{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:QD2ZXITXDOBF3WXDFHZKI632D4","short_pith_number":"pith:QD2ZXITX","canonical_record":{"source":{"id":"1808.02653","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-08-08T08:08:33Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"05f027e5105fdd351ac38cf757ea30a73d7731c9f6e9e46b5a474a93af9d1727","abstract_canon_sha256":"36e86e2067a0bc7e24509fa67e9c4df1093a56628ef50e98776ce015b51f0189"},"schema_version":"1.0"},"canonical_sha256":"80f59ba2771b825ddae329f2a47b7a1f38eac222f7051fe6bdadebdeaef7b388","source":{"kind":"arxiv","id":"1808.02653","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1808.02653","created_at":"2026-05-18T00:08:34Z"},{"alias_kind":"arxiv_version","alias_value":"1808.02653v1","created_at":"2026-05-18T00:08:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.02653","created_at":"2026-05-18T00:08:34Z"},{"alias_kind":"pith_short_12","alias_value":"QD2ZXITXDOBF","created_at":"2026-05-18T12:32:46Z"},{"alias_kind":"pith_short_16","alias_value":"QD2ZXITXDOBF3WXD","created_at":"2026-05-18T12:32:46Z"},{"alias_kind":"pith_short_8","alias_value":"QD2ZXITX","created_at":"2026-05-18T12:32:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:QD2ZXITXDOBF3WXDFHZKI632D4","target":"record","payload":{"canonical_record":{"source":{"id":"1808.02653","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-08-08T08:08:33Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"05f027e5105fdd351ac38cf757ea30a73d7731c9f6e9e46b5a474a93af9d1727","abstract_canon_sha256":"36e86e2067a0bc7e24509fa67e9c4df1093a56628ef50e98776ce015b51f0189"},"schema_version":"1.0"},"canonical_sha256":"80f59ba2771b825ddae329f2a47b7a1f38eac222f7051fe6bdadebdeaef7b388","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:08:34.752602Z","signature_b64":"0LPfqJze8sKIEPcjSUMP6kqIe0Cs8p0FoWCw68HoKRwM5GW143SmGIMks/d5slof2ikio1stBIlCXz0pMLPyBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"80f59ba2771b825ddae329f2a47b7a1f38eac222f7051fe6bdadebdeaef7b388","last_reissued_at":"2026-05-18T00:08:34.751903Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:08:34.751903Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1808.02653","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":"2026-05-18T00:08:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SzxXz82harcm5B+nEmJa5dW2nPML197dNNCwRI6ON7PEdKEXOKwrEUjMSe3e3eO423hduTBFfRwj0+5fCjQ/Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T13:49:24.869888Z"},"content_sha256":"f7a1ece7988b04792716211bc5d75762e672cfa154d1666eb03c754a3eb7cea1","schema_version":"1.0","event_id":"sha256:f7a1ece7988b04792716211bc5d75762e672cfa154d1666eb03c754a3eb7cea1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:QD2ZXITXDOBF3WXDFHZKI632D4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Permutation patterns in genome rearrangement problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Giulio Cerbai, Luca Ferrari","submitted_at":"2018-08-08T08:08:33Z","abstract_excerpt":"In the context of the genome rearrangement problem, we analyze two well known models, namely the block transposition and the prefix block transposition models, by exploiting the connection with the notion of permutation pattern. More specifically, for any $k$, we provide a characterization of the set of permutations having distance $\\leq k$ from the identity (which is known to be a permutation class) in terms of what we call generating permutations and we describe some properties of its basis, which allow to compute such a basis for small values of $k$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.02653","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":"2026-05-18T00:08:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xppBpSuBNkPHEt2SR3ppWl5mB+Nkpq4lDoA7Mu9NWjHthF8rBBUZuuVJVaee2yDkKgWScmCXX4HSBQ0YT0neAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T13:49:24.870240Z"},"content_sha256":"93bd9a814fcaa039f6f0f1ce133f39dc1afde06347ecabcbe543854c964568e2","schema_version":"1.0","event_id":"sha256:93bd9a814fcaa039f6f0f1ce133f39dc1afde06347ecabcbe543854c964568e2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QD2ZXITXDOBF3WXDFHZKI632D4/bundle.json","state_url":"https://pith.science/