{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:WINWAZB763HY4FLG2T6LTUSVQF","short_pith_number":"pith:WINWAZB7","canonical_record":{"source":{"id":"1804.06071","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-04-17T06:48:19Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"33742f561a64bc054c541582affa3c7ef0332a7f9aac8b6e5e49fd71a4438fe7","abstract_canon_sha256":"99c831d600237de03984b950d7bafbb12980ba086f4c0081c4e39ce7ba6d8348"},"schema_version":"1.0"},"canonical_sha256":"b21b60643ff6cf8e1566d4fcb9d255815a141cfb19eaa80a1238dcfe9a4a3656","source":{"kind":"arxiv","id":"1804.06071","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.06071","created_at":"2026-05-18T00:18:21Z"},{"alias_kind":"arxiv_version","alias_value":"1804.06071v1","created_at":"2026-05-18T00:18:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.06071","created_at":"2026-05-18T00:18:21Z"},{"alias_kind":"pith_short_12","alias_value":"WINWAZB763HY","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_16","alias_value":"WINWAZB763HY4FLG","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_8","alias_value":"WINWAZB7","created_at":"2026-05-18T12:32:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:WINWAZB763HY4FLG2T6LTUSVQF","target":"record","payload":{"canonical_record":{"source":{"id":"1804.06071","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-04-17T06:48:19Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"33742f561a64bc054c541582affa3c7ef0332a7f9aac8b6e5e49fd71a4438fe7","abstract_canon_sha256":"99c831d600237de03984b950d7bafbb12980ba086f4c0081c4e39ce7ba6d8348"},"schema_version":"1.0"},"canonical_sha256":"b21b60643ff6cf8e1566d4fcb9d255815a141cfb19eaa80a1238dcfe9a4a3656","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:18:21.815531Z","signature_b64":"nTHSzvYjEa2FFEj+Ie0i0UBRDciD0DZ4dAvCPMHTgqGkkj/MrSTbhDmwFDwC4hEJ6M8WZkal1Ef2eHpIRu+vAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b21b60643ff6cf8e1566d4fcb9d255815a141cfb19eaa80a1238dcfe9a4a3656","last_reissued_at":"2026-05-18T00:18:21.814952Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:18:21.814952Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1804.06071","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":"2026-05-18T00:18:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"S7EYP8P4smv5snYmZtV07tqanhyvxZJji8QLrpxb9jQo07lKu37pJhORxzO7cqpYgEDrg6/ta7HZknQzmVGaBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T13:43:34.577642Z"},"content_sha256":"2fbc6ae4990a9c3304a8d7dcb15c7571a6ffdb9eb2f50e99b03510d2d0ca3312","schema_version":"1.0","event_id":"sha256:2fbc6ae4990a9c3304a8d7dcb15c7571a6ffdb9eb2f50e99b03510d2d0ca3312"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:WINWAZB763HY4FLG2T6LTUSVQF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Patterns in random permutations avoiding some sets of multiple patterns","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.PR","authors_text":"Svante Janson","submitted_at":"2018-04-17T06:48:19Z","abstract_excerpt":"We consider a random permutation drawn from the set of permutations of length $n$ that avoid some given set of patterns of length 3. We show that the number of occurrences of another pattern $\\sigma$ has a limit distribution, after suitable scaling. In several cases, the number is asymptotically normal; this contrasts to the cases of permutations avoiding a single pattern of length 3 studied in earlier papers."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.06071","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":"2026-05-18T00:18:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Mu6Wj0RyIzobAJ4zp5nnxJFufHsYTmJLE8JmFuMsjW3RnVWtYLAVmEhEwDeOQYDRSC/0UFblgh4UJ+Zc4miTDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T13:43:34.578179Z"},"content_sha256":"f9ea27fd7a535b916f36cfae612dea44521891199378c57984fbb685c315fb27","schema_version":"1.0","event_id":"sha256:f9ea27fd7a535b916f36cfae612dea44521891199378c57984fbb685c315fb27"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WINWAZB763HY4FLG2T6LTUSVQF/bundle.json","state_url":"https