{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:6AMICNR7ORLPF3N275OKXJBFNE","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":"7e5e5249f746f3f0d5f51f0e83e9dec9a60740d9b7e26f3647d021e66431376c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2019-04-08T01:05:29Z","title_canon_sha256":"09077de110e07aa6d6a9afd30155187658de76a9a1c7953e7b869ffffb626375"},"schema_version":"1.0","source":{"id":"1904.03789","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1904.03789","created_at":"2026-05-17T23:49:08Z"},{"alias_kind":"arxiv_version","alias_value":"1904.03789v1","created_at":"2026-05-17T23:49:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.03789","created_at":"2026-05-17T23:49:08Z"},{"alias_kind":"pith_short_12","alias_value":"6AMICNR7ORLP","created_at":"2026-05-18T12:33:10Z"},{"alias_kind":"pith_short_16","alias_value":"6AMICNR7ORLPF3N2","created_at":"2026-05-18T12:33:10Z"},{"alias_kind":"pith_short_8","alias_value":"6AMICNR7","created_at":"2026-05-18T12:33:10Z"}],"graph_snapshots":[{"event_id":"sha256:1274b383efe204b14499b5387390b526e8e0759f7a7c423693771e076e0364d7","target":"graph","created_at":"2026-05-17T23:49:08Z","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 Sturm sequence is generated by a pair of polynomials $P(x)$ and $P'(x)$, where $P(x)$ is assumed to have simple real roots. Euclidean algorithm generates then a finite sequence of polynomials orthogonal on the grid $x_s$ of roots of the polynomial $P(x)$. This algorithm can be exploited in order to find the number of roots of the polynomial $P(x)$ inside a given interval. We consider the \"inverse\" problem: what is the explicit system of orthogonal polynomials generated by the prescribed grid $x_s$ of \"classical\" type. The main results are the following. The generic linear grid generates a ","authors_text":"Alexei Zhedanov","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2019-04-08T01:05:29Z","title":"Classical Sturmian sequences"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.03789","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:e2c8de78cde5e8e37b89179a7e51addbb028599ee3f16012e0ba0ad1665ff9bb","target":"record","created_at":"2026-05-17T23:49:08Z","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":"7e5e5249f746f3f0d5f51f0e83e9dec9a60740d9b7e26f3647d021e66431376c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2019-04-08T01:05:29Z","title_canon_sha256":"09077de110e07aa6d6a9afd30155187658de76a9a1c7953e7b869ffffb626375"},"schema_version":"1.0","source":{"id":"1904.03789","kind":"arxiv","version":1}},"canonical_sha256":"f01881363f7456f2edbaff5caba42569352d3410fba68e9d24540ec0efc545f1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f01881363f7456f2edbaff5caba42569352d3410fba68e9d24540ec0efc545f1","first_computed_at":"2026-05-17T23:49:08.138853Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:49:08.138853Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KqxMaRV3SM/dHqZMdfGhIhv7E8ZOzbETm2CZjshQtX2kTa+TV7OooEExzgTvVqxrtN9LJleWbIU7+6kPEvjzDg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:49:08.139401Z","signed_message":"canonical_sha256_bytes"},"source_id":"1904.03789","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e2c8de78cde5e8e37b89179a7e51addbb028599ee3f16012e0ba0ad1665ff9bb","sha256:1274b383efe204b14499b5387390b526e8e0759f7a7c423693771e076e0364d7"],"state_sha256":"04cafbd3668cbbaff630e39093eeff3490eaa9f1f2b66738624f1bdcfd0acbd3"}