889d68c946464555b63afa2599f3"},"schema_version":"1.0"},"canonical_sha256":"9a45fe094c074230487051cf625126e29cf15182245467ba28ecfc3d21d87547","source":{"kind":"arxiv","id":"1205.2766","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.2766","created_at":"2026-05-18T03:51:46Z"},{"alias_kind":"arxiv_version","alias_value":"1205.2766v2","created_at":"2026-05-18T03:51:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.2766","created_at":"2026-05-18T03:51:46Z"},{"alias_kind":"pith_short_12","alias_value":"TJC74CKMA5BD","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_16","alias_value":"TJC74CKMA5BDASDQ","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_8","alias_value":"TJC74CKM","created_at":"2026-05-18T12:27:23Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:TJC74CKMA5BDASDQKHHWEUJG4K","target":"record","payload":{"canonical_record":{"source":{"id":"1205.2766","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2012-05-12T11:12:10Z","cross_cats_sorted":[],"title_canon_sha256":"13bd6568bd3f901b98911e127345d4388e1f4bd5d33a9e88d17cc64b905a1a0d","abstract_canon_sha256":"a7e199e4d9a4341b0ad86b98a7fd50650cf9889d68c946464555b63afa2599f3"},"schema_version":"1.0"},"canonical_sha256":"9a45fe094c074230487051cf625126e29cf15182245467ba28ecfc3d21d87547","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:51:46.989857Z","signature_b64":"n4e4wDPQDMoHrAiwtFcJvMoVUBpEc5G6C2uItsR6lDVVHM7ToOd/0k8MMxkcYxWKr9LOx+26MiO037Up1AFuCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9a45fe094c074230487051cf625126e29cf15182245467ba28ecfc3d21d87547","last_reissued_at":"2026-05-18T03:51:46.988949Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:51:46.988949Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1205.2766","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:51:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dFPDuU/MYHaoL29CTFXs9VnvNKV3GUltmQHpoRkmkCQ0vbg0Je+4CoBtHrnj3hO5GmPOUcTj7qpl4Jk7Q+9oBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T08:01:53.492533Z"},"content_sha256":"15721eff120a27114e253d501d24232f0eb95d610183f6efe53c73acaf18d5f9","schema_version":"1.0","event_id":"sha256:15721eff120a27114e253d501d24232f0eb95d610183f6efe53c73acaf18d5f9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:TJC74CKMA5BDASDQKHHWEUJG4K","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Optimal Listing of Cycles and st-Paths in Undirected Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Andrea Marino, Gustavo Sacomoto, Nadia Pisanti, Roberto Grossi, Romeo Rizzi, Rui Ferreira","submitted_at":"2012-05-12T11:12:10Z","abstract_excerpt":"We present the first optimal algorithm for the classical problem of listing all the cycles in an undirected graph. We exploit their properties so that the total cost is the time taken to read the input graph plus the time to list the output, namely, the edges in each of the cycles. The algorithm uses a reduction to the problem of listing all the paths from a vertex s to a vertex t which we also solve optimally."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.2766","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:51:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0wNkMUQTbokXX1NTfdv1LPJTZyaGbLR10gLJ4P1dSMcZGdG6GjjcMKs/YS3dB/4ASD0wqQqNel4yXl+JGbXAAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T08:01:53.493164Z"},"content_sha256":"6df502afc351f1a76252fc54bd3fb1178c45884166e9e0d303b5c848d3f807d0","schema_version":"1.0","event_id":"sha256:6df502afc351f1a76252fc54bd3fb1178c45884166e9e0d303b5c848d3f807d0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TJC74CKMA5BDASDQKHHWEUJG4K/bundle.json","state_url":"https://pith.science/pith/TJC74CKMA5BDASDQKHHWEUJG4K/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TJC74CKMA5BDASDQKHHWEUJG4K/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":"2026-06-09T08:01:53Z","links":{"resolver":"https://pith.