{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:JUSQNWGFU2QD4VOPBLDLJFXQKR","short_pith_number":"pith:JUSQNWGF","schema_version":"1.0","canonical_sha256":"4d2506d8c5a6a03e55cf0ac6b496f054697bff11b89a470a507e7cc8ee6696de","source":{"kind":"arxiv","id":"1701.02331","version":2},"attestation_state":"computed","paper":{"title":"Invariant bilinear forms on $W$-graph representations and linear algebra over integral domains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"J\\\"urgen M\\\"uller, Meinolf Geck","submitted_at":"2017-01-09T19:56:37Z","abstract_excerpt":"Lie-theoretic structures of type $E_8$ (e.g., Lie groups and algebras, Hecke algebras and Kazhdan-Lusztig cells, ...) are considered to serve as a `gold standard' when it comes to judging the effectiveness of a general algorithm for solving a computational problem in this area. Here, we address a problem that occurred in our previous work on decomposition numbers of Iwahori-Hecke algebras, namely, the computation of invariant bilinear forms on so-called $W$-graph representations. We present a new algorithmic solution which makes it possible to produce and effectively use the main results in fu"},"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":"1701.02331","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2017-01-09T19:56:37Z","cross_cats_sorted":[],"title_canon_sha256":"8b456feff4c2d9c38df7e21a92da97553640880efa00671f35dbab8af4e913dd","abstract_canon_sha256":"f117644402c20f2deef2e7740dccae7a60f6213e25af50c31e2977c22d44528d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:44:57.471095Z","signature_b64":"lbuRatpnkT2vmQLHS1nTavYB1QVCiiRXe27lmU1V5rv0dE1T6YJ26rvzoUV100f8LOYj7dWrFjRuZ87IuzSTDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4d2506d8c5a6a03e55cf0ac6b496f054697bff11b89a470a507e7cc8ee6696de","last_reissued_at":"2026-05-18T00:44:57.470465Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:44:57.470465Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Invariant bilinear forms on $W$-graph representations and linear algebra over integral domains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"J\\\"urgen M\\\"uller, Meinolf Geck","submitted_at":"2017-01-09T19:56:37Z","abstract_excerpt":"Lie-theoretic structures of type $E_8$ (e.g., Lie groups and algebras, Hecke algebras and Kazhdan-Lusztig cells, ...) are considered to serve as a `gold standard' when it comes to judging the effectiveness of a general algorithm for solving a computational problem in this area. Here, we address a problem that occurred in our previous work on decomposition numbers of Iwahori-Hecke algebras, namely, the computation of invariant bilinear forms on so-called $W$-graph representations. We present a new algorithmic solution which makes it possible to produce and effectively use the main results in fu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.02331","kind":"arxiv","version":2},"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":"1701.02331","created_at":"2026-05-18T00:44:57.470562+00:00"},{"alias_kind":"arxiv_version","alias_value":"1701.02331v2","created_at":"2026-05-18T00:44:57.470562+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.02331","created_at":"2026-05-18T00:44:57.470562+00:00"},{"alias_kind":"pith_short_12","alias_value":"JUSQNWGFU2QD","created_at":"2026-05-18T12:31:24.725408+00:00"},{"alias_kind":"pith_short_16","alias_value":"JUSQNWGFU2QD4VOP","created_at":"2026-05-18T12:31:24.725408+00:00"},{"alias_kind":"pith_short_8","alias_value":"JUSQNWGF","created_at":"2026-05-18T12:31:24.725408+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/JUSQNWGFU2QD4VOPBLDLJFXQKR","json":"https://pith.science/pith/JUSQNWGFU2QD4VOPBLDLJFXQKR.json","graph_json":"https://pith.science/api/pith-number/JUSQNWGFU2QD4VOPBLDLJFXQKR/graph.json","events_json":"https://pith.science/api/pith-number/JUSQNWGFU2QD4VOPBLDLJFXQKR/events.json","paper":"https://pith.science/paper/JUSQNWGF"},"agent_actions":{"view_html":"https://pith.science/pith/JUSQNWGFU2QD4VOPBLDLJFXQKR","download_json":"https://pith.science/pith/JUSQNWGFU2QD4VOPBLDLJFXQKR.json","view_paper":"https://pith.science/paper/JUSQNWGF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1701.02331&json=true","fetch_graph":"https://pith.science/api/pith-number/JUSQNWGFU2QD4VOPBLDLJFXQKR/graph.json","fetch_events":"https://pith.science/api/pith-number/JUSQNWGFU2QD4VOPBLDLJFXQKR/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JUSQNWGFU2QD4VOPBLDLJFXQKR/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JUSQNWGFU2QD4VOPBLDLJFXQKR/action/storage_attestation","attest_author":"https://pith.science/pith/JUSQNWGFU2QD4VOPBLDLJFXQKR/action/author_attestation","sign_citation":"https://pith.science/pith/JUSQNWGFU2QD4VOPBLDLJFXQKR/action/citation_signature","submit_replication":"https://pith.science/pith/JUSQNWGFU2QD4VOPBLDLJFXQKR/action/replication_record"}},"created_at":"2026-05-18T00:44:57.470562+00:00","updated_at":"2026-05-18T00:44:57.470562+00:00"}