{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2006:UUD2HO7QG44RXVANFUJA6CUXHU","short_pith_number":"pith:UUD2HO7Q","canonical_record":{"source":{"id":"math/0611679","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.CO","submitted_at":"2006-11-22T10:47:05Z","cross_cats_sorted":["cs.DM","cs.DS"],"title_canon_sha256":"f53b3c041e3fe8f04fdbeaedd00f5304600a1adfdaace2688d351000ea7d5767","abstract_canon_sha256":"47a86fffb8c053c500d25441d636829c6a95b7a45b2578c4dab45d0f7b5c5708"},"schema_version":"1.0"},"canonical_sha256":"a507a3bbf037391bd40d2d120f0a973d2347060bc8befc6d6187e20637d0808b","source":{"kind":"arxiv","id":"math/0611679","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0611679","created_at":"2026-05-18T02:41:26Z"},{"alias_kind":"arxiv_version","alias_value":"math/0611679v1","created_at":"2026-05-18T02:41:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0611679","created_at":"2026-05-18T02:41:26Z"},{"alias_kind":"pith_short_12","alias_value":"UUD2HO7QG44R","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_16","alias_value":"UUD2HO7QG44RXVAN","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_8","alias_value":"UUD2HO7Q","created_at":"2026-05-18T12:25:54Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2006:UUD2HO7QG44RXVANFUJA6CUXHU","target":"record","payload":{"canonical_record":{"source":{"id":"math/0611679","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.CO","submitted_at":"2006-11-22T10:47:05Z","cross_cats_sorted":["cs.DM","cs.DS"],"title_canon_sha256":"f53b3c041e3fe8f04fdbeaedd00f5304600a1adfdaace2688d351000ea7d5767","abstract_canon_sha256":"47a86fffb8c053c500d25441d636829c6a95b7a45b2578c4dab45d0f7b5c5708"},"schema_version":"1.0"},"canonical_sha256":"a507a3bbf037391bd40d2d120f0a973d2347060bc8befc6d6187e20637d0808b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:41:26.676822Z","signature_b64":"nRmBu8D+uUO5V7nxEqzk0H0hjeGSzFmSwqVHAwzJ59hjuL7A0A4UwQu86GNwE+BC+/8bBxHVcxz3BqA85lncAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a507a3bbf037391bd40d2d120f0a973d2347060bc8befc6d6187e20637d0808b","last_reissued_at":"2026-05-18T02:41:26.676362Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:41:26.676362Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0611679","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":"2026-05-18T02:41:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nYmYWExJeUo1sItVvpcFuR26FTUNLMOs6r8YdVVy6LelD2CLJJw1FE1opaflUm2zs5t2bfAZRGC5XKThHfo/Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T12:00:27.387352Z"},"content_sha256":"0b80ad31543262701cd615dc6137c17ce527f8f01b96c3ed5949a5fac560987f","schema_version":"1.0","event_id":"sha256:0b80ad31543262701cd615dc6137c17ce527f8f01b96c3ed5949a5fac560987f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2006:UUD2HO7QG44RXVANFUJA6CUXHU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Longest Common Pattern between two Permutations","license":"","headline":"","cross_cats":["cs.DM","cs.DS"],"primary_cat":"math.CO","authors_text":"Dominique Rossin (LIAFA), Mathilde Bouvel (LIAFA)","submitted_at":"2006-11-22T10:47:05Z","abstract_excerpt":"In this paper, we give a polynomial (O(n^8)) algorithm for finding a longest common pattern between two permutations of size n given that one is separable. We also give an algorithm for general permutations whose complexity depends on the length of the longest simple permutation involved in one of our permutations."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0611679","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":"2026-05-18T02:41:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hG49PO1ImSGhB0fgjP4T5eABMMQt+ujaL/vhD51eVVIqRHdwHaKoFH+4kf/xc7X8NUjVGtbqR1jOCMdU8obmAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T12:00:27.387690Z"},"content_sha256":"cc62f6fc6f4d2a7fa2226d575f9fd263add34294e52c273b41d3417bf0eba94b","schema_version":"1.0","event_id":"sha256:cc62f6fc6f4d2a7fa2226d575f9fd263add34294e52c273b41d3417bf0eba94b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UUD2HO7QG44RXVANFUJA6CUXHU/bundle.json","state_url":"https