{"as_of":"2026-08-18T04:55:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:abb55917fe7c642074042b5b43e66d795cd4415f6dc6878121dd4776ebf260b7","coverage":[{"denominator":65,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":65,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-10T23:59:51.411022Z","state":"measured"},{"denominator":69,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":69,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-17T06:30:58.91139+00:00","state":"measured"},{"denominator":4,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":4,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-10T20:26:29.400073Z","state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"arxiv_reference","source_observed_at":"2026-05-25T03:30:16.973212Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2412.19778","last_updated":"2025-03-12T13:38:59Z","snapshot_observed_at":"2026-08-14T15:49:27.555722Z","submitted_at":"2024-12-27T18:19:26Z","title":"Symbolic Approximations to Ricci-flat Metrics Via Extrinsic Symmetries of Calabi-Yau Hypersurfaces","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2412.19778","snapshot_observed_at":"2026-08-10T20:26:29.400073Z","title":"Mirjanić and C","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2501.08623","last_updated":"2025-08-07T01:11:29Z","snapshot_observed_at":"2026-08-15T04:18:44.503839Z","submitted_at":"2025-01-15T06:58:01Z","title":"Dimensional Reduction and K\\\"ahler Metric for Metric Moduli in Imaginary Self-Dual Flux","version":3},"reference_index":63,"source":"pdf_text","source_observed_at":"2026-08-10T20:26:29.400073Z"},"links":{"cited_paper":"/paper/2412.19778","citing_paper":"/paper/2501.08623"},"observation_digest":"sha256:b6299a8a9b84f8e96430bdd989dad5d8eb059da9557049e581c59657056ad61a","observation_id":"2957dbcc-1353-4605-a5aa-d4d6817eca70","resolution":{"observed_at":"2026-08-10T20:26:29.400073Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2412.19778","last_updated":"2025-03-12T13:38:59Z","snapshot_observed_at":"2026-08-14T15:49:27.555722Z","submitted_at":"2024-12-27T18:19:26Z","title":"Symbolic Approximations to Ricci-flat Metrics Via Extrinsic Symmetries of Calabi-Yau Hypersurfaces","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2412.19778","snapshot_observed_at":"2026-08-03T03:33:22.155207Z","title":"Mirjani´ c and A","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2602.07834","last_updated":"2026-06-04T11:23:53Z","snapshot_observed_at":"2026-08-14T00:06:49.514751Z","submitted_at":"2026-02-08T05:51:35Z","title":"Interpretable Analytic Calabi-Yau Metrics via Symbolic Distillation","version":2},"reference_index":44,"source":"pdf_text","source_observed_at":"2026-08-03T03:33:22.155207Z"},"links":{"cited_paper":"/paper/2412.19778","citing_paper":"/paper/2602.07834"},"observation_digest":"sha256:e8a7c510cfb2d137e69205358cfb2f57fb5ef1dc2abe6b369fcc1461fdea9b08","observation_id":"df8b5cca-67e5-4f7c-bd9a-7de21f958350","resolution":{"observed_at":"2026-08-03T03:33:22.155207Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2412.19778","last_updated":"2025-03-12T13:38:59Z","snapshot_observed_at":"2026-08-14T15:49:27.555722Z","submitted_at":"2024-12-27T18:19:26Z","title":"Symbolic Approximations to Ricci-flat Metrics Via Extrinsic Symmetries of Calabi-Yau Hypersurfaces","version":2},"cited_work":{"arxiv_id":"2412.19778","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2412.19778","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Mirjani´ c and C","venue":null,"work_id":"5ee85bbd-6f48-4b91-b732-466e77a27307","year":null},"citing_paper":{"arxiv_id":"2605.23900","last_updated":"2026-07-27T15:30:11Z","snapshot_observed_at":"2026-08-18T00:30:22.895669Z","submitted_at":"2026-05-22T17:59:20Z","title":"What to do with a Ricci-flat Calabi--Yau