{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:BN2RVNMWBW5OMEJIG2SEAN7TCB","short_pith_number":"pith:BN2RVNMW","canonical_record":{"source":{"id":"1011.1157","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2010-11-04T13:41:12Z","cross_cats_sorted":["cs.CC"],"title_canon_sha256":"31c9d41b49e85fcf3156c88bbf0590e113da29f090f99cc92c1d595ca2e9f119","abstract_canon_sha256":"0507a4bcc334179665dd5499d4e44640050dea86e1114601357a2514f5003da3"},"schema_version":"1.0"},"canonical_sha256":"0b751ab5960dbae6112836a44037f3106dc1e3be3f486fdf454b2cdeaec41189","source":{"kind":"arxiv","id":"1011.1157","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1011.1157","created_at":"2026-05-18T03:46:18Z"},{"alias_kind":"arxiv_version","alias_value":"1011.1157v1","created_at":"2026-05-18T03:46:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1011.1157","created_at":"2026-05-18T03:46:18Z"},{"alias_kind":"pith_short_12","alias_value":"BN2RVNMWBW5O","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_16","alias_value":"BN2RVNMWBW5OMEJI","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_8","alias_value":"BN2RVNMW","created_at":"2026-05-18T12:26:05Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:BN2RVNMWBW5OMEJIG2SEAN7TCB","target":"record","payload":{"canonical_record":{"source":{"id":"1011.1157","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2010-11-04T13:41:12Z","cross_cats_sorted":["cs.CC"],"title_canon_sha256":"31c9d41b49e85fcf3156c88bbf0590e113da29f090f99cc92c1d595ca2e9f119","abstract_canon_sha256":"0507a4bcc334179665dd5499d4e44640050dea86e1114601357a2514f5003da3"},"schema_version":"1.0"},"canonical_sha256":"0b751ab5960dbae6112836a44037f3106dc1e3be3f486fdf454b2cdeaec41189","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:46:18.723576Z","signature_b64":"Tvv+OxYaOyYj8XIzhKQSkvggPi90+IMVYb/CIGSBaLgkxDG7SQlpS00bvtYhKoxHbMMF7kuOE4H/emhZZxBLCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0b751ab5960dbae6112836a44037f3106dc1e3be3f486fdf454b2cdeaec41189","last_reissued_at":"2026-05-18T03:46:18.722991Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:46:18.722991Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1011.1157","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":"2026-05-18T03:46:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5W2nnQEcyJkeJP7FMBaFyuGfr0smV3iBT2efxl4jYOqHURYrwPGQLRvnIpt0EG46nD3lm8Ocigt+jx3oAhsSCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T11:57:38.360589Z"},"content_sha256":"e8b8e83ba96862b7fe0d52cbeaa7d09b0876785401447a09439087cbb66f7d2b","schema_version":"1.0","event_id":"sha256:e8b8e83ba96862b7fe0d52cbeaa7d09b0876785401447a09439087cbb66f7d2b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:BN2RVNMWBW5OMEJIG2SEAN7TCB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Sorting by Transpositions is Difficult","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC"],"primary_cat":"cs.DS","authors_text":"Guillaume Fertin, Irena Rusu, Laurent Bulteau","submitted_at":"2010-11-04T13:41:12Z","abstract_excerpt":"In comparative genomics, a transposition is an operation that exchanges two consecutive sequences of genes in a genome. The transposition distance, that is, the minimum number of transpositions needed to transform a genome into another, is, according to numerous studies, a relevant evolutionary distance. The problem of computing this distance when genomes are represented by permutations, called the Sorting by Transpositions problem, has been introduced by Bafna and Pevzner in 1995. It has naturally been the focus of a number of studies, but the computational complexity of this problem has rema"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.1157","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":"2026-05-18T03:46:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3EHaIdzHwnipkjbgNmSY/qRs4D71DVxQ+V2gJpIPQbg3yuuCkA1/aGUEb2oigOZOwXfkoCDZPk/6NBkUDeeoCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T11:57:38.360934Z"},"content_sha256":"ee50d942f9e0047c76f13511e0f958530892db5031310840ec71be288ac8ba58","schema_version":"1.0","event_id":"sha256:ee50d942f9e0047c76f13511e0f958530892db5031310840ec71be288ac8ba58"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BN2RVNMWBW5OMEJIG2SEAN7TCB/bundle.json","state_url":"https://pith.science/pith