{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2009:EYJJCTCUE6WA6LW3AU34UOUOB5","short_pith_number":"pith:EYJJCTCU","schema_version":"1.0","canonical_sha256":"2612914c5427ac0f2edb0537ca3a8e0f407535ac10ce4541503f644fe70a771d","source":{"kind":"arxiv","id":"0907.4626","version":3},"attestation_state":"computed","paper":{"title":"The second cohomology of simple SL_3-modules","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"David I. Stewart","submitted_at":"2009-07-27T13:35:55Z","abstract_excerpt":"Let G be the simple, simply connected algebraic group SL_3 defined over an algebraically closed field K of characteristic p>0. In this paper, we find H^2(G,V) for any irreducible G-module V. When p>7 we also find H^2(G(q),V) for any irreducible G(q)-module V for the finite Chevalley groups G(q)=SL(3,q) where q is a power of p."},"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":"0907.4626","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2009-07-27T13:35:55Z","cross_cats_sorted":[],"title_canon_sha256":"ba93c0b7db324dca7f12dc17bf6f0b6db76bc92ea6c43f2e012b22f91f0cb1c3","abstract_canon_sha256":"bec26102d8dd848d1959488141018f3efbd3e4f1d1be6468dc26d41160b18703"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:01:47.597994Z","signature_b64":"8TAxWO2pCdwbIDahKKdMrMpgh61jkzHJs7+occcaNL1QPTD0ZM1JIhpkHsJXjsX7/NgZME7bKsB+a/KoHaqZBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2612914c5427ac0f2edb0537ca3a8e0f407535ac10ce4541503f644fe70a771d","last_reissued_at":"2026-05-18T00:01:47.597256Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:01:47.597256Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The second cohomology of simple SL_3-modules","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"David I. Stewart","submitted_at":"2009-07-27T13:35:55Z","abstract_excerpt":"Let G be the simple, simply connected algebraic group SL_3 defined over an algebraically closed field K of characteristic p>0. In this paper, we find H^2(G,V) for any irreducible G-module V. When p>7 we also find H^2(G(q),V) for any irreducible G(q)-module V for the finite Chevalley groups G(q)=SL(3,q) where q is a power of p."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0907.4626","kind":"arxiv","version":3},"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":"0907.4626","created_at":"2026-05-18T00:01:47.597397+00:00"},{"alias_kind":"arxiv_version","alias_value":"0907.4626v3","created_at":"2026-05-18T00:01:47.597397+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0907.4626","created_at":"2026-05-18T00:01:47.597397+00:00"},{"alias_kind":"pith_short_12","alias_value":"EYJJCTCUE6WA","created_at":"2026-05-18T12:25:59.703012+00:00"},{"alias_kind":"pith_short_16","alias_value":"EYJJCTCUE6WA6LW3","created_at":"2026-05-18T12:25:59.703012+00:00"},{"alias_kind":"pith_short_8","alias_value":"EYJJCTCU","created_at":"2026-05-18T12:25:59.703012+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/EYJJCTCUE6WA6LW3AU34UOUOB5","json":"https://pith.science/pith/EYJJCTCUE6WA6LW3AU34UOUOB5.json","graph_json":"https://pith.science/api/pith-number/EYJJCTCUE6WA6LW3AU34UOUOB5/graph.json","events_json":"https://pith.science/api/pith-number/EYJJCTCUE6WA6LW3AU34UOUOB5/events.json","paper":"https://pith.science/paper/EYJJCTCU"},"agent_actions":{"view_html":"https://pith.science/pith/EYJJCTCUE6WA6LW3AU34UOUOB5","download_json":"https://pith.science/pith/EYJJCTCUE6WA6LW3AU34UOUOB5.json","view_paper":"https://pith.science/paper/EYJJCTCU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0907.4626&json=true","fetch_graph":"https://pith.science/api/pith-number/EYJJCTCUE6WA6LW3AU34UOUOB5/graph.json","fetch_events":"https://pith.science/api/pith-number/EYJJCTCUE6WA6LW3AU34UOUOB5/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/EYJJCTCUE6WA6LW3AU34UOUOB5/action/timestamp_anchor","attest_storage":"https://pith.science/pith/EYJJCTCUE6WA6LW3AU34UOUOB5/action/storage_attestation","attest_author":"https://pith.science/pith/EYJJCTCUE6WA6LW3AU34UOUOB5/action/author_attestation","sign_citation":"https://pith.science/pith/EYJJCTCUE6WA6LW3AU34UOUOB5/action/citation_signature","submit_replication":"https://pith.science/pith/EYJJCTCUE6WA6LW3AU34UOUOB5/action/replication_record"}},"created_at":"2026-05-18T00:01:47.597397+00:00","updated_at":"2026-05-18T00:01:47.597397+00:00"}