metric?","version":1},"reference_index":114,"source":"pdf_text","source_observed_at":"2026-05-25T03:30:02.985644Z"},"links":{"cited_paper":"/paper/2412.19778","citing_paper":"/paper/2605.23900"},"observation_digest":"sha256:2322d4b1425c0e360946625dba559bdd40f76f4cc430fc7f623c0ef4b4c3daec","observation_id":"3355b1fa-04fc-4d0b-b815-ec79c978a804","resolution":{"observed_at":"2026-05-25T03:30:16.975780Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2412.19778","last_updated":"2025-03-12T13:38:59Z","snapshot_observed_at":"2026-08-14T15:49:27.555722Z","submitted_at":"2024-12-27T18:19:26Z","title":"Symbolic Approximations to Ricci-flat Metrics Via Extrinsic Symmetries of Calabi-Yau Hypersurfaces","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2412.19778","snapshot_observed_at":"2026-08-02T13:21:49.680593Z","title":"Mirjani´ c and C","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2605.23900","last_updated":"2026-07-27T15:30:11Z","snapshot_observed_at":"2026-08-18T00:30:22.895669Z","submitted_at":"2026-05-22T17:59:20Z","title":"What to do with a Ricci-flat Calabi--Yau metric?","version":2},"reference_index":114,"source":"pdf_text","source_observed_at":"2026-08-02T13:21:49.680593Z"},"links":{"cited_paper":"/paper/2412.19778","citing_paper":"/paper/2605.23900"},"observation_digest":"sha256:1f540dfc99384b73b86bdbe54eafe57753942ad21a7d923fc6f01e9bb3df336d","observation_id":"2a1f134e-057a-4ca0-9382-eba3ed436483","resolution":{"observed_at":"2026-08-02T13:21:49.680593Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"links":{"evidence":"/evidence","html":"/paper/2412.19778/citation-record","integrity":"/paper/2412.19778/integrity","json":"/paper/2412.19778/citation-record.json","paper":"/paper/2412.19778"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T23:59:50.971734Z","title":"On the ricci curvature of a compact k¨ ahler manifold and the complex monge-amp´ ere equation, I","venue":null,"work_id":null,"year":1978},"citing_paper":{"arxiv_id":"2412.19778","last_updated":"2025-03-12T13:38:59Z","snapshot_observed_at":"2026-08-14T15:49:27.555722Z","submitted_at":"2024-12-27T18:19:26Z","title":"Symbolic Approximations to Ricci-flat Metrics Via Extrinsic Symmetries of Calabi-Yau Hypersurfaces","version":2},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-10T23:59:50.971734Z"},"links":{"citing_paper":"/paper/2412.19778"},"observation_digest":"sha256:f49cb531a3e0c57663d8f2ffb82088c497e7243e8ebdb9ce7863014445931d01","observation_id":"217eb195-e427-4a09-a6c1-27af5f0bc2aa","resolution":{"observed_at":"2026-08-10T23:59:50.971734Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T23:59:50.978651Z","title":"Scalar Curvature and Projective Embeddings, I","venue":null,"work_id":null,"year":2001},"citing_paper":{"arxiv_id":"2412.19778","last_updated":"2025-03-12T13:38:59Z","snapshot_observed_at":"2026-08-14T15:49:27.555722Z","submitted_at":"2024-12-27T18:19:26Z","title":"Symbolic Approximations to Ricci-flat Metrics Via Extrinsic Symmetries of Calabi-Yau Hypersurfaces","version":2},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-10T23:59:50.978651Z"},"links":{"citing_paper":"/paper/2412.19778"},"observation_digest":"sha256:f0390547ac227e4f4c3bc77f3fce58d1a78134243733373e552f76866631f96f","observation_id":"65f1e1b7-221a-4b6b-84ec-9e10656dc002","resolution":{"observed_at":"2026-08-10T23:59:50.978651Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T23:59:50.985077Z","title":"Some Numerical Results in Complex Differential Geometry","venue":null,"work_id":null,"year":2005},"citing_paper":{"arxiv_id":"2412.19778","last_updated":"2025-03-12T13:38:59Z","snapshot_observed_at":"2026-08-14T15:49:27.555722Z","submitted_at":"2024-12-27T18:19:26Z","title":"Symbolic Approximations to Ricci-flat Metrics Via Extrinsic Symmetries of Calabi-Yau