{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2022:ODY6BUHHR5A4A2VX22AI4RMLSQ","short_pith_number":"pith:ODY6BUHH","schema_version":"1.0","canonical_sha256":"70f1e0d0e78f41c06ab7d6808e458b9406df6f43e86bb682424576657dac9358","source":{"kind":"arxiv","id":"2211.09801","version":3},"attestation_state":"computed","paper":{"title":"Machine Learned Calabi-Yau Metrics and Curvature","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","math.AG","math.DG"],"primary_cat":"hep-th","authors_text":"Challenger Mishra, Dami\\'an Mayorga Pe\\~na, Giorgi Butbaia, Justin Tan, Per Berglund, Tristan H\\\"ubsch, Vishnu Jejjala","submitted_at":"2022-11-17T18:59:03Z","abstract_excerpt":"Finding Ricci-flat (Calabi-Yau) metrics is a long standing problem in geometry with deep implications for string theory and phenomenology. A new attack on this problem uses neural networks to engineer approximations to the Calabi-Yau metric within a given K\\\"ahler class. In this paper we investigate numerical Ricci-flat metrics over smooth and singular K3 surfaces and Calabi-Yau threefolds. Using these Ricci-flat metric approximations for the Cefal\\'u family of quartic twofolds and the Dwork family of quintic threefolds, we study characteristic forms on these geometries. We observe that the nu"},"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":"2211.09801","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2022-11-17T18:59:03Z","cross_cats_sorted":["cs.LG","math.AG","math.DG"],"title_canon_sha256":"ef553b812dfee3af5df97989b248cff05151b0bc19a591843db364186263b363","abstract_canon_sha256":"2f5ffd8822cd6ae17b67eab1fc1606959e56b69dea4241e52f98144bd9de30be"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:28:31.795712Z","signature_b64":"XRXv9uDG20GoNVOhB51vjUH3VMklrgP3aQvJLphHjlLXTOkqQnUqCkDlgfP5Myu6UbQ/JA5/LJXMPDoQDoPgDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"70f1e0d0e78f41c06ab7d6808e458b9406df6f43e86bb682424576657dac9358","last_reissued_at":"2026-07-05T08:28:31.795154Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:28:31.795154Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Machine Learned Calabi-Yau Metrics and Curvature","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","math.AG","math.DG"],"primary_cat":"hep-th","authors_text":"Challenger Mishra, Dami\\'an Mayorga Pe\\~na, Giorgi Butbaia, Justin Tan, Per Berglund, Tristan H\\\"ubsch, Vishnu Jejjala","submitted_at":"2022-11-17T18:59:03Z","abstract_excerpt":"Finding Ricci-flat (Calabi-Yau) metrics is a long standing problem in geometry with deep implications for string theory and phenomenology. A new attack on this problem uses neural networks to engineer approximations to the Calabi-Yau metric within a given K\\\"ahler class. In this paper we investigate numerical Ricci-flat metrics over smooth and singular K3 surfaces and Calabi-Yau threefolds. Using these Ricci-flat metric approximations for the Cefal\\'u family of quartic twofolds and the Dwork family of quintic threefolds, we study characteristic forms on these geometries. We observe that the nu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2211.09801","kind":"arxiv","version":3},"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/2211.09801/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":"2211.09801","created_at":"2026-07-05T08:28:31.795220+00:00"},{"alias_kind":"arxiv_version","alias_value":"2211.09801v3","created_at":"2026-07-05T08:28:31.795220+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2211.09801","created_at":"2026-07-05T08:28:31.795220+00:00"},{"alias_kind":"pith_short_12","alias_value":"ODY6BUHHR5A4","created_at":"2026-07-05T08:28:31.795220+00:00"},{"alias_kind":"pith_short_16","alias_value":"ODY6BUHHR5A4A2VX","created_at":"2026-07-05T08:28:31.795220+00:00"},{"alias_kind":"pith_short_8","alias_value":"ODY6BUHH","created_at":"2026-07-05T08:28:31.795220+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":7,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2606.25016","citing_title":"Lost in Translation: Moduli Stabilization from EFT to Eleven Dimensions","ref_index":21,"is_internal_anchor":false},{"citing_arxiv_id":"2605.24724","citing_title":"Beyond Algebraic Solutions to Stringy Spacetime","ref_index":56,"is_internal_anchor":false},{"citing_arxiv_id":"2605.23900","citing_title":"What to do with a Ricci-flat Calabi--Yau metric?","ref_index":13,"is_internal_anchor":false},{"citing_arxiv_id":"2604.25020","citing_title":"PINNs in More General Geometry","ref_index":11,"is_internal_anchor":false},{"citing_arxiv_id":"2604.21997","citing_title":"A Physicist's Visit to Exotic Spheres","ref_index":179,"is_internal_anchor":false},{"citing_arxiv_id":"2605.06998","citing_title":"Beyond Algebraic Superstring Compactification: Part II","ref_index":91,"is_internal_anchor":false},{"citing_arxiv_id":"2604.04321","citing_title":"Minimising Willmore Energy via Neural Flow","ref_index":8,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/ODY6BUHHR5A4A2VX22AI4RMLSQ","json":"https://pith.science/pith/ODY6BUHHR5A4A2VX22AI4RMLSQ.json","graph_json":"https://pith.science/api/pith-number/ODY6BUHHR5A4A2VX22AI4RMLSQ/graph.json","events_json":"https://pith.science/api/pith-number/ODY6BUHHR5A4A2VX22AI4RMLSQ/events.json","paper":"https://pith.science/paper/ODY6BUHH"},"agent_actions":{"view_html":"https://pith.science/pith/ODY6BUHHR5A4A2VX22AI4RMLSQ","download_json":"https://pith.science/pith/ODY6BUHHR5A4A2VX22AI4RMLSQ.json","view_paper":"https://pith.science/paper/ODY6BUHH","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2211.09801&json=true","fetch_graph":"https://pith.science/api/pith-number/ODY6BUHHR5A4A2VX22AI4RMLSQ/graph.json","fetch_events":"https://pith.science/api/pith-number/ODY6BUHHR5A4A2VX22AI4RMLSQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ODY6BUHHR5A4A2VX22AI4RMLSQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ODY6BUHHR5A4A2VX22AI4RMLSQ/action/storage_attestation","attest_author":"https://pith.science/pith/ODY6BUHHR5A4A2VX22AI4RMLSQ/action/author_attestation","sign_citation":"https://pith.science/pith/ODY6BUHHR5A4A2VX22AI4RMLSQ/action/citation_signature","submit_replication":"https://pith.science/pith/ODY6BUHHR5A4A2VX22AI4RMLSQ/action/replication_record"}},"created_at":"2026-07-05T08:28:31.795220+00:00","updated_at":"2026-07-05T08:28:31.795220+00:00"}