{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:BLRE4THGSKVFUJRRLUJW4PN4YN","short_pith_number":"pith:BLRE4THG","schema_version":"1.0","canonical_sha256":"0ae24e4ce692aa5a26315d136e3dbcc3442bde44ed6e6fd4359fee1bde9e551d","source":{"kind":"arxiv","id":"1609.07456","version":1},"attestation_state":"computed","paper":{"title":"Bounds on multiplicities of spherical spaces over finite fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Avraham Aizenbud, Nir Avni","submitted_at":"2016-09-23T18:31:18Z","abstract_excerpt":"Let $G$ be a reductive group scheme of type $A$ acting on a spherical scheme $X$. We prove that there exists a number $C$ such that the multiplicity $\\dim Hom(\\rho,\\mathbb{C}[X(F)])$ is bounded by $C$, for any finite field $F$ and any irreducible representation $\\rho$ of $G(F)$. We give an explicit bound for $C$.\n  We conjecture that this result is true for any reductive group scheme and when $F$ ranges (in addition) over all local fields of characteristic $0$."},"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":"1609.07456","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2016-09-23T18:31:18Z","cross_cats_sorted":[],"title_canon_sha256":"1bf216069d69690a015969d9fbb2436bc8cd565dac1bdef7e61e7ef09fd64ed5","abstract_canon_sha256":"a48b038df6b21bc0f6ed7b2c4b18e876194b4021d2952df967839e5053c36472"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:04:00.810388Z","signature_b64":"uGRj7jLN6y06N+699gytjnynGTn6ybV4CrLWcos/E99EwKhzMd+qfS/eDKO2OVvRVrkjgkPa4dXkswUYkHitDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0ae24e4ce692aa5a26315d136e3dbcc3442bde44ed6e6fd4359fee1bde9e551d","last_reissued_at":"2026-05-18T01:04:00.809690Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:04:00.809690Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Bounds on multiplicities of spherical spaces over finite fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Avraham Aizenbud, Nir Avni","submitted_at":"2016-09-23T18:31:18Z","abstract_excerpt":"Let $G$ be a reductive group scheme of type $A$ acting on a spherical scheme $X$. We prove that there exists a number $C$ such that the multiplicity $\\dim Hom(\\rho,\\mathbb{C}[X(F)])$ is bounded by $C$, for any finite field $F$ and any irreducible representation $\\rho$ of $G(F)$. We give an explicit bound for $C$.\n  We conjecture that this result is true for any reductive group scheme and when $F$ ranges (in addition) over all local fields of characteristic $0$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.07456","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":""},"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":"1609.07456","created_at":"2026-05-18T01:04:00.809796+00:00"},{"alias_kind":"arxiv_version","alias_value":"1609.07456v1","created_at":"2026-05-18T01:04:00.809796+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.07456","created_at":"2026-05-18T01:04:00.809796+00:00"},{"alias_kind":"pith_short_12","alias_value":"BLRE4THGSKVF","created_at":"2026-05-18T12:30:07.202191+00:00"},{"alias_kind":"pith_short_16","alias_value":"BLRE4THGSKVFUJRR","created_at":"2026-05-18T12:30:07.202191+00:00"},{"alias_kind":"pith_short_8","alias_value":"BLRE4THG","created_at":"2026-05-18T12:30:07.202191+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/BLRE4THGSKVFUJRRLUJW4PN4YN","json":"https://pith.science/pith/BLRE4THGSKVFUJRRLUJW4PN4YN.json","graph_json":"https://pith.science/api/pith-number/BLRE4THGSKVFUJRRLUJW4PN4YN/graph.json","events_json":"https://pith.science/api/pith-number/BLRE4THGSKVFUJRRLUJW4PN4YN/events.json","paper":"https://pith.science/paper/BLRE4THG"},"agent_actions":{"view_html":"https://pith.science/pith/BLRE4THGSKVFUJRRLUJW4PN4YN","download_json":"https://pith.science/pith/BLRE4THGSKVFUJRRLUJW4PN4YN.json","view_paper":"https://pith.science/paper/BLRE4THG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1609.07456&json=true","fetch_graph":"https://pith.science/api/pith-number/BLRE4THGSKVFUJRRLUJW4PN4YN/graph.json","fetch_events":"https://pith.science/api/pith-number/BLRE4THGSKVFUJRRLUJW4PN4YN/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BLRE4THGSKVFUJRRLUJW4PN4YN/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BLRE4THGSKVFUJRRLUJW4PN4YN/action/storage_attestation","attest_author":"https://pith.science/pith/BLRE4THGSKVFUJRRLUJW4PN4YN/action/author_attestation","sign_citation":"https://pith.science/pith/BLRE4THGSKVFUJRRLUJW4PN4YN/action/citation_signature","submit_replication":"https://pith.science/pith/BLRE4THGSKVFUJRRLUJW4PN4YN/action/replication_record"}},"created_at":"2026-05-18T01:04:00.809796+00:00","updated_at":"2026-05-18T01:04:00.809796+00:00"}