{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:VURWTQY3HEPDIRGLSZGXVIWY4U","short_pith_number":"pith:VURWTQY3","schema_version":"1.0","canonical_sha256":"ad2369c31b391e3444cb964d7aa2d8e5344ee616418d9433d1846d406e95de75","source":{"kind":"arxiv","id":"2504.20564","version":1},"attestation_state":"computed","paper":{"title":"The number of cuspidal representations over a function field and its behavior under base changes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Takuro Fukayama","submitted_at":"2025-04-29T09:09:03Z","abstract_excerpt":"Let $X$ be a smooth projective curve over a finite field $\\mathbb{F}_q$, $k$ be its function field, and $G$ be a simply connected almost simple split group over $\\mathbb{F}_q$. We also write $G$ for its structure over $k$. We calculate the sum of multiplicities of all cuspidal representations of $G$ satisfying a given condition assuming the conjectural trace formula. We also observe how the sum changes if we replace $X$ by its base change $X\\otimes_{\\mathbb{F}_q}\\mathbb{F}_{q^m}$."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2504.20564","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2025-04-29T09:09:03Z","cross_cats_sorted":[],"title_canon_sha256":"de3f9491786ad0824caf6e62f929dc30578eeb6a7f2ac62995ba50f023856209","abstract_canon_sha256":"393450a92cdcc8b2c707040189cb26d5c0108abb12d0d85a94ad0498345418f4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:55:44.814000Z","signature_b64":"b3hz3XwWYWnTfzCiXSm6ZCUsLYqV1SIjYpo8/U/Q5GEkVvn/LFll36tBo5LRc7rLUucJJGW3hh+SftIKxr3ACA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ad2369c31b391e3444cb964d7aa2d8e5344ee616418d9433d1846d406e95de75","last_reissued_at":"2026-07-05T10:55:44.813600Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:55:44.813600Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The number of cuspidal representations over a function field and its behavior under base changes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Takuro Fukayama","submitted_at":"2025-04-29T09:09:03Z","abstract_excerpt":"Let $X$ be a smooth projective curve over a finite field $\\mathbb{F}_q$, $k$ be its function field, and $G$ be a simply connected almost simple split group over $\\mathbb{F}_q$. We also write $G$ for its structure over $k$. We calculate the sum of multiplicities of all cuspidal representations of $G$ satisfying a given condition assuming the conjectural trace formula. We also observe how the sum changes if we replace $X$ by its base change $X\\otimes_{\\mathbb{F}_q}\\mathbb{F}_{q^m}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2504.20564","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2504.20564/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"2504.20564","created_at":"2026-07-05T10:55:44.813655+00:00"},{"alias_kind":"arxiv_version","alias_value":"2504.20564v1","created_at":"2026-07-05T10:55:44.813655+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2504.20564","created_at":"2026-07-05T10:55:44.813655+00:00"},{"alias_kind":"pith_short_12","alias_value":"VURWTQY3HEPD","created_at":"2026-07-05T10:55:44.813655+00:00"},{"alias_kind":"pith_short_16","alias_value":"VURWTQY3HEPDIRGL","created_at":"2026-07-05T10:55:44.813655+00:00"},{"alias_kind":"pith_short_8","alias_value":"VURWTQY3","created_at":"2026-07-05T10:55:44.813655+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/VURWTQY3HEPDIRGLSZGXVIWY4U","json":"https://pith.science/pith/VURWTQY3HEPDIRGLSZGXVIWY4U.json","graph_json":"https://pith.science/api/pith-number/VURWTQY3HEPDIRGLSZGXVIWY4U/graph.json","events_json":"https://pith.science/api/pith-number/VURWTQY3HEPDIRGLSZGXVIWY4U/events.json","paper":"https://pith.science/paper/VURWTQY3"},"agent_actions":{"view_html":"https://pith.science/pith/VURWTQY3HEPDIRGLSZGXVIWY4U","download_json":"https://pith.science/pith/VURWTQY3HEPDIRGLSZGXVIWY4U.json","view_paper":"https://pith.science/paper/VURWTQY3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2504.20564&json=true","fetch_graph":"https://pith.science/api/pith-number/VURWTQY3HEPDIRGLSZGXVIWY4U/graph.json","fetch_events":"https://pith.science/api/pith-number/VURWTQY3HEPDIRGLSZGXVIWY4U/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VURWTQY3HEPDIRGLSZGXVIWY4U/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VURWTQY3HEPDIRGLSZGXVIWY4U/action/storage_attestation","attest_author":"https://pith.science/pith/VURWTQY3HEPDIRGLSZGXVIWY4U/action/author_attestation","sign_citation":"https://pith.science/pith/VURWTQY3HEPDIRGLSZGXVIWY4U/action/citation_signature","submit_replication":"https://pith.science/pith/VURWTQY3HEPDIRGLSZGXVIWY4U/action/replication_record"}},"created_at":"2026-07-05T10:55:44.813655+00:00","updated_at":"2026-07-05T10:55:44.813655+00:00"}