Hypersurfaces","version":2},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-10T23:59:50.985077Z"},"links":{"citing_paper":"/paper/2412.19778"},"observation_digest":"sha256:966a04ad90579e4638351b9891022d2ef969e05bbf55ecc723db58cc6951b34b","observation_id":"5d4d0470-2bdb-4cfd-b7ac-ef2c06d785c0","resolution":{"observed_at":"2026-08-10T23:59:50.985077Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T23:59:52.979828Z","title":"Headrick and A","venue":null,"work_id":"dabd7c05-5cce-4937-9cb2-79bce0815b81","year":2010},"citing_paper":{"arxiv_id":"2412.19778","last_updated":"2025-03-12T13:38:59Z","snapshot_observed_at":"2026-08-14T15:49:27.555722Z","submitted_at":"2024-12-27T18:19:26Z","title":"Symbolic Approximations to Ricci-flat Metrics Via Extrinsic Symmetries of Calabi-Yau Hypersurfaces","version":2},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-10T23:59:50.992474Z"},"links":{"citing_paper":"/paper/2412.19778"},"observation_digest":"sha256:7b3f2f3ad62d3a7b2c5c5225a298ccf47e510bf26742295abae5b256a4824b1d","observation_id":"ce399b8d-e985-4530-a511-579f5ff6ef70","resolution":{"observed_at":"2026-08-10T23:59:52.986069Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T23:59:52.958428Z","title":null,"venue":null,"work_id":"8330a396-aaaf-4619-9274-0141aff23df1","year":2024},"citing_paper":{"arxiv_id":"2412.19778","last_updated":"2025-03-12T13:38:59Z","snapshot_observed_at":"2026-08-14T15:49:27.555722Z","submitted_at":"2024-12-27T18:19:26Z","title":"Symbolic Approximations to Ricci-flat Metrics Via Extrinsic Symmetries of Calabi-Yau Hypersurfaces","version":2},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-10T23:59:50.998140Z"},"links":{"citing_paper":"/paper/2412.19778"},"observation_digest":"sha256:a43954db22fa068d9e3379c04fe22af71c7767ccf7a07340dab7cfe99fabb5b7","observation_id":"d462a5b3-48da-4a1e-8216-b03fa2b96baa","resolution":{"observed_at":"2026-08-10T23:59:52.965750Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1016/0550-3213(91)90292-6","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T23:59:52.106174Z","title":"A pair of Calabi-Yau manifolds as an exactly soluble superconformal theory","venue":null,"work_id":"e06ddfb7-c856-42eb-a44d-90b789a9b926","year":1991},"citing_paper":{"arxiv_id":"2412.19778","last_updated":"2025-03-12T13:38:59Z","snapshot_observed_at":"2026-08-14T15:49:27.555722Z","submitted_at":"2024-12-27T18:19:26Z","title":"Symbolic Approximations to Ricci-flat Metrics Via Extrinsic Symmetries of Calabi-Yau Hypersurfaces","version":2},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-10T23:59:51.004158Z"},"links":{"citing_paper":"/paper/2412.19778"},"observation_digest":"sha256:662ab181b2846634ec8960a00396a937bd505580af2a0bbdf3af619df1cfeabc","observation_id":"81e63863-9b19-499d-b4a7-7703a0b0055a","resolution":{"observed_at":"2026-08-10T23:59:52.114338Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1088/1126-6708/2008/05/080","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T23:59:52.081668Z","title":"Calabi-Yau metrics for quotients and complete intersections","venue":null,"work_id":"a9f0eefb-2853-4958-abca-0628d90a0bad","year":2008},"citing_paper":{"arxiv_id":"2412.19778","last_updated":"2025-03-12T13:38:59Z","snapshot_observed_at":"2026-08-14T15:49:27.555722Z","submitted_at":"2024-12-27T18:19:26Z","title":"Symbolic Approximations to Ricci-flat Metrics Via Extrinsic Symmetries of Calabi-Yau Hypersurfaces","version":2},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-10T23:59:51.011627Z"},"links":{"citing_paper":"/paper/2412.19778"},"observation_digest":"sha256:8d41f6fc79da5e7855600bb374dc1e005ac2be9378ba9002462690c78717bd53","observation_id":"fe28bdec-4f5d-4445-b3bf-89569690be7a","resolution":{"observed_at":"2026-08-10T23:59:52.089276Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1002/prop.200900106","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T11:03:20.376878Z","title":"A three-generation Calabi-Yau manifold with small Hodge