{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:RBSEEWWUUEWMN7P352UZFB4JDX","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":"20303495ebd63f4919818cbd733e056ec8d397aa54a541c3f97d50513a42060f","cross_cats_sorted":["math-ph","math.CO","math.MP","math.OA","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2025-10-11T23:46:56Z","title_canon_sha256":"9370f64d50810183d630f060a4b1424ebd86cdcd2de1dfba4236839c9528d0be"},"schema_version":"1.0","source":{"id":"2510.10370","kind":"arxiv","version":6}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2510.10370","created_at":"2026-07-22T00:22:13Z"},{"alias_kind":"arxiv_version","alias_value":"2510.10370v6","created_at":"2026-07-22T00:22:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2510.10370","created_at":"2026-07-22T00:22:13Z"},{"alias_kind":"pith_short_12","alias_value":"RBSEEWWUUEWM","created_at":"2026-07-22T00:22:13Z"},{"alias_kind":"pith_short_16","alias_value":"RBSEEWWUUEWMN7P3","created_at":"2026-07-22T00:22:13Z"},{"alias_kind":"pith_short_8","alias_value":"RBSEEWWU","created_at":"2026-07-22T00:22:13Z"}],"graph_snapshots":[{"event_id":"sha256:d80cfe41bddfd808af159158a954e9e984cc2a07de1540c62d5a50ce783cccfb","target":"graph","created_at":"2026-07-22T00:22:13Z","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/2510.10370/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We determine equivalent conditions between the asymptotic coefficients of the Bessel generating functions of a sequence of probability measures and the asymptotic expected values of power sums when their inputs are sampled from these measures. We establish these conditions over the $|\\theta N| \\rightarrow\\infty$ regime for the type A and D root systems and over the $|\\theta_0 N|\\rightarrow \\infty, \\frac{\\theta_1}{\\theta_0 N}\\rightarrow c\\in\\mathbb{C}$ regime for the type BC root system. We also establish equivalent conditions over the $\\theta N \\rightarrow c\\in\\mathbb{C}$ regime for the type A","authors_text":"Andrew Yao","cross_cats":["math-ph","math.CO","math.MP","math.OA","math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2025-10-11T23:46:56Z","title":"Approximating the coefficients of the Bessel functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2510.10370","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:f6a96d839c6b45757fedb738f3c820139b02177b394994efb463c577acd6cab6","target":"record","created_at":"2026-07-22T00:22:13Z","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":"20303495ebd63f4919818cbd733e056ec8d397aa54a541c3f97d50513a42060f","cross_cats_sorted":["math-ph","math.CO","math.MP","math.OA","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2025-10-11T23:46:56Z","title_canon_sha256":"9370f64d50810183d630f060a4b1424ebd86cdcd2de1dfba4236839c9528d0be"},"schema_version":"1.0","source":{"id":"2510.10370","kind":"arxiv","version":6}},"canonical_sha256":"8864425ad4a12cc6fdfbeea99287891dc528b8b60a3b5142288b58f80cfa93ab","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8864425ad4a12cc6fdfbeea99287891dc528b8b60a3b5142288b58f80cfa93ab","first_computed_at":"2026-07-22T00:22:13.158621Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-22T00:22:13.158621Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"D31EhcoKP8+mWtxubeUDLgevl24PlSl9FS5he8cXBUZCrFlbmkEFIZvWCkyHwEdvqKzEgz2cGn5qx7Eb7gwtAg==","signature_status":"signed_v1","signed_at":"2026-07-22T00:22:13.159463Z","signed_message":"canonical_sha256_bytes"},"source_id":"2510.10370","source_kind":"arxiv","source_version":6}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f6a96d839c6b45757fedb738f3c820139b02177b394994efb463c577acd6cab6","sha256:d80cfe41bddfd808af159158a954e9e984cc2a07de1540c62d5a50ce783cccfb"],"state_sha256":"7d580a53e4d7492a97858b59d43ff2743a6efff2d785a6b1049fead86b6e022b"}