{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:7VUJ6I4UFSKOK6ADSIJNK5RDHK","short_pith_number":"pith:7VUJ6I4U","schema_version":"1.0","canonical_sha256":"fd689f23942c94e578039212d576233a9a5d447441f47368eae35e0b2f264b33","source":{"kind":"arxiv","id":"1810.09020","version":2},"attestation_state":"computed","paper":{"title":"Locally conformally flat metrics on surfaces of general type","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.DG","authors_text":"Mustafa Kalafat, \\\"Ozg\\\"ur Kelek\\c{c}i","submitted_at":"2018-10-21T20:18:20Z","abstract_excerpt":"We prove a nonexistence theorem for product type manifolds. In particular we show that the 4-manifold $\\Sigma_g\\times\\Sigma_h$ does not admit any locally conformally flat metric arising from discrete and faithful representations for $g\\geq 2$ and $h\\geq 1$"},"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":"1810.09020","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-10-21T20:18:20Z","cross_cats_sorted":["math.GT"],"title_canon_sha256":"4e0a03a7e1135cbc539d9bce5d2b881a335dc3cd9c882e23c0b4bcc7fbc778d6","abstract_canon_sha256":"7076164e160afff06900bf8c7eab6886d57366cf6b94c27778a12586577d56fe"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:56:36.383465Z","signature_b64":"pQY63vUuDCew575BVDrlJkuxJHbDbb4pyXiJH2Jv5/X/uZ/CfuC+vkhKx53KcbSGxvRqFMWKd4cQwK/B6LYSCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fd689f23942c94e578039212d576233a9a5d447441f47368eae35e0b2f264b33","last_reissued_at":"2026-05-17T23:56:36.382916Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:56:36.382916Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Locally conformally flat metrics on surfaces of general type","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.DG","authors_text":"Mustafa Kalafat, \\\"Ozg\\\"ur Kelek\\c{c}i","submitted_at":"2018-10-21T20:18:20Z","abstract_excerpt":"We prove a nonexistence theorem for product type manifolds. In particular we show that the 4-manifold $\\Sigma_g\\times\\Sigma_h$ does not admit any locally conformally flat metric arising from discrete and faithful representations for $g\\geq 2$ and $h\\geq 1$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.09020","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":"1810.09020","created_at":"2026-05-17T23:56:36.383007+00:00"},{"alias_kind":"arxiv_version","alias_value":"1810.09020v2","created_at":"2026-05-17T23:56:36.383007+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.09020","created_at":"2026-05-17T23:56:36.383007+00:00"},{"alias_kind":"pith_short_12","alias_value":"7VUJ6I4UFSKO","created_at":"2026-05-18T12:32:11.075285+00:00"},{"alias_kind":"pith_short_16","alias_value":"7VUJ6I4UFSKOK6AD","created_at":"2026-05-18T12:32:11.075285+00:00"},{"alias_kind":"pith_short_8","alias_value":"7VUJ6I4U","created_at":"2026-05-18T12:32:11.075285+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/7VUJ6I4UFSKOK6ADSIJNK5RDHK","json":"https://pith.science/pith/7VUJ6I4UFSKOK6ADSIJNK5RDHK.json","graph_json":"https://pith.science/api/pith-number/7VUJ6I4UFSKOK6ADSIJNK5RDHK/graph.json","events_json":"https://pith.science/api/pith-number/7VUJ6I4UFSKOK6ADSIJNK5RDHK/events.json","paper":"https://pith.science/paper/7VUJ6I4U"},"agent_actions":{"view_html":"https://pith.science/pith/7VUJ6I4UFSKOK6ADSIJNK5RDHK","download_json":"https://pith.science/pith/7VUJ6I4UFSKOK6ADSIJNK5RDHK.json","view_paper":"https://pith.science/paper/7VUJ6I4U","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1810.09020&json=true","fetch_graph":"https://pith.science/api/pith-number/7VUJ6I4UFSKOK6ADSIJNK5RDHK/graph.json","fetch_events":"https://pith.science/api/pith-number/7VUJ6I4UFSKOK6ADSIJNK5RDHK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7VUJ6I4UFSKOK6ADSIJNK5RDHK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7VUJ6I4UFSKOK6ADSIJNK5RDHK/action/storage_attestation","attest_author":"https://pith.science/pith/7VUJ6I4UFSKOK6ADSIJNK5RDHK/action/author_attestation","sign_citation":"https://pith.science/pith/7VUJ6I4UFSKOK6ADSIJNK5RDHK/action/citation_signature","submit_replication":"https://pith.science/pith/7VUJ6I4UFSKOK6ADSIJNK5RDHK/action/replication_record"}},"created_at":"2026-05-17T23:56:36.383007+00:00","updated_at":"2026-05-17T23:56:36.383007+00:00"}