{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:1998:4YWONEV6HLK7ZHDYSCAVVYXZO4","short_pith_number":"pith:4YWONEV6","schema_version":"1.0","canonical_sha256":"e62ce692be3ad5fc9c7890815ae2f97713a21b99260addd52edf96bfe65ceb44","source":{"kind":"arxiv","id":"math/9811134","version":2},"attestation_state":"computed","paper":{"title":"Computing Hecke eigenvalues below the cohomological dimension","license":"","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Paul E. Gunnells","submitted_at":"1998-11-23T18:11:25Z","abstract_excerpt":"Let G be a torsion-free finite-index subgroup of SL(n,Z) or GL(n,Z), and let d be the cohomological dimension of G. We present an algorithm to compute the eigenvalues of the Hecke operators on the integral cohomology of degree d-1 for n = 2, 3, and 4. In addition, we describe a modification of the modular symbol algorithm of Ash-Rudolph for computing Hecke eigenvalues for the integral cohomology of degree d."},"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":"math/9811134","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.NT","submitted_at":"1998-11-23T18:11:25Z","cross_cats_sorted":[],"title_canon_sha256":"249a4e06da8c4eeec5eae5f5cd5a7b06cc83c148e82d192eda363644313a9af5","abstract_canon_sha256":"a8951db2d216e814ccff8dfd4d6aa8edd10d8b70bef749bffb09a44aad8c209f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:05:33.547815Z","signature_b64":"ZLO7iSOAK7gQh/ClAcFg/KfyvVSihotWLxk+ADCC6e1yG8IcWF9fAwdp1Xafs9nPAFMeulRojmKom8t/IR/WDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e62ce692be3ad5fc9c7890815ae2f97713a21b99260addd52edf96bfe65ceb44","last_reissued_at":"2026-05-18T01:05:33.547198Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:05:33.547198Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Computing Hecke eigenvalues below the cohomological dimension","license":"","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Paul E. Gunnells","submitted_at":"1998-11-23T18:11:25Z","abstract_excerpt":"Let G be a torsion-free finite-index subgroup of SL(n,Z) or GL(n,Z), and let d be the cohomological dimension of G. We present an algorithm to compute the eigenvalues of the Hecke operators on the integral cohomology of degree d-1 for n = 2, 3, and 4. In addition, we describe a modification of the modular symbol algorithm of Ash-Rudolph for computing Hecke eigenvalues for the integral cohomology of degree d."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9811134","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":"math/9811134","created_at":"2026-05-18T01:05:33.547274+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/9811134v2","created_at":"2026-05-18T01:05:33.547274+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/9811134","created_at":"2026-05-18T01:05:33.547274+00:00"},{"alias_kind":"pith_short_12","alias_value":"4YWONEV6HLK7","created_at":"2026-05-18T12:25:49.038998+00:00"},{"alias_kind":"pith_short_16","alias_value":"4YWONEV6HLK7ZHDY","created_at":"2026-05-18T12:25:49.038998+00:00"},{"alias_kind":"pith_short_8","alias_value":"4YWONEV6","created_at":"2026-05-18T12:25:49.038998+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/4YWONEV6HLK7ZHDYSCAVVYXZO4","json":"https://pith.science/pith/4YWONEV6HLK7ZHDYSCAVVYXZO4.json","graph_json":"https://pith.science/api/pith-number/4YWONEV6HLK7ZHDYSCAVVYXZO4/graph.json","events_json":"https://pith.science/api/pith-number/4YWONEV6HLK7ZHDYSCAVVYXZO4/events.json","paper":"https://pith.science/paper/4YWONEV6"},"agent_actions":{"view_html":"https://pith.science/pith/4YWONEV6HLK7ZHDYSCAVVYXZO4","download_json":"https://pith.science/pith/4YWONEV6HLK7ZHDYSCAVVYXZO4.json","view_paper":"https://pith.science/paper/4YWONEV6","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/9811134&json=true","fetch_graph":"https://pith.science/api/pith-number/4YWONEV6HLK7ZHDYSCAVVYXZO4/graph.json","fetch_events":"https://pith.science/api/pith-number/4YWONEV6HLK7ZHDYSCAVVYXZO4/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4YWONEV6HLK7ZHDYSCAVVYXZO4/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4YWONEV6HLK7ZHDYSCAVVYXZO4/action/storage_attestation","attest_author":"https://pith.science/pith/4YWONEV6HLK7ZHDYSCAVVYXZO4/action/author_attestation","sign_citation":"https://pith.science/pith/4YWONEV6HLK7ZHDYSCAVVYXZO4/action/citation_signature","submit_replication":"https://pith.science/pith/4YWONEV6HLK7ZHDYSCAVVYXZO4/action/replication_record"}},"created_at":"2026-05-18T01:05:33.547274+00:00","updated_at":"2026-05-18T01:05:33.547274+00:00"}