{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:USDKQFO737RERTQ7GGN4VZA2AW","short_pith_number":"pith:USDKQFO7","schema_version":"1.0","canonical_sha256":"a486a815dfdfe248ce1f319bcae41a05af2783932cacaa61c9059fec4d8beda9","source":{"kind":"arxiv","id":"1012.5257","version":5},"attestation_state":"computed","paper":{"title":"Geometric approach to Hall algebra of representations of Quivers over local ring","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Zhaobing Fan","submitted_at":"2010-12-23T17:32:42Z","abstract_excerpt":"By using perverse sheaves on representation spaces of quivers over $k[t]/(t^n)$ and jet schemes over flag varieties, we construct a geometric composition algebra $\\mathbf K$ under Lusztig's framework on geometric realizations of the negative part of quantum algebras. Simple perverse sheaves in $\\mathbf K$ form the canonical basis of $\\mathbf K$. The relationships among the algebra $\\mathbf K$, the composition algebra of locally projective representations of quivers over $k[t]/(t^n)$ and quantum generalized Kac-Moody algebra are provided."},"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":"1012.5257","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2010-12-23T17:32:42Z","cross_cats_sorted":[],"title_canon_sha256":"dbe779959fe426d9aeea56266df91246903f502274ed0859ce1aaf684924cfa6","abstract_canon_sha256":"b0fb15ac95a54cacd6cca8358e99cf11904f3d05ddb88a273f0bafd51b18abf3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:39:38.484995Z","signature_b64":"EiY9YxvrgPxiwWkBiC9kVTz7N8dSDxpM1elKuiVu/DXReonfiCgbkXhZDlEpRJb5uMnT47QzPyto6JhpvKOCDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a486a815dfdfe248ce1f319bcae41a05af2783932cacaa61c9059fec4d8beda9","last_reissued_at":"2026-05-18T02:39:38.484630Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:39:38.484630Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Geometric approach to Hall algebra of representations of Quivers over local ring","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Zhaobing Fan","submitted_at":"2010-12-23T17:32:42Z","abstract_excerpt":"By using perverse sheaves on representation spaces of quivers over $k[t]/(t^n)$ and jet schemes over flag varieties, we construct a geometric composition algebra $\\mathbf K$ under Lusztig's framework on geometric realizations of the negative part of quantum algebras. Simple perverse sheaves in $\\mathbf K$ form the canonical basis of $\\mathbf K$. The relationships among the algebra $\\mathbf K$, the composition algebra of locally projective representations of quivers over $k[t]/(t^n)$ and quantum generalized Kac-Moody algebra are provided."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.5257","kind":"arxiv","version":5},"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":"1012.5257","created_at":"2026-05-18T02:39:38.484686+00:00"},{"alias_kind":"arxiv_version","alias_value":"1012.5257v5","created_at":"2026-05-18T02:39:38.484686+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1012.5257","created_at":"2026-05-18T02:39:38.484686+00:00"},{"alias_kind":"pith_short_12","alias_value":"USDKQFO737RE","created_at":"2026-05-18T12:26:15.391820+00:00"},{"alias_kind":"pith_short_16","alias_value":"USDKQFO737RERTQ7","created_at":"2026-05-18T12:26:15.391820+00:00"},{"alias_kind":"pith_short_8","alias_value":"USDKQFO7","created_at":"2026-05-18T12:26:15.391820+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/USDKQFO737RERTQ7GGN4VZA2AW","json":"https://pith.science/pith/USDKQFO737RERTQ7GGN4VZA2AW.json","graph_json":"https://pith.science/api/pith-number/USDKQFO737RERTQ7GGN4VZA2AW/graph.json","events_json":"https://pith.science/api/pith-number/USDKQFO737RERTQ7GGN4VZA2AW/events.json","paper":"https://pith.science/paper/USDKQFO7"},"agent_actions":{"view_html":"https://pith.science/pith/USDKQFO737RERTQ7GGN4VZA2AW","download_json":"https://pith.science/pith/USDKQFO737RERTQ7GGN4VZA2AW.json","view_paper":"https://pith.science/paper/USDKQFO7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1012.5257&json=true","fetch_graph":"https://pith.science/api/pith-number/USDKQFO737RERTQ7GGN4VZA2AW/graph.json","fetch_events":"https://pith.science/api/pith-number/USDKQFO737RERTQ7GGN4VZA2AW/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/USDKQFO737RERTQ7GGN4VZA2AW/action/timestamp_anchor","attest_storage":"https://pith.science/pith/USDKQFO737RERTQ7GGN4VZA2AW/action/storage_attestation","attest_author":"https://pith.science/pith/USDKQFO737RERTQ7GGN4VZA2AW/action/author_attestation","sign_citation":"https://pith.science/pith/USDKQFO737RERTQ7GGN4VZA2AW/action/citation_signature","submit_replication":"https://pith.science/pith/USDKQFO737RERTQ7GGN4VZA2AW/action/replication_record"}},"created_at":"2026-05-18T02:39:38.484686+00:00","updated_at":"2026-05-18T02:39:38.484686+00:00"}