{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2005:3ASXSQEBL4LWMF7RSB64G6BWPG","short_pith_number":"pith:3ASXSQEB","schema_version":"1.0","canonical_sha256":"d8257940815f176617f1907dc37836799f66ce271ac2b6fac5a857203ac7bb6f","source":{"kind":"arxiv","id":"math/0512247","version":2},"attestation_state":"computed","paper":{"title":"D-bar Sparks, I","license":"","headline":"","cross_cats":["math.CV"],"primary_cat":"math.DG","authors_text":"F. Reese Harvey, H. Blaine Lawson Jr","submitted_at":"2005-12-12T18:47:57Z","abstract_excerpt":"A d-bar-analogue of differential characters for complex manifolds is introduced and studied using a new theory of homological spark complexes. Many essentially different spark complexes are shown to have isomorphic groups of spark classes. This has many consequences: It leads to an analytic representation of O*-gerbes with connection, it yields a soft resolution of the sheaf O* by currents on the manifold, and more generally it gives a Dolbeault-Federer representation of Deligne cohomology as the cohomology of certain complexes of currents.\n  It is shown that the d-bar-spark classes H^*(X) car"},"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/0512247","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.DG","submitted_at":"2005-12-12T18:47:57Z","cross_cats_sorted":["math.CV"],"title_canon_sha256":"3655837673ed2d24f3146b96d671c815a6fb27fb5703afb7cd6d70b2c4e3ff14","abstract_canon_sha256":"248d136063f168c339f7f04f101858e556a23cfd00e974ab96c32d90ad3f031e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:28:19.434867Z","signature_b64":"Gym9vHkgl2iySK78AVP8FB2ToQlSnR7E0GSghNH1EmHF7re4Mj8pECU9MulZJ61ohbMYg+JXYXPpS3BWhuOcAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d8257940815f176617f1907dc37836799f66ce271ac2b6fac5a857203ac7bb6f","last_reissued_at":"2026-05-18T00:28:19.434076Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:28:19.434076Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"D-bar Sparks, I","license":"","headline":"","cross_cats":["math.CV"],"primary_cat":"math.DG","authors_text":"F. Reese Harvey, H. Blaine Lawson Jr","submitted_at":"2005-12-12T18:47:57Z","abstract_excerpt":"A d-bar-analogue of differential characters for complex manifolds is introduced and studied using a new theory of homological spark complexes. Many essentially different spark complexes are shown to have isomorphic groups of spark classes. This has many consequences: It leads to an analytic representation of O*-gerbes with connection, it yields a soft resolution of the sheaf O* by currents on the manifold, and more generally it gives a Dolbeault-Federer representation of Deligne cohomology as the cohomology of certain complexes of currents.\n  It is shown that the d-bar-spark classes H^*(X) car"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0512247","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/0512247","created_at":"2026-05-18T00:28:19.434210+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/0512247v2","created_at":"2026-05-18T00:28:19.434210+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0512247","created_at":"2026-05-18T00:28:19.434210+00:00"},{"alias_kind":"pith_short_12","alias_value":"3ASXSQEBL4LW","created_at":"2026-05-18T12:25:52.687210+00:00"},{"alias_kind":"pith_short_16","alias_value":"3ASXSQEBL4LWMF7R","created_at":"2026-05-18T12:25:52.687210+00:00"},{"alias_kind":"pith_short_8","alias_value":"3ASXSQEB","created_at":"2026-05-18T12:25:52.687210+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/3ASXSQEBL4LWMF7RSB64G6BWPG","json":"https://pith.science/pith/3ASXSQEBL4LWMF7RSB64G6BWPG.json","graph_json":"https://pith.science/api/pith-number/3ASXSQEBL4LWMF7RSB64G6BWPG/graph.json","events_json":"https://pith.science/api/pith-number/3ASXSQEBL4LWMF7RSB64G6BWPG/events.json","paper":"https://pith.science/paper/3ASXSQEB"},"agent_actions":{"view_html":"https://pith.science/pith/3ASXSQEBL4LWMF7RSB64G6BWPG","download_json":"https://pith.science/pith/3ASXSQEBL4LWMF7RSB64G6BWPG.json","view_paper":"https://pith.science/paper/3ASXSQEB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/0512247&json=true","fetch_graph":"https://pith.science/api/pith-number/3ASXSQEBL4LWMF7RSB64G6BWPG/graph.json","fetch_events":"https://pith.science/api/pith-number/3ASXSQEBL4LWMF7RSB64G6BWPG/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3ASXSQEBL4LWMF7RSB64G6BWPG/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3ASXSQEBL4LWMF7RSB64G6BWPG/action/storage_attestation","attest_author":"https://pith.science/pith/3ASXSQEBL4LWMF7RSB64G6BWPG/action/author_attestation","sign_citation":"https://pith.science/pith/3ASXSQEBL4LWMF7RSB64G6BWPG/action/citation_signature","submit_replication":"https://pith.science/pith/3ASXSQEBL4LWMF7RSB64G6BWPG/action/replication_record"}},"created_at":"2026-05-18T00:28:19.434210+00:00","updated_at":"2026-05-18T00:28:19.434210+00:00"}