numbers","venue":"Fortschritte der Physik","work_id":"fe70a021-9bb7-4cf8-b6d8-60a224810f58","year":2010},"citing_paper":{"arxiv_id":"2412.19778","last_updated":"2025-03-12T13:38:59Z","snapshot_observed_at":"2026-08-14T15:49:27.555722Z","submitted_at":"2024-12-27T18:19:26Z","title":"Symbolic Approximations to Ricci-flat Metrics Via Extrinsic Symmetries of Calabi-Yau Hypersurfaces","version":2},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-10T23:59:51.017547Z"},"links":{"citing_paper":"/paper/2412.19778"},"observation_digest":"sha256:8e7651c49b2e8bae2d36db8fb9ef55dbd92f6307fc5f509aca497f28cdfd8f4d","observation_id":"eb849724-66fa-41b7-b3e6-8780296b861b","resolution":{"observed_at":"2026-08-10T23:59:52.065506Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T23:59:52.938781Z","title":"Calabi-Yau threefolds and heterotic string compactification","venue":null,"work_id":"f1cd6c29-3bec-4255-b522-4d63aafd1512","year":2010},"citing_paper":{"arxiv_id":"2412.19778","last_updated":"2025-03-12T13:38:59Z","snapshot_observed_at":"2026-08-14T15:49:27.555722Z","submitted_at":"2024-12-27T18:19:26Z","title":"Symbolic Approximations to Ricci-flat Metrics Via Extrinsic Symmetries of Calabi-Yau Hypersurfaces","version":2},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-10T23:59:51.023853Z"},"links":{"citing_paper":"/paper/2412.19778"},"observation_digest":"sha256:4d845a84d7c8bb4ccbc0e82c2cfbd02558cf221ddc648f9341b1736dc23b71b6","observation_id":"f19a6a9d-a95c-4300-aee6-04ec4c4cca99","resolution":{"observed_at":"2026-08-10T23:59:52.945590Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T23:59:51.030411Z","title":"On free quotients of complete intersection Calabi-Yau manifolds","venue":null,"work_id":null,"year":2011},"citing_paper":{"arxiv_id":"2412.19778","last_updated":"2025-03-12T13:38:59Z","snapshot_observed_at":"2026-08-14T15:49:27.555722Z","submitted_at":"2024-12-27T18:19:26Z","title":"Symbolic Approximations to Ricci-flat Metrics Via Extrinsic Symmetries of Calabi-Yau Hypersurfaces","version":2},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-10T23:59:51.030411Z"},"links":{"citing_paper":"/paper/2412.19778"},"observation_digest":"sha256:a6048be51500bc0033b3af7daaa605a79f3e4e414060932a54559517a38be245","observation_id":"0c3e1b54-eb13-4c96-8006-847c0b4ce51d","resolution":{"observed_at":"2026-08-10T23:59:51.030411Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T23:59:52.917019Z","title":"Calabi-Yau manifolds, discrete symmetries and string theory","venue":null,"work_id":"36fb5554-224d-4060-b8a1-e11ec6d0f5e4","year":2017},"citing_paper":{"arxiv_id":"2412.19778","last_updated":"2025-03-12T13:38:59Z","snapshot_observed_at":"2026-08-14T15:49:27.555722Z","submitted_at":"2024-12-27T18:19:26Z","title":"Symbolic Approximations to Ricci-flat Metrics Via Extrinsic Symmetries of Calabi-Yau Hypersurfaces","version":2},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-10T23:59:51.039119Z"},"links":{"citing_paper":"/paper/2412.19778"},"observation_digest":"sha256:d6941480e6cf8439095c7a7de5951a2c74db85f95c9f5b8f4b616ecdb91bd024","observation_id":"e7053e40-7ca9-4731-af8a-35ec685bb583","resolution":{"observed_at":"2026-08-10T23:59:52.925158Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T23:59:52.897081Z","title":"Calabi-Yau Threefolds with Small Hodge Numbers","venue":null,"work_id":"9ad348d2-a5a6-43bc-92e0-d581e9520768","year":2018},"citing_paper":{"arxiv_id":"2412.19778","last_updated":"2025-03-12T13:38:59Z","snapshot_observed_at":"2026-08-14T15:49:27.555722Z","submitted_at":"2024-12-27T18:19:26Z","title":"Symbolic Approximations to Ricci-flat Metrics Via Extrinsic Symmetries of Calabi-Yau