{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:DOAVWPSSH3TFJNXRP27J3ZZ3HM","short_pith_number":"pith:DOAVWPSS","canonical_record":{"source":{"id":"1311.6151","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-11-24T18:23:43Z","cross_cats_sorted":["q-bio.QM"],"title_canon_sha256":"9fd653d10820adca755c4b7f4a20c2187ee73fc28f9993fedc346045c6feef65","abstract_canon_sha256":"66215e3ddaee566ba37d536e75134bd0d37d5a5f50001cefd8db1bf54a4e2b1a"},"schema_version":"1.0"},"canonical_sha256":"1b815b3e523ee654b6f17ebe9de73b3b1124f6b9cf2120afdd09e243e0577956","source":{"kind":"arxiv","id":"1311.6151","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1311.6151","created_at":"2026-05-18T03:05:17Z"},{"alias_kind":"arxiv_version","alias_value":"1311.6151v2","created_at":"2026-05-18T03:05:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.6151","created_at":"2026-05-18T03:05:17Z"},{"alias_kind":"pith_short_12","alias_value":"DOAVWPSSH3TF","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_16","alias_value":"DOAVWPSSH3TFJNXR","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_8","alias_value":"DOAVWPSS","created_at":"2026-05-18T12:27:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:DOAVWPSSH3TFJNXRP27J3ZZ3HM","target":"record","payload":{"canonical_record":{"source":{"id":"1311.6151","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-11-24T18:23:43Z","cross_cats_sorted":["q-bio.QM"],"title_canon_sha256":"9fd653d10820adca755c4b7f4a20c2187ee73fc28f9993fedc346045c6feef65","abstract_canon_sha256":"66215e3ddaee566ba37d536e75134bd0d37d5a5f50001cefd8db1bf54a4e2b1a"},"schema_version":"1.0"},"canonical_sha256":"1b815b3e523ee654b6f17ebe9de73b3b1124f6b9cf2120afdd09e243e0577956","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:05:17.703234Z","signature_b64":"JfLgc/qPlqbV8G1GF8JVZF3UAoaUU2cFO8czrPAhZyuZIGv1xhaAUCqYot9oycBmKfdXgAKGNtEq7KkNbNtFCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1b815b3e523ee654b6f17ebe9de73b3b1124f6b9cf2120afdd09e243e0577956","last_reissued_at":"2026-05-18T03:05:17.702628Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:05:17.702628Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1311.6151","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":"2026-05-18T03:05:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QqyM5VyIO52e4H7Wr3yt9Ty0k9Jh/VEtsNp67uAt0CzO+U+JktvIax6HD+MN4OY4/mVgdUqYMAmB9I2YJug7BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T21:26:03.753598Z"},"content_sha256":"860cb8d8b53b8dc5ad8a046c74cce2a31338427d42ae28298f899263fa8e2750","schema_version":"1.0","event_id":"sha256:860cb8d8b53b8dc5ad8a046c74cce2a31338427d42ae28298f899263fa8e2750"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:DOAVWPSSH3TFJNXRP27J3ZZ3HM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"An algebraic view of bacterial genome evolution","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["q-bio.QM"],"primary_cat":"math.GR","authors_text":"Andrew R. Francis","submitted_at":"2013-11-24T18:23:43Z","abstract_excerpt":"Rearrangements of bacterial chromosomes can be studied mathematically at several levels, most prominently at a local, or sequence level, as well as at a topological level. The biological changes involved locally are inversions, deletions, and transpositions, while topologically they are knotting and catenation. These two modelling approaches share some surprising algebraic features related to braid groups and Coxeter groups. The structural approach that is at the core of algebra has long found applications in sciences such as physics and analytical chemistry, but only in a small number of ways"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.6151","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":"2026-05-18T03:05:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dX8gVNveRyTpk6vRkrEispOwVomXo3PZiEPixNyWv4ojdaqJOEHDQ2qSLE6dKD36LixgRUyugjXLcThtOC+EBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T21:26:03.753952Z"},"content_sha256":"10acb29ba7b16000f2decb3915db662dbc95f11690abc2dbd373be0a4393cf73","schema_version":"1.0","event_id":"sha256:10acb29ba7b16000f2decb3915db662dbc95f11690abc2dbd373be0a4393cf73"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DOAVWPSSH3TFJNXRP27J3ZZ3HM/bundle.json","state_url":"https://pith.science/pith