{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:OE2EYU2GMML7Z2JS5KFVY5KGBF","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":"d61d215bc68ff6cd537f73a68d9e921dd6aea320b212434eaeec8d12108fd6c7","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-02-02T19:16:41Z","title_canon_sha256":"42ac1cd34ad251bc684b7a792d25a4ea46644f995bed683112e8efc51b354322"},"schema_version":"1.0","source":{"id":"1702.00802","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1702.00802","created_at":"2026-05-18T00:51:29Z"},{"alias_kind":"arxiv_version","alias_value":"1702.00802v1","created_at":"2026-05-18T00:51:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.00802","created_at":"2026-05-18T00:51:29Z"},{"alias_kind":"pith_short_12","alias_value":"OE2EYU2GMML7","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_16","alias_value":"OE2EYU2GMML7Z2JS","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_8","alias_value":"OE2EYU2G","created_at":"2026-05-18T12:31:34Z"}],"graph_snapshots":[{"event_id":"sha256:495d3c8c0d45e342ec09a2394b16e95450cab5c6566b17f5369c8c39cfdfcedf","target":"graph","created_at":"2026-05-18T00:51:29Z","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 function D_s(n) that sends n to the least integer m such that the numbers s(0), s(1), ..., s(n-1) are pairwise incongruent modulo m. In this note we present a class of exponential sequences that have the special property that their discriminators are shift-invariant, i.e., that the discriminator of the sequence is the same even if the sequence is shifted by any positive constant.","authors_text":"Jeffrey Shallit, Sajed Haque","cross_cats":["cs.DM"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-02-02T19:16:41Z","title":"A Class of Exponential Sequences with Shift-Invariant Discriminators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.00802","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:f38c84bfb264746a1f3d06814618d8693d4b9d6f57e4ee1af158f2e56a36c531","target":"record","created_at":"2026-05-18T00:51:29Z","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":"d61d215bc68ff6cd537f73a68d9e921dd6aea320b212434eaeec8d12108fd6c7","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-02-02T19:16:41Z","title_canon_sha256":"42ac1cd34ad251bc684b7a792d25a4ea46644f995bed683112e8efc51b354322"},"schema_version":"1.0","source":{"id":"1702.00802","kind":"arxiv","version":1}},"canonical_sha256":"71344c53466317fce932ea8b5c7546095bc530a6870ccc2f26968553f35b6e89","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"71344c53466317fce932ea8b5c7546095bc530a6870ccc2f26968553f35b6e89","first_computed_at":"2026-05-18T00:51:29.743027Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:51:29.743027Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Nj1J34J9PN2E+nIbb3ZRqXzftS9VSsFQ7bZdDe6PHUb6JJGWLIKgyysz+uViiSOISzHsO88L+oNUDIFlF0nuCg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:51:29.743456Z","signed_message":"canonical_sha256_bytes"},"source_id":"1702.00802","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f38c84bfb264746a1f3d06814618d8693d4b9d6f57e4ee1af158f2e56a36c531","sha256:495d3c8c0d45e342ec09a2394b16e95450cab5c6566b17f5369c8c39cfdfcedf"],"state_sha256":"9de029af5184afd0acaf0e0c64318e8fb4a7890014eee068cffcff8bf6894a39"}