://pith.science/pith/WINWAZB763HY4FLG2T6LTUSVQF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WINWAZB763HY4FLG2T6LTUSVQF/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":"2026-05-25T13:43:34Z","links":{"resolver":"https://pith.science/pith/WINWAZB763HY4FLG2T6LTUSVQF","bundle":"https://pith.science/pith/WINWAZB763HY4FLG2T6LTUSVQF/bundle.json","state":"https://pith.science/pith/WINWAZB763HY4FLG2T6LTUSVQF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WINWAZB763HY4FLG2T6LTUSVQF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:WINWAZB763HY4FLG2T6LTUSVQF","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":"99c831d600237de03984b950d7bafbb12980ba086f4c0081c4e39ce7ba6d8348","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-04-17T06:48:19Z","title_canon_sha256":"33742f561a64bc054c541582affa3c7ef0332a7f9aac8b6e5e49fd71a4438fe7"},"schema_version":"1.0","source":{"id":"1804.06071","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.06071","created_at":"2026-05-18T00:18:21Z"},{"alias_kind":"arxiv_version","alias_value":"1804.06071v1","created_at":"2026-05-18T00:18:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.06071","created_at":"2026-05-18T00:18:21Z"},{"alias_kind":"pith_short_12","alias_value":"WINWAZB763HY","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_16","alias_value":"WINWAZB763HY4FLG","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_8","alias_value":"WINWAZB7","created_at":"2026-05-18T12:32:59Z"}],"graph_snapshots":[{"event_id":"sha256:f9ea27fd7a535b916f36cfae612dea44521891199378c57984fbb685c315fb27","target":"graph","created_at":"2026-05-18T00:18:21Z","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":"We consider a random permutation drawn from the set of permutations of length $n$ that avoid some given set of patterns of length 3. We show that the number of occurrences of another pattern $\\sigma$ has a limit distribution, after suitable scaling. In several cases, the number is asymptotically normal; this contrasts to the cases of permutations avoiding a single pattern of length 3 studied in earlier papers.","authors_text":"Svante Janson","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-04-17T06:48:19Z","title":"Patterns in random permutations avoiding some sets of multiple patterns"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.06071","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":"sha256:2fbc6ae4990a9c3304a8d7dcb15c7571a6ffdb9eb2f50e99b03510d2d0ca3312","target":"record","created_at":"2026-05-18T00:18:21Z","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":"99c831d600237de03984b950d7bafbb12980ba086f4c0081c4e39ce7ba6d8348","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-04-17T06:48:19Z","title_canon_sha256":"33742f561a64bc054c541582affa3c7ef0332a7f9aac8b6e5e49fd71a4438fe7"},"schema_version":"1.0","source":{"id":"1804.06071","kind":"arxiv","version":1}},"canonical_sha256":"b21b60643ff6cf8e1566d4fcb9d255815a141cfb19eaa80a1238dcfe9a4a3656","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b21b60643ff6cf8e1566d4fcb9d255815a141cfb19eaa80a1238dcfe9a4a3656","first_computed_at":"2026-05-18T00:18:21.814952Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:18:21.814952Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nTHSzvYjEa2FFEj+Ie0i0UBRDciD0DZ4dAvCPMHTgqGkkj/MrSTbhDmwFDwC4hEJ6M8WZkal1Ef2eHpIRu+vAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:18:21.815531Z","signed_message":"canonical_sha256_bytes"},"source_id":"1804.06071","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2fbc6ae4990a9c3304a8d7dcb15c7571a6ffdb9eb2f50e99b03510d2d0ca3312","sha256:f9ea27fd7a535b916f36cfae612dea44521891199378c57984fbb685c315fb27"],"state_sha256":"6873d5f3a810ed9d032a4ed482c81b6e1523b888b419d0ec5064ac36d88e8cde"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"labhrx0H7pdxWg+7zPc5YNm1ycHyV3T3W0qNnLl4GqKRzQN6vshpbmSL1XJDpL9OwblbgZEEKlj+prQZ1fJ/AQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T13:43:34.581463Z","bundle_sha256":"2a30f9be516ca7bd8e93d424fb737e364cfa549e046e75faf1df50d314701c6b"}}