{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:IZMIUWIE6HIVVPSPBNR4WHFZ3M","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":"deaf93e5b07e96c8747ef64d6da37612ca387a256c190bd8a76e3bb398d21df5","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-08-25T02:11:31Z","title_canon_sha256":"085e6bb6ad47c67a8a1212d540fdded92faed271c4f7f4e2a96ed954ed8e56dc"},"schema_version":"1.0","source":{"id":"1408.5652","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1408.5652","created_at":"2026-05-18T00:51:58Z"},{"alias_kind":"arxiv_version","alias_value":"1408.5652v5","created_at":"2026-05-18T00:51:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.5652","created_at":"2026-05-18T00:51:58Z"},{"alias_kind":"pith_short_12","alias_value":"IZMIUWIE6HIV","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_16","alias_value":"IZMIUWIE6HIVVPSP","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_8","alias_value":"IZMIUWIE","created_at":"2026-05-18T12:28:33Z"}],"graph_snapshots":[{"event_id":"sha256:a10bdc215629d590a2716a83b40cfa02d38905e55f2dcdab4f68c84a9978feb0","target":"graph","created_at":"2026-05-18T00:51:58Z","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 article we introduce a new category of special functions called fundamental Bessel functions arising from the Voronoi summation formula for $\\mathrm{GL}_n (\\mathbb{R})$. The fundamental Bessel functions of rank one and two are the oscillatory exponential functions $e^{\\pm i x}$ and the classical Bessel functions respectively. The main implements and subjects of our study of fundamental Bessel functions are their formal integral representations and Bessel equations.","authors_text":"Zhi Qi","cross_cats":["math.CA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-08-25T02:11:31Z","title":"Theory of Bessel Functions of High Rank - I: Fundamental Bessel Functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.5652","kind":"arxiv","version":5},"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:a11f12d07e31dfd6df59ab07e2afe1c9717ff77166be8e04d52b29d9dc8cd9d2","target":"record","created_at":"2026-05-18T00:51:58Z","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":"deaf93e5b07e96c8747ef64d6da37612ca387a256c190bd8a76e3bb398d21df5","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-08-25T02:11:31Z","title_canon_sha256":"085e6bb6ad47c67a8a1212d540fdded92faed271c4f7f4e2a96ed954ed8e56dc"},"schema_version":"1.0","source":{"id":"1408.5652","kind":"arxiv","version":5}},"canonical_sha256":"46588a5904f1d15abe4f0b63cb1cb9db14a049b77bfad1f10e074da978675c8a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"46588a5904f1d15abe4f0b63cb1cb9db14a049b77bfad1f10e074da978675c8a","first_computed_at":"2026-05-18T00:51:58.513223Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:51:58.513223Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Hgm+NIAZV5YH4XC0CCc/CDySwNQzd0RyAp4hxCNW6+ZSZnNQl9UGLF4CjjSHSvBCkSpV4mD4K3ezNGXDsz1hBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:51:58.513843Z","signed_message":"canonical_sha256_bytes"},"source_id":"1408.5652","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a11f12d07e31dfd6df59ab07e2afe1c9717ff77166be8e04d52b29d9dc8cd9d2","sha256:a10bdc215629d590a2716a83b40cfa02d38905e55f2dcdab4f68c84a9978feb0"],"state_sha256":"cbbbc1c158473249440cc9a875e48421fb6868461fa620b1892934d1b6bf8781"}