{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:VBK7P4NW5YQXBRVTL6A63URYPU","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":"bc78305f9c3f204c5589f7c9eb21eb3531c805778726b218bf1d892676786b4e","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2024-04-06T15:49:08Z","title_canon_sha256":"7e4dd63dd3e2fc523c14e4b2a91ea7e7ee64207f9bce916a3e1358487a702077"},"schema_version":"1.0","source":{"id":"2404.04666","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2404.04666","created_at":"2026-07-05T08:05:58Z"},{"alias_kind":"arxiv_version","alias_value":"2404.04666v2","created_at":"2026-07-05T08:05:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2404.04666","created_at":"2026-07-05T08:05:58Z"},{"alias_kind":"pith_short_12","alias_value":"VBK7P4NW5YQX","created_at":"2026-07-05T08:05:58Z"},{"alias_kind":"pith_short_16","alias_value":"VBK7P4NW5YQXBRVT","created_at":"2026-07-05T08:05:58Z"},{"alias_kind":"pith_short_8","alias_value":"VBK7P4NW","created_at":"2026-07-05T08:05:58Z"}],"graph_snapshots":[{"event_id":"sha256:ba1cbcea3e13397e2486f8a90cc15e0d6141c5d35abd225439fb4f663d746a7d","target":"graph","created_at":"2026-07-05T08:05:58Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2404.04666/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We provide the explicit formula for orbital integrals associated with elliptic regular semisimple elements in $\\mathrm{GL}_n(F) \\cap \\mathrm{M}_n(\\mathfrak{o})$ and associated with arbitrary elements of the spherical Hecke algebra of $\\mathrm{GL}_n(F)$ when $n=2, 3$, using results of [CKL]. Here $F$ is a non-Archimedean local field of any characteristic with $\\mathfrak{o}$ its ring of integers.","authors_text":"Sungmun Cho, Yuchan Lee","cross_cats":["math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2024-04-06T15:49:08Z","title":"An explicit formula for the orbital integrals on the spherical Hecke algebra of $\\mathrm{GL}_3$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2404.04666","kind":"arxiv","version":2},"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:e177cf91e71f3b280f5ee32c7d840d597babadef351905b0576e5cf7ae106c98","target":"record","created_at":"2026-07-05T08:05:58Z","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":"bc78305f9c3f204c5589f7c9eb21eb3531c805778726b218bf1d892676786b4e","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2024-04-06T15:49:08Z","title_canon_sha256":"7e4dd63dd3e2fc523c14e4b2a91ea7e7ee64207f9bce916a3e1358487a702077"},"schema_version":"1.0","source":{"id":"2404.04666","kind":"arxiv","version":2}},"canonical_sha256":"a855f7f1b6ee2170c6b35f81edd2387d3db41c4667cb747493effbe3d09b1b30","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a855f7f1b6ee2170c6b35f81edd2387d3db41c4667cb747493effbe3d09b1b30","first_computed_at":"2026-07-05T08:05:58.444124Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:05:58.444124Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jFkCyYvF1/o7nxcEl4rOqz3ojD9MAv04Dt1mDVhVbanPQioQUYwTiLNpIyalt0K9DAz/d8cbAsoi94jJlRUbAQ==","signature_status":"signed_v1","signed_at":"2026-07-05T08:05:58.444538Z","signed_message":"canonical_sha256_bytes"},"source_id":"2404.04666","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e177cf91e71f3b280f5ee32c7d840d597babadef351905b0576e5cf7ae106c98","sha256:ba1cbcea3e13397e2486f8a90cc15e0d6141c5d35abd225439fb4f663d746a7d"],"state_sha256":"da48285a047d7714eeda4b77c934ca3044846f55192465e84e8f7028685cf03f"}