{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:EQMS5RIRQTZHLVNCZZ7LN2LB5W","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":"02e6b98c5e6b60e85fcc28f75ecea4088faf60aeecf1f1d3877aad95b5bc4135","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-11-20T10:15:37Z","title_canon_sha256":"3039eb2364b80976e3f7c7fb4c72d56c10b02da63991401e98d031c42a1e0078"},"schema_version":"1.0","source":{"id":"1311.4999","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1311.4999","created_at":"2026-05-18T03:06:42Z"},{"alias_kind":"arxiv_version","alias_value":"1311.4999v1","created_at":"2026-05-18T03:06:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.4999","created_at":"2026-05-18T03:06:42Z"},{"alias_kind":"pith_short_12","alias_value":"EQMS5RIRQTZH","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_16","alias_value":"EQMS5RIRQTZHLVNC","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_8","alias_value":"EQMS5RIR","created_at":"2026-05-18T12:27:43Z"}],"graph_snapshots":[{"event_id":"sha256:8f5c61b82138d6a13492c1d30b9fe42e94416682115b36f8991ed791ea250f05","target":"graph","created_at":"2026-05-18T03:06:42Z","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"},"paper":{"abstract_excerpt":"In this paper we study Appell polynomials by connecting them to random variables. This probabilistic approach yields, e.g., the mean value property which is fundamental in the sense that many other properties can be derived from it. We also discuss moment representations of Appell polynomials. In the latter part of the paper the presented general theory is applied to study some classical explicitly given polynomials.","authors_text":"Bao Quoc Ta","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-11-20T10:15:37Z","title":"Probabilistic approach to Appell polynomials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.4999","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:f08506871f7daffd745a894e271cbced21faf1479500c2583144c478eaf5c6d8","target":"record","created_at":"2026-05-18T03:06:42Z","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":"02e6b98c5e6b60e85fcc28f75ecea4088faf60aeecf1f1d3877aad95b5bc4135","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-11-20T10:15:37Z","title_canon_sha256":"3039eb2364b80976e3f7c7fb4c72d56c10b02da63991401e98d031c42a1e0078"},"schema_version":"1.0","source":{"id":"1311.4999","kind":"arxiv","version":1}},"canonical_sha256":"24192ec51184f275d5a2ce7eb6e961edbf1ddab0f41ea23476e54f762a6fe50d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"24192ec51184f275d5a2ce7eb6e961edbf1ddab0f41ea23476e54f762a6fe50d","first_computed_at":"2026-05-18T03:06:42.230884Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:06:42.230884Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kP964eAe1Fm02kJngKy8IdQbrJmyP9gYl3TQmajX+TM2TItdbDJXgX9mIH/2sqAiOXsqk/4ieHLYezWqeWSSDg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:06:42.231355Z","signed_message":"canonical_sha256_bytes"},"source_id":"1311.4999","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f08506871f7daffd745a894e271cbced21faf1479500c2583144c478eaf5c6d8","sha256:8f5c61b82138d6a13492c1d30b9fe42e94416682115b36f8991ed791ea250f05"],"state_sha256":"9329f32ea46905af07d2a8d665cbfda4db3b47ae062f94b0b4162b7ba5f91496"}