{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:JY7PM7FLGWVJIOXMH36WFIV6VZ","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":"01723051b46016bc8c5fc8be5acc2f90b7b135b7f8af80471a08babb75975b27","cross_cats_sorted":["cs.FL","math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2016-04-30T11:04:12Z","title_canon_sha256":"72ef2ea752bfb9024889a832a1782f01fb429e773f2bd723fe493f40d36850de"},"schema_version":"1.0","source":{"id":"1605.00092","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.00092","created_at":"2026-05-18T01:12:24Z"},{"alias_kind":"arxiv_version","alias_value":"1605.00092v2","created_at":"2026-05-18T01:12:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.00092","created_at":"2026-05-18T01:12:24Z"},{"alias_kind":"pith_short_12","alias_value":"JY7PM7FLGWVJ","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_16","alias_value":"JY7PM7FLGWVJIOXM","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_8","alias_value":"JY7PM7FL","created_at":"2026-05-18T12:30:25Z"}],"graph_snapshots":[{"event_id":"sha256:7c8c258201f690d6b3e1a0d8243b57e31dd2da28703e2017b28cc3cc988bb326","target":"graph","created_at":"2026-05-18T01:12:24Z","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":"The discriminator of an integer sequence s = (s(i))_{i >=0}, introduced by Arnold, Benkoski, and McCabe in 1985, is the map D_s(n) that sends n >= 1 to the least positive integer m such that the n numbers s(0), s(1), ..., s(n-1) are pairwise incongruent modulo m. In this note we consider the discriminators of a certain class of sequences, the k-regular sequences. We compute the discriminators of two such sequences, the so-called \"evil\" and \"odious\" numbers, and show they are 2-regular. We also give an example of a k-regular sequence whose discriminator is not k-regular.\n  Finally, we examine s","authors_text":"Jeffrey Shallit, Sajed Haque","cross_cats":["cs.FL","math.NT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2016-04-30T11:04:12Z","title":"Discriminators and k-Regular Sequences"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.00092","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":"sha256:4566333851b1c2797b3e9fcbf6d711467b9b3135d9dac147eb8db22902222e55","target":"record","created_at":"2026-05-18T01:12:24Z","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":"01723051b46016bc8c5fc8be5acc2f90b7b135b7f8af80471a08babb75975b27","cross_cats_sorted":["cs.FL","math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2016-04-30T11:04:12Z","title_canon_sha256":"72ef2ea752bfb9024889a832a1782f01fb429e773f2bd723fe493f40d36850de"},"schema_version":"1.0","source":{"id":"1605.00092","kind":"arxiv","version":2}},"canonical_sha256":"4e3ef67cab35aa943aec3efd62a2beae4398fcf6428b8f02e5cee10ab37f921a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4e3ef67cab35aa943aec3efd62a2beae4398fcf6428b8f02e5cee10ab37f921a","first_computed_at":"2026-05-18T01:12:24.923293Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:12:24.923293Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"67Qy6xGrng3EXSGy5cocZKuOI/y7z3AO0G6q6L/WcF8Y6m7tnMk5F/CI49ALEpKQEqRERS/ilsKeptFAZxwvBg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:12:24.923634Z","signed_message":"canonical_sha256_bytes"},"source_id":"1605.00092","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4566333851b1c2797b3e9fcbf6d711467b9b3135d9dac147eb8db22902222e55","sha256:7c8c258201f690d6b3e1a0d8243b57e31dd2da28703e2017b28cc3cc988bb326"],"state_sha256":"0c9c5b2b42c3d91d25358937268d5373eae4a9fea120b452899c62fd8c137d9f"}