{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:SOZA44L6DRQCO5QATJDPLIR3DI","short_pith_number":"pith:SOZA44L6","canonical_record":{"source":{"id":"1505.06508","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-05-25T01:11:09Z","cross_cats_sorted":["cs.CC","cs.FL"],"title_canon_sha256":"1620bcab4d273128e27c7e969498587c549794faae6899f94169ce6afd98ac59","abstract_canon_sha256":"53a2598ba1d93bcef7a0c62fd34ac4d3e9e648c7ff26ef47ab71998277350274"},"schema_version":"1.0"},"canonical_sha256":"93b20e717e1c602776009a46f5a23b1a248d4fd85a5beba4a46dc7dcf4f12d75","source":{"kind":"arxiv","id":"1505.06508","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1505.06508","created_at":"2026-05-18T02:03:44Z"},{"alias_kind":"arxiv_version","alias_value":"1505.06508v1","created_at":"2026-05-18T02:03:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.06508","created_at":"2026-05-18T02:03:44Z"},{"alias_kind":"pith_short_12","alias_value":"SOZA44L6DRQC","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_16","alias_value":"SOZA44L6DRQCO5QA","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_8","alias_value":"SOZA44L6","created_at":"2026-05-18T12:29:42Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:SOZA44L6DRQCO5QATJDPLIR3DI","target":"record","payload":{"canonical_record":{"source":{"id":"1505.06508","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-05-25T01:11:09Z","cross_cats_sorted":["cs.CC","cs.FL"],"title_canon_sha256":"1620bcab4d273128e27c7e969498587c549794faae6899f94169ce6afd98ac59","abstract_canon_sha256":"53a2598ba1d93bcef7a0c62fd34ac4d3e9e648c7ff26ef47ab71998277350274"},"schema_version":"1.0"},"canonical_sha256":"93b20e717e1c602776009a46f5a23b1a248d4fd85a5beba4a46dc7dcf4f12d75","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:03:44.804433Z","signature_b64":"G9wMvGMdo8CJZbSJwUYWkYZnaOjVy8XV9GdQfkTqimr7B3GeVfRH5A3NJwWxdR6EJypr9dv9NxY1OKnCvXZkCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"93b20e717e1c602776009a46f5a23b1a248d4fd85a5beba4a46dc7dcf4f12d75","last_reissued_at":"2026-05-18T02:03:44.803748Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:03:44.803748Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1505.06508","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":"2026-05-18T02:03:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FLswG8ZlBGL3zw7y2DR81NNlqYnMSZfyml4BwOaGRCaFKy5+w9NduQmwNIZlrNJkYoU1FOLmMMdlovujwJALDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T01:58:28.282221Z"},"content_sha256":"cd22c81f809103ceebba379eb796012dd361d3cf0e8a7901c421ab68c08d1997","schema_version":"1.0","event_id":"sha256:cd22c81f809103ceebba379eb796012dd361d3cf0e8a7901c421ab68c08d1997"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:SOZA44L6DRQCO5QATJDPLIR3DI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Pattern avoidance is not P-recursive","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","cs.FL"],"primary_cat":"math.CO","authors_text":"Igor Pak, Scott Garrabrant","submitted_at":"2015-05-25T01:11:09Z","abstract_excerpt":"Let $F \\subset S_k$ be a finite set of permutations and let $C_n(F)$ denote the number of permutations $\\sigma$ in $S_n$ avoiding the set of patterns $F$. The Noonan-Zeilberger conjecture states that the sequence ${C_n(F)}$ is P-recursive. We use Computability Theory to disprove this conjecture."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.06508","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":"2026-05-18T02:03:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KnsdEbiyUlavvDtWHozWIqMExOMc3Fuek920i94v/RQ7CunbNM742B1M8TyN+eVQRZa2yvCe5cCHeM5Jat9zDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T01:58:28.282594Z"},"content_sha256":"472c1799aa37d2fb55de21cba983511d9b7b46e3b3f80908a458f2669de65c8f","schema_version":"1.0","event_id":"sha256:472c1799aa37d2fb55de21cba983511d9b7b46e3b3f80908a458f2669de65c8f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SOZA44L6DRQCO5QATJDPLIR3DI/bundle.json","state_url":"https://pith.science/pith