pith/QD2ZXITXDOBF3WXDFHZKI632D4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QD2ZXITXDOBF3WXDFHZKI632D4/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":"2026-06-08T13:49:24Z","links":{"resolver":"https://pith.science/pith/QD2ZXITXDOBF3WXDFHZKI632D4","bundle":"https://pith.science/pith/QD2ZXITXDOBF3WXDFHZKI632D4/bundle.json","state":"https://pith.science/pith/QD2ZXITXDOBF3WXDFHZKI632D4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QD2ZXITXDOBF3WXDFHZKI632D4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:QD2ZXITXDOBF3WXDFHZKI632D4","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":"36e86e2067a0bc7e24509fa67e9c4df1093a56628ef50e98776ce015b51f0189","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-08-08T08:08:33Z","title_canon_sha256":"05f027e5105fdd351ac38cf757ea30a73d7731c9f6e9e46b5a474a93af9d1727"},"schema_version":"1.0","source":{"id":"1808.02653","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1808.02653","created_at":"2026-05-18T00:08:34Z"},{"alias_kind":"arxiv_version","alias_value":"1808.02653v1","created_at":"2026-05-18T00:08:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.02653","created_at":"2026-05-18T00:08:34Z"},{"alias_kind":"pith_short_12","alias_value":"QD2ZXITXDOBF","created_at":"2026-05-18T12:32:46Z"},{"alias_kind":"pith_short_16","alias_value":"QD2ZXITXDOBF3WXD","created_at":"2026-05-18T12:32:46Z"},{"alias_kind":"pith_short_8","alias_value":"QD2ZXITX","created_at":"2026-05-18T12:32:46Z"}],"graph_snapshots":[{"event_id":"sha256:93bd9a814fcaa039f6f0f1ce133f39dc1afde06347ecabcbe543854c964568e2","target":"graph","created_at":"2026-05-18T00:08:34Z","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 the context of the genome rearrangement problem, we analyze two well known models, namely the block transposition and the prefix block transposition models, by exploiting the connection with the notion of permutation pattern. More specifically, for any $k$, we provide a characterization of the set of permutations having distance $\\leq k$ from the identity (which is known to be a permutation class) in terms of what we call generating permutations and we describe some properties of its basis, which allow to compute such a basis for small values of $k$.","authors_text":"Giulio Cerbai, Luca Ferrari","cross_cats":["cs.DM"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-08-08T08:08:33Z","title":"Permutation patterns in genome rearrangement problems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.02653","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:f7a1ece7988b04792716211bc5d75762e672cfa154d1666eb03c754a3eb7cea1","target":"record","created_at":"2026-05-18T00:08:34Z","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":"36e86e2067a0bc7e24509fa67e9c4df1093a56628ef50e98776ce015b51f0189","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-08-08T08:08:33Z","title_canon_sha256":"05f027e5105fdd351ac38cf757ea30a73d7731c9f6e9e46b5a474a93af9d1727"},"schema_version":"1.0","source":{"id":"1808.02653","kind":"arxiv","version":1}},"canonical_sha256":"80f59ba2771b825ddae329f2a47b7a1f38eac222f7051fe6bdadebdeaef7b388","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"80f59ba2771b825ddae329f2a47b7a1f38eac222f7051fe6bdadebdeaef7b388","first_computed_at":"2026-05-18T00:08:34.751903Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:08:34.751903Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0LPfqJze8sKIEPcjSUMP6kqIe0Cs8p0FoWCw68HoKRwM5GW143SmGIMks/d5slof2ikio1stBIlCXz0pMLPyBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:08:34.752602Z","signed_message":"canonical_sha256_bytes"},"source_id":"1808.02653","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f7a1ece7988b04792716211bc5d75762e672cfa154d1666eb03c754a3eb7cea1","sha256:93bd9a814fcaa039f6f0f1ce133f39dc1afde06347ecabcbe543854c964568e2"],"state_sha256":"3daf51d8c303794acff34fec71668ca0d7b7f06dbc98068673b61c5eb6b7aea5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9ZfoHwz7tEd9VOKJbR+kedfTmKIvnpUdpRua29slpw0eAgIhvHVBIvbNj+i4ow+upZsnjAcUcph0zPixcUiSAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T13:49:24.872354Z","bundle_sha256":"0880907a13385952cf72949cfd7cb3d7807e7443b2018ec6fe171ac36841622d"}}