{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:L6A4S7BWK3ICMJ4EJA6PJGZHK2","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":"1eab61b07495fe470756705a6a83475a5ee625621ff3cbd62f1236fca9c983bd","cross_cats_sorted":["math.AP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CA","submitted_at":"2022-04-10T15:31:47Z","title_canon_sha256":"9d2c1eb30d3820492d4e705413858cbdce4595ca8fea40caea2609229e39f4ed"},"schema_version":"1.0","source":{"id":"2204.04706","kind":"arxiv","version":6}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2204.04706","created_at":"2026-06-23T03:13:42Z"},{"alias_kind":"arxiv_version","alias_value":"2204.04706v6","created_at":"2026-06-23T03:13:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2204.04706","created_at":"2026-06-23T03:13:42Z"},{"alias_kind":"pith_short_12","alias_value":"L6A4S7BWK3IC","created_at":"2026-06-23T03:13:42Z"},{"alias_kind":"pith_short_16","alias_value":"L6A4S7BWK3ICMJ4E","created_at":"2026-06-23T03:13:42Z"},{"alias_kind":"pith_short_8","alias_value":"L6A4S7BW","created_at":"2026-06-23T03:13:42Z"}],"graph_snapshots":[{"event_id":"sha256:c0a3680a597cdecc5c116f80da2020a42a68377cd114fc364d788efaceecf725","target":"graph","created_at":"2026-06-23T03:13:42Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2204.04706/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We recall the definition and properties of a moment sequence and show that all real sequences whose Hankel matrices have finite rank (see definition in the sequel) satisfy a homogeneous linear equation with constant coefficients. Then we analyze the cases in which a difference equation with constant coefficients and suitably chosen initial conditions and having as an input a positive moment sequence has a solution that is a positive moment sequence. We give one general simple result and give many examples illustrating the theory. The main result states that the roots of the odd multiplicity of","authors_text":"Pawe{\\l} J. Szab{\\l}owski","cross_cats":["math.AP"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CA","submitted_at":"2022-04-10T15:31:47Z","title":"Moment sequences and difference equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2204.04706","kind":"arxiv","version":6},"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:b45058d862fe8ad668270efd70b91e6eee861c100ba330a856f065ab2fbd34e4","target":"record","created_at":"2026-06-23T03:13:42Z","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":"1eab61b07495fe470756705a6a83475a5ee625621ff3cbd62f1236fca9c983bd","cross_cats_sorted":["math.AP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CA","submitted_at":"2022-04-10T15:31:47Z","title_canon_sha256":"9d2c1eb30d3820492d4e705413858cbdce4595ca8fea40caea2609229e39f4ed"},"schema_version":"1.0","source":{"id":"2204.04706","kind":"arxiv","version":6}},"canonical_sha256":"5f81c97c3656d0262784483cf49b2756962544cf49e24269ed1e30928df9d635","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5f81c97c3656d0262784483cf49b2756962544cf49e24269ed1e30928df9d635","first_computed_at":"2026-06-23T03:13:42.161521Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-23T03:13:42.161521Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wMfFwigl8KRRwY0m2GNTMhkRBNVb9qCEQJbQdn21sKhV88MKOi9T190OLddcZmhtIFC670Slu3N6SBAU41XlAQ==","signature_status":"signed_v1","signed_at":"2026-06-23T03:13:42.161992Z","signed_message":"canonical_sha256_bytes"},"source_id":"2204.04706","source_kind":"arxiv","source_version":6}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b45058d862fe8ad668270efd70b91e6eee861c100ba330a856f065ab2fbd34e4","sha256:c0a3680a597cdecc5c116f80da2020a42a68377cd114fc364d788efaceecf725"],"state_sha256":"78de8dda1dd3adfee05a942c3b6c8687c3c7ebb0db757f34e9a1e45a631cf325"}