{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:QQSCWPWKPBZQKAUP5MECYT6V2P","short_pith_number":"pith:QQSCWPWK","schema_version":"1.0","canonical_sha256":"84242b3eca787305028feb082c4fd5d3c82a4d9cc70af2a29d8f8eeec440062d","source":{"kind":"arxiv","id":"1012.5247","version":2},"attestation_state":"computed","paper":{"title":"Infinite bubbling in non-K\\\"ahlerian geometry","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Andrei Teleman, Georges Dloussky","submitted_at":"2010-12-23T16:56:17Z","abstract_excerpt":"In a holomorphic family $(X_b)_{b\\in B}$ of non-K\\\"ahlerian compact manifolds, the holomorphic curves representing a fixed 2-homology class do not form a proper family in general. The deep source of this fundamental difficulty in non-K\\\"ahler geometry is the {\\it explosion of the area} phenomenon: the area of a curve $C_b\\subset X_b$ in a fixed 2-homology class can diverge as $b\\to b_0$. This phenomenon occurs frequently in the deformation theory of class VII surfaces. For instance it is well known that any minimal GSS surface $X_0$ is a degeneration of a 1-parameter family of simply blown up "},"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":"1012.5247","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2010-12-23T16:56:17Z","cross_cats_sorted":[],"title_canon_sha256":"2005bb823e6ec44fcbce2362611f9628aac3fcda4bc1089c3480b2aa928331eb","abstract_canon_sha256":"ee92a6ff7748fab7791ae91eb6c4b825f9a3f82ec87b2d1d2959fb3ed8fbca9a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:11:40.735803Z","signature_b64":"+m4SZwtGPyVRT+MMiT6SDs4V/6XfMvzfXLgGG3cNKX+MY0+pYr7tZ8AOxh1ox5+IhbyocAln9w9+6EJwo1fPCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"84242b3eca787305028feb082c4fd5d3c82a4d9cc70af2a29d8f8eeec440062d","last_reissued_at":"2026-05-18T04:11:40.735191Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:11:40.735191Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Infinite bubbling in non-K\\\"ahlerian geometry","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Andrei Teleman, Georges Dloussky","submitted_at":"2010-12-23T16:56:17Z","abstract_excerpt":"In a holomorphic family $(X_b)_{b\\in B}$ of non-K\\\"ahlerian compact manifolds, the holomorphic curves representing a fixed 2-homology class do not form a proper family in general. The deep source of this fundamental difficulty in non-K\\\"ahler geometry is the {\\it explosion of the area} phenomenon: the area of a curve $C_b\\subset X_b$ in a fixed 2-homology class can diverge as $b\\to b_0$. This phenomenon occurs frequently in the deformation theory of class VII surfaces. For instance it is well known that any minimal GSS surface $X_0$ is a degeneration of a 1-parameter family of simply blown up "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.5247","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":"1012.5247","created_at":"2026-05-18T04:11:40.735280+00:00"},{"alias_kind":"arxiv_version","alias_value":"1012.5247v2","created_at":"2026-05-18T04:11:40.735280+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1012.5247","created_at":"2026-05-18T04:11:40.735280+00:00"},{"alias_kind":"pith_short_12","alias_value":"QQSCWPWKPBZQ","created_at":"2026-05-18T12:26:12.377268+00:00"},{"alias_kind":"pith_short_16","alias_value":"QQSCWPWKPBZQKAUP","created_at":"2026-05-18T12:26:12.377268+00:00"},{"alias_kind":"pith_short_8","alias_value":"QQSCWPWK","created_at":"2026-05-18T12:26:12.377268+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/QQSCWPWKPBZQKAUP5MECYT6V2P","json":"https://pith.science/pith/QQSCWPWKPBZQKAUP5MECYT6V2P.json","graph_json":"https://pith.science/api/pith-number/QQSCWPWKPBZQKAUP5MECYT6V2P/graph.json","events_json":"https://pith.science/api/pith-number/QQSCWPWKPBZQKAUP5MECYT6V2P/events.json","paper":"https://pith.science/paper/QQSCWPWK"},"agent_actions":{"view_html":"https://pith.science/pith/QQSCWPWKPBZQKAUP5MECYT6V2P","download_json":"https://pith.science/pith/QQSCWPWKPBZQKAUP5MECYT6V2P.json","view_paper":"https://pith.science/paper/QQSCWPWK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1012.5247&json=true","fetch_graph":"https://pith.science/api/pith-number/QQSCWPWKPBZQKAUP5MECYT6V2P/graph.json","fetch_events":"https://pith.science/api/pith-number/QQSCWPWKPBZQKAUP5MECYT6V2P/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QQSCWPWKPBZQKAUP5MECYT6V2P/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QQSCWPWKPBZQKAUP5MECYT6V2P/action/storage_attestation","attest_author":"https://pith.science/pith/QQSCWPWKPBZQKAUP5MECYT6V2P/action/author_attestation","sign_citation":"https://pith.science/pith/QQSCWPWKPBZQKAUP5MECYT6V2P/action/citation_signature","submit_replication":"https://pith.science/pith/QQSCWPWKPBZQKAUP5MECYT6V2P/action/replication_record"}},"created_at":"2026-05-18T04:11:40.735280+00:00","updated_at":"2026-05-18T04:11:40.735280+00:00"}