{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2003:BPFIVQF43CUE2ILGM6I5BBDWNU","short_pith_number":"pith:BPFIVQF4","schema_version":"1.0","canonical_sha256":"0bca8ac0bcd8a84d21666791d084766d3ccf6701d4ef89e2f04a86a70b036056","source":{"kind":"arxiv","id":"math/0301176","version":4},"attestation_state":"computed","paper":{"title":"Uhlenbeck spaces via affine Lie algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"A.Braverman, D.Gaitsgory, M.Finkelberg","submitted_at":"2003-01-16T18:51:28Z","abstract_excerpt":"Let $G$ be an almost simple simply connected group over $\\BC$, and let $\\Bun^a_G(\\BP^2,\\BP^1)$ be the moduli scheme of principal $G$-bundles on the projective plave $\\BP^2$, of second Chern class $a$, trivialized along a line $\\BP^1\\subset \\BP^2$.\n  We define the Uhlenbeck compactification $\\fU^a_G$ of $\\Bun^a_G(\\BP^2,\\BP^1)$, which classifies, roughly, pairs $(\\F_G,D)$, where $D$ is a 0-cycle on $\\BA^2=\\BP^2-\\BP^1$ of degree $b$, and $\\F_G$ is a point of $\\Bun^{a-b}_G(\\BP^2,\\BP^1)$, for varying $b$.\n  In addition, we calculate the stalks of the Intersection Cohomology sheaf of $\\fU^a_G$. To 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/0301176","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2003-01-16T18:51:28Z","cross_cats_sorted":[],"title_canon_sha256":"c39bf9b65f72151f13a466fc7a159ba48d0aacd9bcae02aba97018fb02118399","abstract_canon_sha256":"2ab5767967019da99960109c7f917d35b5b699db8933db2744ec86e32b0eb046"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:40:26.498697Z","signature_b64":"xT3p5zccNSyE9NMz8I38kJ4fFdJ841wwBNs4UDMdydhpYzLpzFZ1PPtLMupFqWmnP4h8NY75u5ummB2IpWEQCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0bca8ac0bcd8a84d21666791d084766d3ccf6701d4ef89e2f04a86a70b036056","last_reissued_at":"2026-05-18T03:40:26.498210Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:40:26.498210Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Uhlenbeck spaces via affine Lie algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"A.Braverman, D.Gaitsgory, M.Finkelberg","submitted_at":"2003-01-16T18:51:28Z","abstract_excerpt":"Let $G$ be an almost simple simply connected group over $\\BC$, and let $\\Bun^a_G(\\BP^2,\\BP^1)$ be the moduli scheme of principal $G$-bundles on the projective plave $\\BP^2$, of second Chern class $a$, trivialized along a line $\\BP^1\\subset \\BP^2$.\n  We define the Uhlenbeck compactification $\\fU^a_G$ of $\\Bun^a_G(\\BP^2,\\BP^1)$, which classifies, roughly, pairs $(\\F_G,D)$, where $D$ is a 0-cycle on $\\BA^2=\\BP^2-\\BP^1$ of degree $b$, and $\\F_G$ is a point of $\\Bun^{a-b}_G(\\BP^2,\\BP^1)$, for varying $b$.\n  In addition, we calculate the stalks of the Intersection Cohomology sheaf of $\\fU^a_G$. To d"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0301176","kind":"arxiv","version":4},"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/0301176","created_at":"2026-05-18T03:40:26.498285+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/0301176v4","created_at":"2026-05-18T03:40:26.498285+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0301176","created_at":"2026-05-18T03:40:26.498285+00:00"},{"alias_kind":"pith_short_12","alias_value":"BPFIVQF43CUE","created_at":"2026-05-18T12:25:51.375804+00:00"},{"alias_kind":"pith_short_16","alias_value":"BPFIVQF43CUE2ILG","created_at":"2026-05-18T12:25:51.375804+00:00"},{"alias_kind":"pith_short_8","alias_value":"BPFIVQF4","created_at":"2026-05-18T12:25:51.375804+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/BPFIVQF43CUE2ILGM6I5BBDWNU","json":"https://pith.science/pith/BPFIVQF43CUE2ILGM6I5BBDWNU.json","graph_json":"https://pith.science/api/pith-number/BPFIVQF43CUE2ILGM6I5BBDWNU/graph.json","events_json":"https://pith.science/api/pith-number/BPFIVQF43CUE2ILGM6I5BBDWNU/events.json","paper":"https://pith.science/paper/BPFIVQF4"},"agent_actions":{"view_html":"https://pith.science/pith/BPFIVQF43CUE2ILGM6I5BBDWNU","download_json":"https://pith.science/pith/BPFIVQF43CUE2ILGM6I5BBDWNU.json","view_paper":"https://pith.science/paper/BPFIVQF4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/0301176&json=true","fetch_graph":"https://pith.science/api/pith-number/BPFIVQF43CUE2ILGM6I5BBDWNU/graph.json","fetch_events":"https://pith.science/api/pith-number/BPFIVQF43CUE2ILGM6I5BBDWNU/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BPFIVQF43CUE2ILGM6I5BBDWNU/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BPFIVQF43CUE2ILGM6I5BBDWNU/action/storage_attestation","attest_author":"https://pith.science/pith/BPFIVQF43CUE2ILGM6I5BBDWNU/action/author_attestation","sign_citation":"https://pith.science/pith/BPFIVQF43CUE2ILGM6I5BBDWNU/action/citation_signature","submit_replication":"https://pith.science/pith/BPFIVQF43CUE2ILGM6I5BBDWNU/action/replication_record"}},"created_at":"2026-05-18T03:40:26.498285+00:00","updated_at":"2026-05-18T03:40:26.498285+00:00"}