{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:RF5YDI7RD6SN6NN6MLL53SFI37","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":"5997333ee5a8d06c058d017dc4917cd2ef06f2f976e52f82efc2f4bbd842ee36","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-06-05T15:43:49Z","title_canon_sha256":"6d2f5e88ce7cd898d7f13dac239719bdcb4c31f96d013d79d1a6e28cab628f42"},"schema_version":"1.0","source":{"id":"1206.0966","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1206.0966","created_at":"2026-05-18T03:53:54Z"},{"alias_kind":"arxiv_version","alias_value":"1206.0966v2","created_at":"2026-05-18T03:53:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1206.0966","created_at":"2026-05-18T03:53:54Z"},{"alias_kind":"pith_short_12","alias_value":"RF5YDI7RD6SN","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_16","alias_value":"RF5YDI7RD6SN6NN6","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_8","alias_value":"RF5YDI7R","created_at":"2026-05-18T12:27:20Z"}],"graph_snapshots":[{"event_id":"sha256:710ba2985de7b46757e88879f7281325a2cb3c04d89985c7d7c4ca0ade63f9ef","target":"graph","created_at":"2026-05-18T03:53:54Z","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":"For each integer k >= 2, let F(k) denote the largest n for which there exists a permutation \\sigma \\in S_n, all of whose patterns of length k are distinct. We prove that F(k) = k + \\lfloor \\sqrt{2k-3} \\rfloor + e_k, where e_k \\in {-1,0} for every k. Suggestions for further investigations along these lines are discussed.","authors_text":"Peter Hegarty","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-06-05T15:43:49Z","title":"Permutations all of whose patterns of a given length are distinct"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.0966","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:c097fdbfa53beb04caa7923cbd4d0666a624c4f3058869a49c3104a07223dfda","target":"record","created_at":"2026-05-18T03:53:54Z","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":"5997333ee5a8d06c058d017dc4917cd2ef06f2f976e52f82efc2f4bbd842ee36","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-06-05T15:43:49Z","title_canon_sha256":"6d2f5e88ce7cd898d7f13dac239719bdcb4c31f96d013d79d1a6e28cab628f42"},"schema_version":"1.0","source":{"id":"1206.0966","kind":"arxiv","version":2}},"canonical_sha256":"897b81a3f11fa4df35be62d7ddc8a8dffe556d935810e9c315d62d68e2ad74e1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"897b81a3f11fa4df35be62d7ddc8a8dffe556d935810e9c315d62d68e2ad74e1","first_computed_at":"2026-05-18T03:53:54.016097Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:53:54.016097Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KPpsRz+GdoF6MAHXW5HvKTzXBCA7jzX/Dpt55TFosB+GmWYiw6rUVcu5hS3TXoUlEICP0miQnwIjYtgGT9h2AQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:53:54.016910Z","signed_message":"canonical_sha256_bytes"},"source_id":"1206.0966","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c097fdbfa53beb04caa7923cbd4d0666a624c4f3058869a49c3104a07223dfda","sha256:710ba2985de7b46757e88879f7281325a2cb3c04d89985c7d7c4ca0ade63f9ef"],"state_sha256":"fb8a9e60e66b26dc447560e41bea39536af673c94098d177bcdea48badf7b9c5"}