Hypersurfaces","version":2},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-10T23:59:51.046403Z"},"links":{"citing_paper":"/paper/2412.19778"},"observation_digest":"sha256:611c571e5f189846e9ac4db9e04ef9328547a85c9a9fe8956d221810f7e4a0a2","observation_id":"10583e47-47eb-4570-a278-ffebed3b38c6","resolution":{"observed_at":"2026-08-10T23:59:52.903282Z","resolver_source":"raw_fallback","status":"malformed_identifier"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T23:59:51.053114Z","title":"Discrete Symmetries of Complete Intersection Calabi–Yau Manifolds","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2412.19778","last_updated":"2025-03-12T13:38:59Z","snapshot_observed_at":"2026-08-14T15:49:27.555722Z","submitted_at":"2024-12-27T18:19:26Z","title":"Symbolic Approximations to Ricci-flat Metrics Via Extrinsic Symmetries of Calabi-Yau Hypersurfaces","version":2},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-10T23:59:51.053114Z"},"links":{"citing_paper":"/paper/2412.19778"},"observation_digest":"sha256:1c35503816bf81e2c72895e9d1a2ae37d88b0c6d7b1e018e309d0c360238c2f1","observation_id":"10b54262-dba5-42db-878a-389dffe8bf3c","resolution":{"observed_at":"2026-08-10T23:59:51.053114Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T23:59:52.875859Z","title":"Heterotic and M-theory compactifications for string phenomenology","venue":null,"work_id":"05fbbf7c-846a-4a20-abc4-b4be51a819f7","year":2008},"citing_paper":{"arxiv_id":"2412.19778","last_updated":"2025-03-12T13:38:59Z","snapshot_observed_at":"2026-08-14T15:49:27.555722Z","submitted_at":"2024-12-27T18:19:26Z","title":"Symbolic Approximations to Ricci-flat Metrics Via Extrinsic Symmetries of Calabi-Yau Hypersurfaces","version":2},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-10T23:59:51.063687Z"},"links":{"citing_paper":"/paper/2412.19778"},"observation_digest":"sha256:a30b37407f9dfc84c89797b938a7ee491333706b56d09192b6c9ca9b1d0aa2c0","observation_id":"88535339-a5ec-4be1-afb8-b7c6bd0d405e","resolution":{"observed_at":"2026-08-10T23:59:52.883712Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2410.17704","last_updated":"2025-06-02T11:21:24Z","snapshot_observed_at":"2026-08-16T13:06:41.845554Z","submitted_at":"2024-10-23T09:27:14Z","title":"Fermion Masses and Mixing in String-Inspired Models","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2410.17704","snapshot_observed_at":"2026-08-10T23:59:51.071951Z","title":"Constantin, C","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2412.19778","last_updated":"2025-03-12T13:38:59Z","snapshot_observed_at":"2026-08-14T15:49:27.555722Z","submitted_at":"2024-12-27T18:19:26Z","title":"Symbolic Approximations to Ricci-flat Metrics Via Extrinsic Symmetries of Calabi-Yau Hypersurfaces","version":2},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-10T23:59:51.071951Z"},"links":{"cited_paper":"/paper/2410.17704","citing_paper":"/paper/2412.19778"},"observation_digest":"sha256:7dc013e826da85dfdd6eebfac131dcd91d594d730b77172557ebd0d8fb184264","observation_id":"ec9538f7-a889-4b33-a276-31a118eff092","resolution":{"observed_at":"2026-08-10T23:59:51.071951Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T23:59:52.856372Z","title":"Discrete gauge symmetries and the origin of baryon and lepton number conservation in supersymmetric versions of the standard model","venue":null,"work_id":"d74b91d7-c4e4-4282-b7b2-8a5067229ff6","year":1992},"citing_paper":{"arxiv_id":"2412.19778","last_updated":"2025-03-12T13:38:59Z","snapshot_observed_at":"2026-08-14T15:49:27.555722Z","submitted_at":"2024-12-27T18:19:26Z","title":"Symbolic Approximations to Ricci-flat Metrics Via Extrinsic Symmetries of Calabi-Yau Hypersurfaces","version":2},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-10T23:59:51.080149Z"},"links":{"citing_paper":"/paper/2412.19778"},"observation_digest":"sha256:0690c749246e1aaaf286c2771ff8229156f46402aa7e093840028c5d55a22cc5","observation_id":"cb234b91-9fd4-4014-8f85-da4ef9ac5461","resolution":{"observed_at":"2026-08-10T23:59:52.863458Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1002/prop.200900105","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T11:03:20.376878Z","title":"New