science/pith/TJC74CKMA5BDASDQKHHWEUJG4K","bundle":"https://pith.science/pith/TJC74CKMA5BDASDQKHHWEUJG4K/bundle.json","state":"https://pith.science/pith/TJC74CKMA5BDASDQKHHWEUJG4K/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TJC74CKMA5BDASDQKHHWEUJG4K/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:TJC74CKMA5BDASDQKHHWEUJG4K","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":"a7e199e4d9a4341b0ad86b98a7fd50650cf9889d68c946464555b63afa2599f3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2012-05-12T11:12:10Z","title_canon_sha256":"13bd6568bd3f901b98911e127345d4388e1f4bd5d33a9e88d17cc64b905a1a0d"},"schema_version":"1.0","source":{"id":"1205.2766","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.2766","created_at":"2026-05-18T03:51:46Z"},{"alias_kind":"arxiv_version","alias_value":"1205.2766v2","created_at":"2026-05-18T03:51:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.2766","created_at":"2026-05-18T03:51:46Z"},{"alias_kind":"pith_short_12","alias_value":"TJC74CKMA5BD","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_16","alias_value":"TJC74CKMA5BDASDQ","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_8","alias_value":"TJC74CKM","created_at":"2026-05-18T12:27:23Z"}],"graph_snapshots":[{"event_id":"sha256:6df502afc351f1a76252fc54bd3fb1178c45884166e9e0d303b5c848d3f807d0","target":"graph","created_at":"2026-05-18T03:51:46Z","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 present the first optimal algorithm for the classical problem of listing all the cycles in an undirected graph. We exploit their properties so that the total cost is the time taken to read the input graph plus the time to list the output, namely, the edges in each of the cycles. The algorithm uses a reduction to the problem of listing all the paths from a vertex s to a vertex t which we also solve optimally.","authors_text":"Andrea Marino, Gustavo Sacomoto, Nadia Pisanti, Roberto Grossi, Romeo Rizzi, Rui Ferreira","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2012-05-12T11:12:10Z","title":"Optimal Listing of Cycles and st-Paths in Undirected Graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.2766","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":"sha256:15721eff120a27114e253d501d24232f0eb95d610183f6efe53c73acaf18d5f9","target":"record","created_at":"2026-05-18T03:51:46Z","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":"a7e199e4d9a4341b0ad86b98a7fd50650cf9889d68c946464555b63afa2599f3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2012-05-12T11:12:10Z","title_canon_sha256":"13bd6568bd3f901b98911e127345d4388e1f4bd5d33a9e88d17cc64b905a1a0d"},"schema_version":"1.0","source":{"id":"1205.2766","kind":"arxiv","version":2}},"canonical_sha256":"9a45fe094c074230487051cf625126e29cf15182245467ba28ecfc3d21d87547","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9a45fe094c074230487051cf625126e29cf15182245467ba28ecfc3d21d87547","first_computed_at":"2026-05-18T03:51:46.988949Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:51:46.988949Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"n4e4wDPQDMoHrAiwtFcJvMoVUBpEc5G6C2uItsR6lDVVHM7ToOd/0k8MMxkcYxWKr9LOx+26MiO037Up1AFuCg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:51:46.989857Z","signed_message":"canonical_sha256_bytes"},"source_id":"1205.2766","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:15721eff120a27114e253d501d24232f0eb95d610183f6efe53c73acaf18d5f9","sha256:6df502afc351f1a76252fc54bd3fb1178c45884166e9e0d303b5c848d3f807d0"],"state_sha256":"35082f370c06d04dfef3fdf01d1d5ec28de7bc1fd7e9e94009fa15922405d887"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IYkklungkP2k0gCv3ezggi9WEdPcwJ3mkbvlrtvS9JMPmQtDL9Hyfj/ZxVq4MptA2no2wdhMaksDKRvse21+Bw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T08:01:53.496940Z","bundle_sha256":"a674afc51205904933b485dafaef986bda88e92e8aace035c84412401732fde7"}}