{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:LJDQSXPR4GPAVTWH6H5ANSLFOZ","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":"890734e7ab147611051b03b11fbd45ceb0ee549cf7bd4739aead716ee77392af","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2012-04-12T11:38:52Z","title_canon_sha256":"4e9dfaa4436149440c12e86d20a51609df0431895afbcd9842d788c9647bd818"},"schema_version":"1.0","source":{"id":"1204.2690","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1204.2690","created_at":"2026-05-18T03:58:03Z"},{"alias_kind":"arxiv_version","alias_value":"1204.2690v1","created_at":"2026-05-18T03:58:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.2690","created_at":"2026-05-18T03:58:03Z"},{"alias_kind":"pith_short_12","alias_value":"LJDQSXPR4GPA","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_16","alias_value":"LJDQSXPR4GPAVTWH","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_8","alias_value":"LJDQSXPR","created_at":"2026-05-18T12:27:14Z"}],"graph_snapshots":[{"event_id":"sha256:1ce32ce74bf7ba0ca84c7f4dc7966f0645c6a672868bde9badd2fc5993a25aec","target":"graph","created_at":"2026-05-18T03:58:03Z","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":"We study multiplicities of unipotent characters in tensor products of unipotent characters of GL(n,q). We prove that these multiplicities are polynomials in q with non-negative integer coefficients. We study the degree of these polynomials and give a necessary and sufficient condition in terms of the representation theory of symmetric groups for these polynomials to be non-zero.","authors_text":"Emmanuel Letellier","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2012-04-12T11:38:52Z","title":"Tensor products of unipotent characters of general linear groups over finite fields"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.2690","kind":"arxiv","version":1},"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":"sha256:300d95bcd2f62415163dddc89804e03f413d3ae0437a228d9174d1c2a4b1c0d3","target":"record","created_at":"2026-05-18T03:58:03Z","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":"890734e7ab147611051b03b11fbd45ceb0ee549cf7bd4739aead716ee77392af","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2012-04-12T11:38:52Z","title_canon_sha256":"4e9dfaa4436149440c12e86d20a51609df0431895afbcd9842d788c9647bd818"},"schema_version":"1.0","source":{"id":"1204.2690","kind":"arxiv","version":1}},"canonical_sha256":"5a47095df1e19e0acec7f1fa06c965767343f591a7f05c9898ebc433f8bd9e0d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5a47095df1e19e0acec7f1fa06c965767343f591a7f05c9898ebc433f8bd9e0d","first_computed_at":"2026-05-18T03:58:03.715359Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:58:03.715359Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"q0RFNTcb8ph+gEJPnDuiL1IrJhgK3+YOjmeEOg3O/qKpsPClkpTBgmRAAyGGo+VpsVpkR8E2Ymd+n4oLzzgbBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:58:03.717038Z","signed_message":"canonical_sha256_bytes"},"source_id":"1204.2690","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:300d95bcd2f62415163dddc89804e03f413d3ae0437a228d9174d1c2a4b1c0d3","sha256:1ce32ce74bf7ba0ca84c7f4dc7966f0645c6a672868bde9badd2fc5993a25aec"],"state_sha256":"091bd46ddd5213e8a3ba787291164878aa0fb80ec7c2fdcd2a414de8bf8d82a2"}