Calabi-Yau manifolds with small Hodge numbers","venue":"Fortschritte der Physik","work_id":"db59657a-5c07-4d67-a965-ad6f1061ee29","year":2010},"citing_paper":{"arxiv_id":"2412.19778","last_updated":"2025-03-12T13:38:59Z","snapshot_observed_at":"2026-08-14T15:49:27.555722Z","submitted_at":"2024-12-27T18:19:26Z","title":"Symbolic Approximations to Ricci-flat Metrics Via Extrinsic Symmetries of Calabi-Yau Hypersurfaces","version":2},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-10T23:59:51.086529Z"},"links":{"citing_paper":"/paper/2412.19778"},"observation_digest":"sha256:f27bf73cf6e0f0c18fd756a87f9d3cfbdef9fcbf0832f34d85500b37b3061852","observation_id":"73a2f21f-df5e-44fe-b9b7-713da9085d35","resolution":{"observed_at":"2026-08-10T23:59:51.998060Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T23:59:51.093043Z","title":"Highly Symmetric Quintic Quotients","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2412.19778","last_updated":"2025-03-12T13:38:59Z","snapshot_observed_at":"2026-08-14T15:49:27.555722Z","submitted_at":"2024-12-27T18:19:26Z","title":"Symbolic Approximations to Ricci-flat Metrics Via Extrinsic Symmetries of Calabi-Yau Hypersurfaces","version":2},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-10T23:59:51.093043Z"},"links":{"citing_paper":"/paper/2412.19778"},"observation_digest":"sha256:c2c6d799a6a1f27aa3fd9c0afd7acd7158c055c5e0618672ae67d95f5351e68a","observation_id":"7b5ae574-5448-45f0-89ef-dd2e42b21f58","resolution":{"observed_at":"2026-08-10T23:59:51.093043Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T23:59:52.834784Z","title":"Hodge numbers for CICYs with sym- metries of order divisible by 4","venue":null,"work_id":"5814313f-d80d-49df-b4ab-a156ab5087fc","year":2016},"citing_paper":{"arxiv_id":"2412.19778","last_updated":"2025-03-12T13:38:59Z","snapshot_observed_at":"2026-08-14T15:49:27.555722Z","submitted_at":"2024-12-27T18:19:26Z","title":"Symbolic Approximations to Ricci-flat Metrics Via Extrinsic Symmetries of Calabi-Yau Hypersurfaces","version":2},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-10T23:59:51.099202Z"},"links":{"citing_paper":"/paper/2412.19778"},"observation_digest":"sha256:5c2b47edc16650caa6e4b92cdb0ceb5cc2ca08ca8c0e7488870b885c25c50c1a","observation_id":"673db746-9b04-4ec4-82f5-a762b4891c46","resolution":{"observed_at":"2026-08-10T23:59:52.839912Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T23:59:52.815117Z","title":"The family problem: hints from heterotic line bundle models","venue":null,"work_id":"cf7bd355-0cf4-4878-8b77-8f6befe34970","year":2016},"citing_paper":{"arxiv_id":"2412.19778","last_updated":"2025-03-12T13:38:59Z","snapshot_observed_at":"2026-08-14T15:49:27.555722Z","submitted_at":"2024-12-27T18:19:26Z","title":"Symbolic Approximations to Ricci-flat Metrics Via Extrinsic Symmetries of Calabi-Yau Hypersurfaces","version":2},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-10T23:59:51.107106Z"},"links":{"citing_paper":"/paper/2412.19778"},"observation_digest":"sha256:f34d9057f155fa180b4fe61b708320afe98461885a7358c4265cf9d9fd333311","observation_id":"124e31da-2ef4-4903-be8b-28bee374abdb","resolution":{"observed_at":"2026-08-10T23:59:52.821516Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T23:59:51.115188Z","title":"Neural network approximations for Calabi- Yau metrics","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2412.19778","last_updated":"2025-03-12T13:38:59Z","snapshot_observed_at":"2026-08-14T15:49:27.555722Z","submitted_at":"2024-12-27T18:19:26Z","title":"Symbolic Approximations to Ricci-flat Metrics Via Extrinsic Symmetries of Calabi-Yau