{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2007:VAPXY24U5U64JXMYE3FBJGU6NY","short_pith_number":"pith:VAPXY24U","schema_version":"1.0","canonical_sha256":"a81f7c6b94ed3dc4dd9826ca149a9e6e2f1a4414570818177bc231da6fcfd883","source":{"kind":"arxiv","id":"0711.1155","version":1},"attestation_state":"computed","paper":{"title":"L^2 Castelnuovo-de Franchis, the cup product lemma, and filtered ends of Kaehler manifolds","license":"","headline":"","cross_cats":["math.CV"],"primary_cat":"math.DG","authors_text":"Mohan Ramachandran, Terrence Napier","submitted_at":"2007-11-07T20:29:46Z","abstract_excerpt":"Simple approaches to the proofs of the L^2 Castelnuovo-de Franchis theorem and the cup product lemma which give new versions are developed. For example, suppose u and v are two linearly independent closed holomorphic 1-forms on a bounded geometry connected complete Kaehler manifold X with v in L^2. According to a version of the L^2 Castelnuovo-de Franchis theorem obtained in this paper, if u and v are pointwise linearly dependent, then there exists a surjective proper holomorphic mapping of X onto a Riemann surface for which u and v are pull-backs. Previous versions required both forms to be i"},"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":"0711.1155","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.DG","submitted_at":"2007-11-07T20:29:46Z","cross_cats_sorted":["math.CV"],"title_canon_sha256":"5776ce39eeff432a73bcb63effd87285243d740448e914016d742bd140aaa86f","abstract_canon_sha256":"05192fce691427fcb21027c67f24a6b58664e6342252c942b1e0670a2c2320e9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:49:54.419844Z","signature_b64":"2amMLDQjhBhI3HlN4qdt93KEpSduUJtOvyQ/lPNjJU7EzDQDbVpmZtAe/fmBAO5M4YUsVXSoaYeueRRc/YwlCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a81f7c6b94ed3dc4dd9826ca149a9e6e2f1a4414570818177bc231da6fcfd883","last_reissued_at":"2026-05-18T01:49:54.419387Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:49:54.419387Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"L^2 Castelnuovo-de Franchis, the cup product lemma, and filtered ends of Kaehler manifolds","license":"","headline":"","cross_cats":["math.CV"],"primary_cat":"math.DG","authors_text":"Mohan Ramachandran, Terrence Napier","submitted_at":"2007-11-07T20:29:46Z","abstract_excerpt":"Simple approaches to the proofs of the L^2 Castelnuovo-de Franchis theorem and the cup product lemma which give new versions are developed. For example, suppose u and v are two linearly independent closed holomorphic 1-forms on a bounded geometry connected complete Kaehler manifold X with v in L^2. According to a version of the L^2 Castelnuovo-de Franchis theorem obtained in this paper, if u and v are pointwise linearly dependent, then there exists a surjective proper holomorphic mapping of X onto a Riemann surface for which u and v are pull-backs. Previous versions required both forms to be i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0711.1155","kind":"arxiv","version":1},"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":"0711.1155","created_at":"2026-05-18T01:49:54.419451+00:00"},{"alias_kind":"arxiv_version","alias_value":"0711.1155v1","created_at":"2026-05-18T01:49:54.419451+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0711.1155","created_at":"2026-05-18T01:49:54.419451+00:00"},{"alias_kind":"pith_short_12","alias_value":"VAPXY24U5U64","created_at":"2026-05-18T12:25:56.245647+00:00"},{"alias_kind":"pith_short_16","alias_value":"VAPXY24U5U64JXMY","created_at":"2026-05-18T12:25:56.245647+00:00"},{"alias_kind":"pith_short_8","alias_value":"VAPXY24U","created_at":"2026-05-18T12:25:56.245647+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/VAPXY24U5U64JXMYE3FBJGU6NY","json":"https://pith.science/pith/VAPXY24U5U64JXMYE3FBJGU6NY.json","graph_json":"https://pith.science/api/pith-number/VAPXY24U5U64JXMYE3FBJGU6NY/graph.json","events_json":"https://pith.science/api/pith-number/VAPXY24U5U64JXMYE3FBJGU6NY/events.json","paper":"https://pith.science/paper/VAPXY24U"},"agent_actions":{"view_html":"https://pith.science/pith/VAPXY24U5U64JXMYE3FBJGU6NY","download_json":"https://pith.science/pith/VAPXY24U5U64JXMYE3FBJGU6NY.json","view_paper":"https://pith.science/paper/VAPXY24U","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0711.1155&json=true","fetch_graph":"https://pith.science/api/pith-number/VAPXY24U5U64JXMYE3FBJGU6NY/graph.json","fetch_events":"https://pith.science/api/pith-number/VAPXY24U5U64JXMYE3FBJGU6NY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VAPXY24U5U64JXMYE3FBJGU6NY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VAPXY24U5U64JXMYE3FBJGU6NY/action/storage_attestation","attest_author":"https://pith.science/pith/VAPXY24U5U64JXMYE3FBJGU6NY/action/author_attestation","sign_citation":"https://pith.science/pith/VAPXY24U5U64JXMYE3FBJGU6NY/action/citation_signature","submit_replication":"https://pith.science/pith/VAPXY24U5U64JXMYE3FBJGU6NY/action/replication_record"}},"created_at":"2026-05-18T01:49:54.419451+00:00","updated_at":"2026-05-18T01:49:54.419451+00:00"}