/BN2RVNMWBW5OMEJIG2SEAN7TCB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BN2RVNMWBW5OMEJIG2SEAN7TCB/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":"2026-06-21T11:57:38Z","links":{"resolver":"https://pith.science/pith/BN2RVNMWBW5OMEJIG2SEAN7TCB","bundle":"https://pith.science/pith/BN2RVNMWBW5OMEJIG2SEAN7TCB/bundle.json","state":"https://pith.science/pith/BN2RVNMWBW5OMEJIG2SEAN7TCB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BN2RVNMWBW5OMEJIG2SEAN7TCB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:BN2RVNMWBW5OMEJIG2SEAN7TCB","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":"0507a4bcc334179665dd5499d4e44640050dea86e1114601357a2514f5003da3","cross_cats_sorted":["cs.CC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2010-11-04T13:41:12Z","title_canon_sha256":"31c9d41b49e85fcf3156c88bbf0590e113da29f090f99cc92c1d595ca2e9f119"},"schema_version":"1.0","source":{"id":"1011.1157","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1011.1157","created_at":"2026-05-18T03:46:18Z"},{"alias_kind":"arxiv_version","alias_value":"1011.1157v1","created_at":"2026-05-18T03:46:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1011.1157","created_at":"2026-05-18T03:46:18Z"},{"alias_kind":"pith_short_12","alias_value":"BN2RVNMWBW5O","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_16","alias_value":"BN2RVNMWBW5OMEJI","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_8","alias_value":"BN2RVNMW","created_at":"2026-05-18T12:26:05Z"}],"graph_snapshots":[{"event_id":"sha256:ee50d942f9e0047c76f13511e0f958530892db5031310840ec71be288ac8ba58","target":"graph","created_at":"2026-05-18T03:46:18Z","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 comparative genomics, a transposition is an operation that exchanges two consecutive sequences of genes in a genome. The transposition distance, that is, the minimum number of transpositions needed to transform a genome into another, is, according to numerous studies, a relevant evolutionary distance. The problem of computing this distance when genomes are represented by permutations, called the Sorting by Transpositions problem, has been introduced by Bafna and Pevzner in 1995. It has naturally been the focus of a number of studies, but the computational complexity of this problem has rema","authors_text":"Guillaume Fertin, Irena Rusu, Laurent Bulteau","cross_cats":["cs.CC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2010-11-04T13:41:12Z","title":"Sorting by Transpositions is Difficult"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.1157","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:e8b8e83ba96862b7fe0d52cbeaa7d09b0876785401447a09439087cbb66f7d2b","target":"record","created_at":"2026-05-18T03:46:18Z","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":"0507a4bcc334179665dd5499d4e44640050dea86e1114601357a2514f5003da3","cross_cats_sorted":["cs.CC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2010-11-04T13:41:12Z","title_canon_sha256":"31c9d41b49e85fcf3156c88bbf0590e113da29f090f99cc92c1d595ca2e9f119"},"schema_version":"1.0","source":{"id":"1011.1157","kind":"arxiv","version":1}},"canonical_sha256":"0b751ab5960dbae6112836a44037f3106dc1e3be3f486fdf454b2cdeaec41189","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0b751ab5960dbae6112836a44037f3106dc1e3be3f486fdf454b2cdeaec41189","first_computed_at":"2026-05-18T03:46:18.722991Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:46:18.722991Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Tvv+OxYaOyYj8XIzhKQSkvggPi90+IMVYb/CIGSBaLgkxDG7SQlpS00bvtYhKoxHbMMF7kuOE4H/emhZZxBLCA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:46:18.723576Z","signed_message":"canonical_sha256_bytes"},"source_id":"1011.1157","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e8b8e83ba96862b7fe0d52cbeaa7d09b0876785401447a09439087cbb66f7d2b","sha256:ee50d942f9e0047c76f13511e0f958530892db5031310840ec71be288ac8ba58"],"state_sha256":"6c08f293a687f49e0289b593207f297c362bd7a03336e9032a6fc7441e48428b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"q0F4Al/aW3QPtUK00je03SqGBLKLEHiDw/0YQanYJGLz4nRLoGbw6/L8F5xl8lXtpa06lZJRjFEmX3UhyqsADQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-21T11:57:38.362827Z","bundle_sha256":"cf2bccd907174461b55b225c1c36af35e9441bffaf3eefa1bc790badc75b71df"}}