Hypersurfaces","version":2},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-10T23:59:51.115188Z"},"links":{"citing_paper":"/paper/2412.19778"},"observation_digest":"sha256:0d66ea90b24d3aed13308ffc5ecb2b895b6590c308c2a226ac52d19adb8f3994","observation_id":"2913a8a0-bcae-420f-8317-6f67a53ec61f","resolution":{"observed_at":"2026-08-10T23:59:51.115188Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T23:59:52.791893Z","title":null,"venue":null,"work_id":"2b9571d4-c1d8-4e84-8933-7e8dfee90731","year":2021},"citing_paper":{"arxiv_id":"2412.19778","last_updated":"2025-03-12T13:38:59Z","snapshot_observed_at":"2026-08-14T15:49:27.555722Z","submitted_at":"2024-12-27T18:19:26Z","title":"Symbolic Approximations to Ricci-flat Metrics Via Extrinsic Symmetries of Calabi-Yau Hypersurfaces","version":2},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-10T23:59:51.120871Z"},"links":{"citing_paper":"/paper/2412.19778"},"observation_digest":"sha256:8b8f93fb862679621cfd9fe20629fa5393a399c758f52ce5e33cdd59641d2de2","observation_id":"9207a3d2-3190-4c1a-9d00-7836ee7a0923","resolution":{"observed_at":"2026-08-10T23:59:52.803108Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T23:59:51.126229Z","title":"Approximation by superpositions of a sigmoidal function","venue":null,"work_id":null,"year":1989},"citing_paper":{"arxiv_id":"2412.19778","last_updated":"2025-03-12T13:38:59Z","snapshot_observed_at":"2026-08-14T15:49:27.555722Z","submitted_at":"2024-12-27T18:19:26Z","title":"Symbolic Approximations to Ricci-flat Metrics Via Extrinsic Symmetries of Calabi-Yau Hypersurfaces","version":2},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-10T23:59:51.126229Z"},"links":{"citing_paper":"/paper/2412.19778"},"observation_digest":"sha256:4e2a64590c0759cec7a5dc0e014d26de514416750db368be7502c0cb6fd0db4c","observation_id":"82b8fa56-9af3-429f-a84c-60f95057a0a0","resolution":{"observed_at":"2026-08-10T23:59:51.126229Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T23:59:51.132337Z","title":"Multilayer feedforward networks are universal approximators","venue":null,"work_id":null,"year":1989},"citing_paper":{"arxiv_id":"2412.19778","last_updated":"2025-03-12T13:38:59Z","snapshot_observed_at":"2026-08-14T15:49:27.555722Z","submitted_at":"2024-12-27T18:19:26Z","title":"Symbolic Approximations to Ricci-flat Metrics Via Extrinsic Symmetries of Calabi-Yau Hypersurfaces","version":2},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-10T23:59:51.132337Z"},"links":{"citing_paper":"/paper/2412.19778"},"observation_digest":"sha256:1e33b99642edc2a9181e58c7347fb8e097dc9025aca400ea01e275da4ca52ecc","observation_id":"c0c4e5c4-65e0-43b1-a533-809134d44ddf","resolution":{"observed_at":"2026-08-10T23:59:51.132337Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T23:59:51.142367Z","title":"Approximation capabilities of multilayer feedforward networks","venue":null,"work_id":null,"year":1991},"citing_paper":{"arxiv_id":"2412.19778","last_updated":"2025-03-12T13:38:59Z","snapshot_observed_at":"2026-08-14T15:49:27.555722Z","submitted_at":"2024-12-27T18:19:26Z","title":"Symbolic Approximations to Ricci-flat Metrics Via Extrinsic Symmetries of Calabi-Yau Hypersurfaces","version":2},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-10T23:59:51.142367Z"},"links":{"citing_paper":"/paper/2412.19778"},"observation_digest":"sha256:ef6c0e7f676166ed98e28933c29de71e92f7835d812030249a0f259a1e0a6ed2","observation_id":"d8e406a3-3c7e-4e1e-b67d-3a043008cd8c","resolution":{"observed_at":"2026-08-10T23:59:51.142367Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T23:59:52.772069Z","title":null,"venue":null,"work_id":"89f255de-2731-4d76-9cfe-e5425530fb2b","year":2019},"citing_paper":{"arxiv_id":"2412.19778","last_updated":"2025-03-12T13:38:59Z","snapshot_observed_at":"2026-08-14T15:49:27.555722Z","submitted_at":"2024-12-27T18:19:26Z","title":"Symbolic Approximations to Ricci-flat Metrics Via Extrinsic Symmetries of Calabi-Yau