{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:TU3HNA2THXJ3IPJCLYNON57PVW","short_pith_number":"pith:TU3HNA2T","schema_version":"1.0","canonical_sha256":"9d367683533dd3b43d225e1ae6f7efadb83ddc80bfa760dd9ac9d5fee1d48cbe","source":{"kind":"arxiv","id":"2506.15766","version":1},"attestation_state":"computed","paper":{"title":"Approximate Ricci-flat Metrics for Calabi-Yau Manifolds","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.LG","math.DG"],"primary_cat":"hep-th","authors_text":"Andre Lukas, Seung-Joo Lee","submitted_at":"2025-06-18T18:00:00Z","abstract_excerpt":"We outline a method to determine analytic K\\\"ahler potentials with associated approximately Ricci-flat K\\\"ahler metrics on Calabi-Yau manifolds. Key ingredients are numerically calculating Ricci-flat K\\\"ahler potentials via machine learning techniques and fitting the numerical results to Donaldson's Ansatz. We apply this method to the Dwork family of quintic hypersurfaces in $\\mathbb{P}^4$ and an analogous one-parameter family of bi-cubic CY hypersurfaces in $\\mathbb{P}^2\\times\\mathbb{P}^2$. In each case, a relatively simple analytic expression is obtained for the approximately Ricci-flat K\\\"a"},"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":"2506.15766","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2025-06-18T18:00:00Z","cross_cats_sorted":["cs.LG","math.DG"],"title_canon_sha256":"4fb8efd89f0e3f8297bd99a1afdc944970497a5dae71843f5e957bc8c4613bbe","abstract_canon_sha256":"fca74da7ee64f99805bdfff220bb3a747ffcad945d35932b693abc07455aefe7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:23:51.834734Z","signature_b64":"OgPgikJGMkZW71L988O7JziyDZR8d02U6xPJ2J1CNoir4iWjcdQPe/PB+ym33KBXeK/cvoBA9a71HARVlArXAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9d367683533dd3b43d225e1ae6f7efadb83ddc80bfa760dd9ac9d5fee1d48cbe","last_reissued_at":"2026-07-05T11:23:51.834209Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:23:51.834209Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Approximate Ricci-flat Metrics for Calabi-Yau Manifolds","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.LG","math.DG"],"primary_cat":"hep-th","authors_text":"Andre Lukas, Seung-Joo Lee","submitted_at":"2025-06-18T18:00:00Z","abstract_excerpt":"We outline a method to determine analytic K\\\"ahler potentials with associated approximately Ricci-flat K\\\"ahler metrics on Calabi-Yau manifolds. Key ingredients are numerically calculating Ricci-flat K\\\"ahler potentials via machine learning techniques and fitting the numerical results to Donaldson's Ansatz. We apply this method to the Dwork family of quintic hypersurfaces in $\\mathbb{P}^4$ and an analogous one-parameter family of bi-cubic CY hypersurfaces in $\\mathbb{P}^2\\times\\mathbb{P}^2$. In each case, a relatively simple analytic expression is obtained for the approximately Ricci-flat K\\\"a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.15766","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2506.15766/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2506.15766","created_at":"2026-07-05T11:23:51.834267+00:00"},{"alias_kind":"arxiv_version","alias_value":"2506.15766v1","created_at":"2026-07-05T11:23:51.834267+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.15766","created_at":"2026-07-05T11:23:51.834267+00:00"},{"alias_kind":"pith_short_12","alias_value":"TU3HNA2THXJ3","created_at":"2026-07-05T11:23:51.834267+00:00"},{"alias_kind":"pith_short_16","alias_value":"TU3HNA2THXJ3IPJC","created_at":"2026-07-05T11:23:51.834267+00:00"},{"alias_kind":"pith_short_8","alias_value":"TU3HNA2T","created_at":"2026-07-05T11:23:51.834267+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":3,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2606.28487","citing_title":"Calabi-Yau Metrics with Full Moduli Dependence","ref_index":19,"is_internal_anchor":false},{"citing_arxiv_id":"2606.26892","citing_title":"The Sharp Edges of Calabi-Yau Manifolds: Designing Symmetric Models for Ricci-flat Metrics","ref_index":43,"is_internal_anchor":false},{"citing_arxiv_id":"2605.23900","citing_title":"What to do with a Ricci-flat Calabi--Yau metric?","ref_index":115,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/TU3HNA2THXJ3IPJCLYNON57PVW","json":"https://pith.science/pith/TU3HNA2THXJ3IPJCLYNON57PVW.json","graph_json":"https://pith.science/api/pith-number/TU3HNA2THXJ3IPJCLYNON57PVW/graph.json","events_json":"https://pith.science/api/pith-number/TU3HNA2THXJ3IPJCLYNON57PVW/events.json","paper":"https://pith.science/paper/TU3HNA2T"},"agent_actions":{"view_html":"https://pith.science/pith/TU3HNA2THXJ3IPJCLYNON57PVW","download_json":"https://pith.science/pith/TU3HNA2THXJ3IPJCLYNON57PVW.json","view_paper":"https://pith.science/paper/TU3HNA2T","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2506.15766&json=true","fetch_graph":"https://pith.science/api/pith-number/TU3HNA2THXJ3IPJCLYNON57PVW/graph.json","fetch_events":"https://pith.science/api/pith-number/TU3HNA2THXJ3IPJCLYNON57PVW/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/TU3HNA2THXJ3IPJCLYNON57PVW/action/timestamp_anchor","attest_storage":"https://pith.science/pith/TU3HNA2THXJ3IPJCLYNON57PVW/action/storage_attestation","attest_author":"https://pith.science/pith/TU3HNA2THXJ3IPJCLYNON57PVW/action/author_attestation","sign_citation":"https://pith.science/pith/TU3HNA2THXJ3IPJCLYNON57PVW/action/citation_signature","submit_replication":"https://pith.science/pith/TU3HNA2THXJ3IPJCLYNON57PVW/action/replication_record"}},"created_at":"2026-07-05T11:23:51.834267+00:00","updated_at":"2026-07-05T11:23:51.834267+00:00"}