/SOZA44L6DRQCO5QATJDPLIR3DI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SOZA44L6DRQCO5QATJDPLIR3DI/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":"2026-05-28T01:58:28Z","links":{"resolver":"https://pith.science/pith/SOZA44L6DRQCO5QATJDPLIR3DI","bundle":"https://pith.science/pith/SOZA44L6DRQCO5QATJDPLIR3DI/bundle.json","state":"https://pith.science/pith/SOZA44L6DRQCO5QATJDPLIR3DI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SOZA44L6DRQCO5QATJDPLIR3DI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:SOZA44L6DRQCO5QATJDPLIR3DI","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":"53a2598ba1d93bcef7a0c62fd34ac4d3e9e648c7ff26ef47ab71998277350274","cross_cats_sorted":["cs.CC","cs.FL"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-05-25T01:11:09Z","title_canon_sha256":"1620bcab4d273128e27c7e969498587c549794faae6899f94169ce6afd98ac59"},"schema_version":"1.0","source":{"id":"1505.06508","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1505.06508","created_at":"2026-05-18T02:03:44Z"},{"alias_kind":"arxiv_version","alias_value":"1505.06508v1","created_at":"2026-05-18T02:03:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.06508","created_at":"2026-05-18T02:03:44Z"},{"alias_kind":"pith_short_12","alias_value":"SOZA44L6DRQC","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_16","alias_value":"SOZA44L6DRQCO5QA","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_8","alias_value":"SOZA44L6","created_at":"2026-05-18T12:29:42Z"}],"graph_snapshots":[{"event_id":"sha256:472c1799aa37d2fb55de21cba983511d9b7b46e3b3f80908a458f2669de65c8f","target":"graph","created_at":"2026-05-18T02:03:44Z","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":"Let $F \\subset S_k$ be a finite set of permutations and let $C_n(F)$ denote the number of permutations $\\sigma$ in $S_n$ avoiding the set of patterns $F$. The Noonan-Zeilberger conjecture states that the sequence ${C_n(F)}$ is P-recursive. We use Computability Theory to disprove this conjecture.","authors_text":"Igor Pak, Scott Garrabrant","cross_cats":["cs.CC","cs.FL"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-05-25T01:11:09Z","title":"Pattern avoidance is not P-recursive"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.06508","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:cd22c81f809103ceebba379eb796012dd361d3cf0e8a7901c421ab68c08d1997","target":"record","created_at":"2026-05-18T02:03:44Z","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":"53a2598ba1d93bcef7a0c62fd34ac4d3e9e648c7ff26ef47ab71998277350274","cross_cats_sorted":["cs.CC","cs.FL"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-05-25T01:11:09Z","title_canon_sha256":"1620bcab4d273128e27c7e969498587c549794faae6899f94169ce6afd98ac59"},"schema_version":"1.0","source":{"id":"1505.06508","kind":"arxiv","version":1}},"canonical_sha256":"93b20e717e1c602776009a46f5a23b1a248d4fd85a5beba4a46dc7dcf4f12d75","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"93b20e717e1c602776009a46f5a23b1a248d4fd85a5beba4a46dc7dcf4f12d75","first_computed_at":"2026-05-18T02:03:44.803748Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:03:44.803748Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"G9wMvGMdo8CJZbSJwUYWkYZnaOjVy8XV9GdQfkTqimr7B3GeVfRH5A3NJwWxdR6EJypr9dv9NxY1OKnCvXZkCw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:03:44.804433Z","signed_message":"canonical_sha256_bytes"},"source_id":"1505.06508","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cd22c81f809103ceebba379eb796012dd361d3cf0e8a7901c421ab68c08d1997","sha256:472c1799aa37d2fb55de21cba983511d9b7b46e3b3f80908a458f2669de65c8f"],"state_sha256":"714980cc811a7a3712b801dec815c25c88437a3e51fc5e388907c26e9e3ba7b9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MkMI6YmXyzt8bAjg4WXoM7fVwC1h+50Ebn1MN6v2eIcD8Q6njsuki78vJBXZV88tYOSkH4TW1ydlh9AsEwSOCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T01:58:28.284586Z","bundle_sha256":"8950d40ad9ce9c866ac549630d3514069c96cebc7bd58a97448879792484a52a"}}