{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:T4UQVKEWMIUVAOWINSOEIREXB2","short_pith_number":"pith:T4UQVKEW","canonical_record":{"source":{"id":"1106.4489","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2011-06-22T15:59:40Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"39d1c5825b07f2dd2e03687e974555d2cc43b4df322dfa4b0874ac7259d0db61","abstract_canon_sha256":"865341149b10c2c2e58bf716737df88c86b7ae2f08bc953d1f62cb9f1b40db08"},"schema_version":"1.0"},"canonical_sha256":"9f290aa8966229503ac86c9c4444970e9eaf5f26e1d4c951dc5157f562991f55","source":{"kind":"arxiv","id":"1106.4489","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1106.4489","created_at":"2026-05-18T04:19:32Z"},{"alias_kind":"arxiv_version","alias_value":"1106.4489v1","created_at":"2026-05-18T04:19:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1106.4489","created_at":"2026-05-18T04:19:32Z"},{"alias_kind":"pith_short_12","alias_value":"T4UQVKEWMIUV","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_16","alias_value":"T4UQVKEWMIUVAOWI","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_8","alias_value":"T4UQVKEW","created_at":"2026-05-18T12:26:41Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:T4UQVKEWMIUVAOWINSOEIREXB2","target":"record","payload":{"canonical_record":{"source":{"id":"1106.4489","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2011-06-22T15:59:40Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"39d1c5825b07f2dd2e03687e974555d2cc43b4df322dfa4b0874ac7259d0db61","abstract_canon_sha256":"865341149b10c2c2e58bf716737df88c86b7ae2f08bc953d1f62cb9f1b40db08"},"schema_version":"1.0"},"canonical_sha256":"9f290aa8966229503ac86c9c4444970e9eaf5f26e1d4c951dc5157f562991f55","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:19:32.882169Z","signature_b64":"j0STtzgOUDoIp1XhMYXlTs5qoy961Ei7NsD95QiPRJA27SFIUM1IOZcZumitZzFE48aRsAuI2D4OpujC5apyAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9f290aa8966229503ac86c9c4444970e9eaf5f26e1d4c951dc5157f562991f55","last_reissued_at":"2026-05-18T04:19:32.881752Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:19:32.881752Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1106.4489","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":"2026-05-18T04:19:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZkmdmGie+L1z1qWTLL0eElG8YrDY701QHF6qpen8nIWNxVfr42dtFq7VHjIKV7InhslzxXfaqgDZQ1c6Vt5zBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-02T07:08:42.465732Z"},"content_sha256":"a5cc63e0d14382f6561de98de4237583d3ad07d18cea64cc38bcab32e9f95821","schema_version":"1.0","event_id":"sha256:a5cc63e0d14382f6561de98de4237583d3ad07d18cea64cc38bcab32e9f95821"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:T4UQVKEWMIUVAOWINSOEIREXB2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Fast Isomorphism Testing of Graphs with Regularly-Connected Components","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"cs.DS","authors_text":"Antonio Fernandez Anta, Jose Luis Lopez-Presa","submitted_at":"2011-06-22T15:59:40Z","abstract_excerpt":"The Graph Isomorphism problem has both theoretical and practical interest. In this paper we present an algorithm, called conauto-1.2, that efficiently tests whether two graphs are isomorphic, and finds an isomorphism if they are. This algorithm is an improved version of the algorithm conauto, which has been shown to be very fast for random graphs and several families of hard graphs. In this paper we establish a new theorem that allows, at very low cost, the easy discovery of many automorphisms. This result is especially suited for graphs with regularly connected components, and can be applied "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.4489","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":"2026-05-18T04:19:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IHSxeCAtP5McdZC31IKS1Md+WI7C/e7GhapY6o3rEPvBY8UEE+gec6xiTnTggDXGBY/ekngH6aiw4f5bYpjvCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-02T07:08:42.466087Z"},"content_sha256":"521241401f8db6089861514b5dc329ba6a380e375a7b3a2ae694f5c313a0cfe6","schema_version":"1.0","event_id":"sha256:521241401f8db6089861514b5dc329ba6a380e375a7b3a2ae694f5c313a0cfe6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/T4UQVKEWMIUVAOWINSOEIREXB2/bundle.json","state_url":"https://pith.science/pith/T4UQVKEWMIUVAOWINSOEIREXB2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/T4UQVKEWMIUVAOWINSOEIREXB2/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":"2026-07-02T07:08:42Z","links":{"resolver":"https://pith.science/pith/T4UQVKEWMIUVAOWINSOEIREXB2","bundle":"https://pith.science/pith/T4UQVKEWMIUVAOWINSOEIREXB2/bundle.json","state":"https://pith.science/pith/T4UQVKEWMIUVAOWINSOEIREXB2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/T4UQVKEWMIUVAOWINSOEIREXB2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:T4UQVKEWMIUVAOWINSOEIREXB2","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":"865341149b10c2c2e58bf716737df88c86b7ae2f08bc953d1f62cb9f1b40db08","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2011-06-22T15:59:40Z","title_canon_sha256":"39d1c5825b07f2dd2e03687e974555d2cc43b4df322dfa4b0874ac7259d0db61"},"schema_version":"1.0","source":{"id":"1106.4489","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1106.4489","created_at":"2026-05-18T04:19:32Z"},{"alias_kind":"arxiv_version","alias_value":"1106.4489v1","created_at":"2026-05-18T04:19:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1106.4489","created_at":"2026-05-18T04:19:32Z"},{"alias_kind":"pith_short_12","alias_value":"T4UQVKEWMIUV","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_16","alias_value":"T4UQVKEWMIUVAOWI","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_8","alias_value":"T4UQVKEW","created_at":"2026-05-18T12:26:41Z"}],"graph_snapshots":[{"event_id":"sha256:521241401f8db6089861514b5dc329ba6a380e375a7b3a2ae694f5c313a0cfe6","target":"graph","created_at":"2026-05-18T04:19:32Z","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":"The Graph Isomorphism problem has both theoretical and practical interest. In this paper we present an algorithm, called conauto-1.2, that efficiently tests whether two graphs are isomorphic, and finds an isomorphism if they are. This algorithm is an improved version of the algorithm conauto, which has been shown to be very fast for random graphs and several families of hard graphs. In this paper we establish a new theorem that allows, at very low cost, the easy discovery of many automorphisms. This result is especially suited for graphs with regularly connected components, and can be applied ","authors_text":"Antonio Fernandez Anta, Jose Luis Lopez-Presa","cross_cats":["cs.DM"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2011-06-22T15:59:40Z","title":"Fast Isomorphism Testing of Graphs with Regularly-Connected Components"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.4489","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:a5cc63e0d14382f6561de98de4237583d3ad07d18cea64cc38bcab32e9f95821","target":"record","created_at":"2026-05-18T04:19:32Z","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":"865341149b10c2c2e58bf716737df88c86b7ae2f08bc953d1f62cb9f1b40db08","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2011-06-22T15:59:40Z","title_canon_sha256":"39d1c5825b07f2dd2e03687e974555d2cc43b4df322dfa4b0874ac7259d0db61"},"schema_version":"1.0","source":{"id":"1106.4489","kind":"arxiv","version":1}},"canonical_sha256":"9f290aa8966229503ac86c9c4444970e9eaf5f26e1d4c951dc5157f562991f55","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9f290aa8966229503ac86c9c4444970e9eaf5f26e1d4c951dc5157f562991f55","first_computed_at":"2026-05-18T04:19:32.881752Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:19:32.881752Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"j0STtzgOUDoIp1XhMYXlTs5qoy961Ei7NsD95QiPRJA27SFIUM1IOZcZumitZzFE48aRsAuI2D4OpujC5apyAg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:19:32.882169Z","signed_message":"canonical_sha256_bytes"},"source_id":"1106.4489","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a5cc63e0d14382f6561de98de4237583d3ad07d18cea64cc38bcab32e9f95821","sha256:521241401f8db6089861514b5dc329ba6a380e375a7b3a2ae694f5c313a0cfe6"],"state_sha256":"9b49519473a3839d998343fa1f3567d52543ea36983a14983b12607700515811"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XOMSNhzQnBZkDLy4Zg71IcLDDeV9sCzLJKhyMaYo2hMcXkbjSI10HfC57iRCMgHhf2MWGidjjafKPV8R25EVDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-02T07:08:42.468137Z","bundle_sha256":"36cf023e6b2d654a21b5194b3b9ebfcedf0f45137a2c8718f58cc6d2640da044"}}