/DOAVWPSSH3TFJNXRP27J3ZZ3HM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DOAVWPSSH3TFJNXRP27J3ZZ3HM/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":"2026-06-01T21:26:03Z","links":{"resolver":"https://pith.science/pith/DOAVWPSSH3TFJNXRP27J3ZZ3HM","bundle":"https://pith.science/pith/DOAVWPSSH3TFJNXRP27J3ZZ3HM/bundle.json","state":"https://pith.science/pith/DOAVWPSSH3TFJNXRP27J3ZZ3HM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DOAVWPSSH3TFJNXRP27J3ZZ3HM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:DOAVWPSSH3TFJNXRP27J3ZZ3HM","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":"66215e3ddaee566ba37d536e75134bd0d37d5a5f50001cefd8db1bf54a4e2b1a","cross_cats_sorted":["q-bio.QM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-11-24T18:23:43Z","title_canon_sha256":"9fd653d10820adca755c4b7f4a20c2187ee73fc28f9993fedc346045c6feef65"},"schema_version":"1.0","source":{"id":"1311.6151","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1311.6151","created_at":"2026-05-18T03:05:17Z"},{"alias_kind":"arxiv_version","alias_value":"1311.6151v2","created_at":"2026-05-18T03:05:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.6151","created_at":"2026-05-18T03:05:17Z"},{"alias_kind":"pith_short_12","alias_value":"DOAVWPSSH3TF","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_16","alias_value":"DOAVWPSSH3TFJNXR","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_8","alias_value":"DOAVWPSS","created_at":"2026-05-18T12:27:43Z"}],"graph_snapshots":[{"event_id":"sha256:10acb29ba7b16000f2decb3915db662dbc95f11690abc2dbd373be0a4393cf73","target":"graph","created_at":"2026-05-18T03:05:17Z","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":"Rearrangements of bacterial chromosomes can be studied mathematically at several levels, most prominently at a local, or sequence level, as well as at a topological level. The biological changes involved locally are inversions, deletions, and transpositions, while topologically they are knotting and catenation. These two modelling approaches share some surprising algebraic features related to braid groups and Coxeter groups. The structural approach that is at the core of algebra has long found applications in sciences such as physics and analytical chemistry, but only in a small number of ways","authors_text":"Andrew R. Francis","cross_cats":["q-bio.QM"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-11-24T18:23:43Z","title":"An algebraic view of bacterial genome evolution"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.6151","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":"sha256:860cb8d8b53b8dc5ad8a046c74cce2a31338427d42ae28298f899263fa8e2750","target":"record","created_at":"2026-05-18T03:05:17Z","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":"66215e3ddaee566ba37d536e75134bd0d37d5a5f50001cefd8db1bf54a4e2b1a","cross_cats_sorted":["q-bio.QM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-11-24T18:23:43Z","title_canon_sha256":"9fd653d10820adca755c4b7f4a20c2187ee73fc28f9993fedc346045c6feef65"},"schema_version":"1.0","source":{"id":"1311.6151","kind":"arxiv","version":2}},"canonical_sha256":"1b815b3e523ee654b6f17ebe9de73b3b1124f6b9cf2120afdd09e243e0577956","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1b815b3e523ee654b6f17ebe9de73b3b1124f6b9cf2120afdd09e243e0577956","first_computed_at":"2026-05-18T03:05:17.702628Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:05:17.702628Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"JfLgc/qPlqbV8G1GF8JVZF3UAoaUU2cFO8czrPAhZyuZIGv1xhaAUCqYot9oycBmKfdXgAKGNtEq7KkNbNtFCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:05:17.703234Z","signed_message":"canonical_sha256_bytes"},"source_id":"1311.6151","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:860cb8d8b53b8dc5ad8a046c74cce2a31338427d42ae28298f899263fa8e2750","sha256:10acb29ba7b16000f2decb3915db662dbc95f11690abc2dbd373be0a4393cf73"],"state_sha256":"0fdfbfab689738f10f45d9e180640f1f27ccf7a68df5ed813bf78d4717eb0dfa"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FTXSsCxAcXM9dGQv5vUOBfzo8tlAiBS0PjIc7XClMZDs3a0VH70cvqVDIp0WwmisSJJiZelzuaSVln8pSqEuDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T21:26:03.756082Z","bundle_sha256":"2a54d58eb95ba6eaa26563df14ee142455b19a9be7bd8f8e4d6b5d4d2e16a7e5"}}