{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:ICVIOLO2VDZWFQ5Y4XUZIQUJSM","short_pith_number":"pith:ICVIOLO2","schema_version":"1.0","canonical_sha256":"40aa872ddaa8f362c3b8e5e99442899332d08e56cdeff97d5e237eef17f3864b","source":{"kind":"arxiv","id":"1302.6975","version":1},"attestation_state":"computed","paper":{"title":"Ambitoric geometry I: Einstein metrics and extremal ambikaehler structures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["gr-qc","math-ph","math.MP"],"primary_cat":"math.DG","authors_text":"David M.J. Calderbank, Paul Gauduchon, Vestislav Apostolov","submitted_at":"2013-02-27T20:04:52Z","abstract_excerpt":"We present a local classification of conformally equivalent but oppositely oriented 4-dimensional Kaehler metrics which are toric with respect to a common 2-torus action. In the generic case, these \"ambitoric\" structures have an intriguing local geometry depending on a quadratic polynomial q and arbitrary functions A and B of one variable.\n  We use this description to classify Einstein 4-metrics which are hermitian with respect to both orientations, as well a class of solutions to the Einstein-Maxwell equations including riemannian analogues of the Plebanski-Demianski metrics. Our classificati"},"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":"1302.6975","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-02-27T20:04:52Z","cross_cats_sorted":["gr-qc","math-ph","math.MP"],"title_canon_sha256":"5c9b6c0759c2404ad4d26a790679014b9a58b335ebdd11a51780f39fdefb0ef8","abstract_canon_sha256":"9dd0e8560abfd27ffee91c0415af3f8ab40cf475c46c4582a7f94331eb73ac8c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:56:47.075917Z","signature_b64":"B2UzdbxDj51UpprqN/i4anT/rBxXJFg881A7lMSI+lEcQlnUS62y+OLJM6oUzJBuYychZW9ovCfxQvP+bmD0Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"40aa872ddaa8f362c3b8e5e99442899332d08e56cdeff97d5e237eef17f3864b","last_reissued_at":"2026-05-18T00:56:47.075419Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:56:47.075419Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Ambitoric geometry I: Einstein metrics and extremal ambikaehler structures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["gr-qc","math-ph","math.MP"],"primary_cat":"math.DG","authors_text":"David M.J. Calderbank, Paul Gauduchon, Vestislav Apostolov","submitted_at":"2013-02-27T20:04:52Z","abstract_excerpt":"We present a local classification of conformally equivalent but oppositely oriented 4-dimensional Kaehler metrics which are toric with respect to a common 2-torus action. In the generic case, these \"ambitoric\" structures have an intriguing local geometry depending on a quadratic polynomial q and arbitrary functions A and B of one variable.\n  We use this description to classify Einstein 4-metrics which are hermitian with respect to both orientations, as well a class of solutions to the Einstein-Maxwell equations including riemannian analogues of the Plebanski-Demianski metrics. Our classificati"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.6975","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":"1302.6975","created_at":"2026-05-18T00:56:47.075508+00:00"},{"alias_kind":"arxiv_version","alias_value":"1302.6975v1","created_at":"2026-05-18T00:56:47.075508+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.6975","created_at":"2026-05-18T00:56:47.075508+00:00"},{"alias_kind":"pith_short_12","alias_value":"ICVIOLO2VDZW","created_at":"2026-05-18T12:27:46.883200+00:00"},{"alias_kind":"pith_short_16","alias_value":"ICVIOLO2VDZWFQ5Y","created_at":"2026-05-18T12:27:46.883200+00:00"},{"alias_kind":"pith_short_8","alias_value":"ICVIOLO2","created_at":"2026-05-18T12:27:46.883200+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2604.20772","citing_title":"General Relativity via differential forms -- explorations in Plebanski's Formalism for GR","ref_index":51,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/ICVIOLO2VDZWFQ5Y4XUZIQUJSM","json":"https://pith.science/pith/ICVIOLO2VDZWFQ5Y4XUZIQUJSM.json","graph_json":"https://pith.science/api/pith-number/ICVIOLO2VDZWFQ5Y4XUZIQUJSM/graph.json","events_json":"https://pith.science/api/pith-number/ICVIOLO2VDZWFQ5Y4XUZIQUJSM/events.json","paper":"https://pith.science/paper/ICVIOLO2"},"agent_actions":{"view_html":"https://pith.science/pith/ICVIOLO2VDZWFQ5Y4XUZIQUJSM","download_json":"https://pith.science/pith/ICVIOLO2VDZWFQ5Y4XUZIQUJSM.json","view_paper":"https://pith.science/paper/ICVIOLO2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1302.6975&json=true","fetch_graph":"https://pith.science/api/pith-number/ICVIOLO2VDZWFQ5Y4XUZIQUJSM/graph.json","fetch_events":"https://pith.science/api/pith-number/ICVIOLO2VDZWFQ5Y4XUZIQUJSM/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ICVIOLO2VDZWFQ5Y4XUZIQUJSM/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ICVIOLO2VDZWFQ5Y4XUZIQUJSM/action/storage_attestation","attest_author":"https://pith.science/pith/ICVIOLO2VDZWFQ5Y4XUZIQUJSM/action/author_attestation","sign_citation":"https://pith.science/pith/ICVIOLO2VDZWFQ5Y4XUZIQUJSM/action/citation_signature","submit_replication":"https://pith.science/pith/ICVIOLO2VDZWFQ5Y4XUZIQUJSM/action/replication_record"}},"created_at":"2026-05-18T00:56:47.075508+00:00","updated_at":"2026-05-18T00:56:47.075508+00:00"}