{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:7CLZ3EKA5THUKJJSAYIBR6RGM7","short_pith_number":"pith:7CLZ3EKA","schema_version":"1.0","canonical_sha256":"f8979d9140eccf452532061018fa2667f3d675f057b06253efd3d0fec710d8cd","source":{"kind":"arxiv","id":"1410.6461","version":2},"attestation_state":"computed","paper":{"title":"A sm\\\"org\\r{a}sbord of scalar-flat K\\\"ahler ALE surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Jeff A. Viaclovsky, Michael T. Lock","submitted_at":"2014-10-23T19:28:17Z","abstract_excerpt":"There are many known examples of scalar-flat K\\\"ahler ALE surfaces, all of which have group at infinity either cyclic or contained in ${\\rm{SU}}(2)$. The main result in this paper shows that for any non-cyclic finite subgroup $\\Gamma \\subset {\\rm{U}}(2)$ containing no complex reflections, there exist scalar-flat K\\\"ahler ALE metrics on the minimal resolution of $\\mathbb{C}^2 / \\Gamma$, for which $\\Gamma$ occurs as the group at infinity. Furthermore, we show that these metrics admit a holomorphic isometric circle action. It is also shown that there exist scalar-flat K\\\"ahler ALE metrics with re"},"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":"1410.6461","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-10-23T19:28:17Z","cross_cats_sorted":[],"title_canon_sha256":"d7825cb8abf7f9ca5587b6d41670762b04cae9e36dbcd472f855e4906fb9d2ed","abstract_canon_sha256":"6adb36b960fea68dad7b94091036a47bfdd5b8f0ef05ff1ef0c7b970a2a82989"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:14:26.230184Z","signature_b64":"ex/9R7LZfUCPy+2JHShSwfiGB0NK3aHFnqt/aTyHJiJzL4rf5jQaLKqPwdJpmUjFFooEANTpJnpcmuQyjxLeAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f8979d9140eccf452532061018fa2667f3d675f057b06253efd3d0fec710d8cd","last_reissued_at":"2026-05-18T01:14:26.229465Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:14:26.229465Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A sm\\\"org\\r{a}sbord of scalar-flat K\\\"ahler ALE surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Jeff A. Viaclovsky, Michael T. Lock","submitted_at":"2014-10-23T19:28:17Z","abstract_excerpt":"There are many known examples of scalar-flat K\\\"ahler ALE surfaces, all of which have group at infinity either cyclic or contained in ${\\rm{SU}}(2)$. The main result in this paper shows that for any non-cyclic finite subgroup $\\Gamma \\subset {\\rm{U}}(2)$ containing no complex reflections, there exist scalar-flat K\\\"ahler ALE metrics on the minimal resolution of $\\mathbb{C}^2 / \\Gamma$, for which $\\Gamma$ occurs as the group at infinity. Furthermore, we show that these metrics admit a holomorphic isometric circle action. It is also shown that there exist scalar-flat K\\\"ahler ALE metrics with re"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.6461","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":"1410.6461","created_at":"2026-05-18T01:14:26.229572+00:00"},{"alias_kind":"arxiv_version","alias_value":"1410.6461v2","created_at":"2026-05-18T01:14:26.229572+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.6461","created_at":"2026-05-18T01:14:26.229572+00:00"},{"alias_kind":"pith_short_12","alias_value":"7CLZ3EKA5THU","created_at":"2026-05-18T12:28:16.859392+00:00"},{"alias_kind":"pith_short_16","alias_value":"7CLZ3EKA5THUKJJS","created_at":"2026-05-18T12:28:16.859392+00:00"},{"alias_kind":"pith_short_8","alias_value":"7CLZ3EKA","created_at":"2026-05-18T12:28:16.859392+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/7CLZ3EKA5THUKJJSAYIBR6RGM7","json":"https://pith.science/pith/7CLZ3EKA5THUKJJSAYIBR6RGM7.json","graph_json":"https://pith.science/api/pith-number/7CLZ3EKA5THUKJJSAYIBR6RGM7/graph.json","events_json":"https://pith.science/api/pith-number/7CLZ3EKA5THUKJJSAYIBR6RGM7/events.json","paper":"https://pith.science/paper/7CLZ3EKA"},"agent_actions":{"view_html":"https://pith.science/pith/7CLZ3EKA5THUKJJSAYIBR6RGM7","download_json":"https://pith.science/pith/7CLZ3EKA5THUKJJSAYIBR6RGM7.json","view_paper":"https://pith.science/paper/7CLZ3EKA","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1410.6461&json=true","fetch_graph":"https://pith.science/api/pith-number/7CLZ3EKA5THUKJJSAYIBR6RGM7/graph.json","fetch_events":"https://pith.science/api/pith-number/7CLZ3EKA5THUKJJSAYIBR6RGM7/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7CLZ3EKA5THUKJJSAYIBR6RGM7/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7CLZ3EKA5THUKJJSAYIBR6RGM7/action/storage_attestation","attest_author":"https://pith.science/pith/7CLZ3EKA5THUKJJSAYIBR6RGM7/action/author_attestation","sign_citation":"https://pith.science/pith/7CLZ3EKA5THUKJJSAYIBR6RGM7/action/citation_signature","submit_replication":"https://pith.science/pith/7CLZ3EKA5THUKJJSAYIBR6RGM7/action/replication_record"}},"created_at":"2026-05-18T01:14:26.229572+00:00","updated_at":"2026-05-18T01:14:26.229572+00:00"}