://pith.science/pith/UUD2HO7QG44RXVANFUJA6CUXHU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UUD2HO7QG44RXVANFUJA6CUXHU/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":"2026-06-08T12:00:27Z","links":{"resolver":"https://pith.science/pith/UUD2HO7QG44RXVANFUJA6CUXHU","bundle":"https://pith.science/pith/UUD2HO7QG44RXVANFUJA6CUXHU/bundle.json","state":"https://pith.science/pith/UUD2HO7QG44RXVANFUJA6CUXHU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UUD2HO7QG44RXVANFUJA6CUXHU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2006:UUD2HO7QG44RXVANFUJA6CUXHU","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":"47a86fffb8c053c500d25441d636829c6a95b7a45b2578c4dab45d0f7b5c5708","cross_cats_sorted":["cs.DM","cs.DS"],"license":"","primary_cat":"math.CO","submitted_at":"2006-11-22T10:47:05Z","title_canon_sha256":"f53b3c041e3fe8f04fdbeaedd00f5304600a1adfdaace2688d351000ea7d5767"},"schema_version":"1.0","source":{"id":"math/0611679","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0611679","created_at":"2026-05-18T02:41:26Z"},{"alias_kind":"arxiv_version","alias_value":"math/0611679v1","created_at":"2026-05-18T02:41:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0611679","created_at":"2026-05-18T02:41:26Z"},{"alias_kind":"pith_short_12","alias_value":"UUD2HO7QG44R","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_16","alias_value":"UUD2HO7QG44RXVAN","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_8","alias_value":"UUD2HO7Q","created_at":"2026-05-18T12:25:54Z"}],"graph_snapshots":[{"event_id":"sha256:cc62f6fc6f4d2a7fa2226d575f9fd263add34294e52c273b41d3417bf0eba94b","target":"graph","created_at":"2026-05-18T02:41:26Z","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 polynomial (O(n^8)) algorithm for finding a longest common pattern between two permutations of size n given that one is separable. We also give an algorithm for general permutations whose complexity depends on the length of the longest simple permutation involved in one of our permutations.","authors_text":"Dominique Rossin (LIAFA), Mathilde Bouvel (LIAFA)","cross_cats":["cs.DM","cs.DS"],"headline":"","license":"","primary_cat":"math.CO","submitted_at":"2006-11-22T10:47:05Z","title":"Longest Common Pattern between two Permutations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0611679","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":"sha256:0b80ad31543262701cd615dc6137c17ce527f8f01b96c3ed5949a5fac560987f","target":"record","created_at":"2026-05-18T02:41:26Z","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":"47a86fffb8c053c500d25441d636829c6a95b7a45b2578c4dab45d0f7b5c5708","cross_cats_sorted":["cs.DM","cs.DS"],"license":"","primary_cat":"math.CO","submitted_at":"2006-11-22T10:47:05Z","title_canon_sha256":"f53b3c041e3fe8f04fdbeaedd00f5304600a1adfdaace2688d351000ea7d5767"},"schema_version":"1.0","source":{"id":"math/0611679","kind":"arxiv","version":1}},"canonical_sha256":"a507a3bbf037391bd40d2d120f0a973d2347060bc8befc6d6187e20637d0808b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a507a3bbf037391bd40d2d120f0a973d2347060bc8befc6d6187e20637d0808b","first_computed_at":"2026-05-18T02:41:26.676362Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:41:26.676362Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nRmBu8D+uUO5V7nxEqzk0H0hjeGSzFmSwqVHAwzJ59hjuL7A0A4UwQu86GNwE+BC+/8bBxHVcxz3BqA85lncAw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:41:26.676822Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0611679","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0b80ad31543262701cd615dc6137c17ce527f8f01b96c3ed5949a5fac560987f","sha256:cc62f6fc6f4d2a7fa2226d575f9fd263add34294e52c273b41d3417bf0eba94b"],"state_sha256":"7bb7c5821aa43ac78af1cffdb130f951f003ed2fd096e4b45b02c2a64fe1554e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"E7k4FVCf+jSBJzkGtioTRCXTxe5eJFuBKKFv6DnQz88oWCz+R79t4VN55NfmD9QJg5ce6X1Ngpgzja0Ngl2xCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T12:00:27.389663Z","bundle_sha256":"d4ac62d9196fc2f1581abae2ed025ac33ae779079086d1183652872f132729ac"}}