Hypersurfaces","version":2},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-10T23:59:51.148823Z"},"links":{"citing_paper":"/paper/2412.19778"},"observation_digest":"sha256:2367dc41bdd686eeefa7d9f000b681655951d3f9b0250e87243d54c19bdfb876","observation_id":"05f43cad-8202-4f97-866f-b317bf4260d4","resolution":{"observed_at":"2026-08-10T23:59:52.778915Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T23:59:52.750172Z","title":"Raissi, P","venue":null,"work_id":"0bd520f7-c410-4273-be9f-f2497f25d271","year":2017},"citing_paper":{"arxiv_id":"2412.19778","last_updated":"2025-03-12T13:38:59Z","snapshot_observed_at":"2026-08-14T15:49:27.555722Z","submitted_at":"2024-12-27T18:19:26Z","title":"Symbolic Approximations to Ricci-flat Metrics Via Extrinsic Symmetries of Calabi-Yau Hypersurfaces","version":2},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-10T23:59:51.154445Z"},"links":{"citing_paper":"/paper/2412.19778"},"observation_digest":"sha256:b0a437bbecd6e3f4db097f370df4162cf5e590439734ccd831539689a7fe2e64","observation_id":"9b0f0353-496b-49c6-9be7-06d184330ac1","resolution":{"observed_at":"2026-08-10T23:59:52.758512Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T23:59:51.160227Z","title":"Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2412.19778","last_updated":"2025-03-12T13:38:59Z","snapshot_observed_at":"2026-08-14T15:49:27.555722Z","submitted_at":"2024-12-27T18:19:26Z","title":"Symbolic Approximations to Ricci-flat Metrics Via Extrinsic Symmetries of Calabi-Yau Hypersurfaces","version":2},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-10T23:59:51.160227Z"},"links":{"citing_paper":"/paper/2412.19778"},"observation_digest":"sha256:e122da197a40405fec9967c0da4cb3d345b72472795b6f5471b576b05980c0a2","observation_id":"484cf5bf-9f0d-4e54-80c7-64aa62fd4dcd","resolution":{"observed_at":"2026-08-10T23:59:51.160227Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T23:59:52.725258Z","title":"Vacuum configurations for superstrings","venue":null,"work_id":"b65e9329-73f8-48cf-9dbc-f25c802b9474","year":1985},"citing_paper":{"arxiv_id":"2412.19778","last_updated":"2025-03-12T13:38:59Z","snapshot_observed_at":"2026-08-14T15:49:27.555722Z","submitted_at":"2024-12-27T18:19:26Z","title":"Symbolic Approximations to Ricci-flat Metrics Via Extrinsic Symmetries of Calabi-Yau Hypersurfaces","version":2},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-10T23:59:51.167719Z"},"links":{"citing_paper":"/paper/2412.19778"},"observation_digest":"sha256:0b65da9b85a4edd3365ea94558bef3d3302922dcf3e965cc70322f8c04e08d0e","observation_id":"e4964b0a-b34b-42be-8dfb-5575a94acca4","resolution":{"observed_at":"2026-08-10T23:59:52.730838Z","resolver_source":"raw_fallback","status":"malformed_identifier"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1088/1126-6708/2004/05/072","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T23:59:51.879238Z","title":"Distributions of flux vacua","venue":null,"work_id":"bd3b26c8-2523-4fe0-8e0c-70fbe6edb9fe","year":2004},"citing_paper":{"arxiv_id":"2412.19778","last_updated":"2025-03-12T13:38:59Z","snapshot_observed_at":"2026-08-14T15:49:27.555722Z","submitted_at":"2024-12-27T18:19:26Z","title":"Symbolic Approximations to Ricci-flat Metrics Via Extrinsic Symmetries of Calabi-Yau Hypersurfaces","version":2},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-10T23:59:51.174316Z"},"links":{"citing_paper":"/paper/2412.19778"},"observation_digest":"sha256:30174acc3fc0f6866a308ce45c9a68e56f971fff57ea605a36a713086c536cc4","observation_id":"b58a8cbe-9c8c-467a-b806-f2715f0aa679","resolution":{"observed_at":"2026-08-10T23:59:51.887590Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T23:59:52.705421Z","title":"Candelas and X","venue":null,"work_id":"e12df75d-e612-4137-9c69-95270e54bcff","year":1987},"citing_paper":{"arxiv_id":"2412.19778","last_updated":"2025-03-12T13:38:59Z","snapshot_observed_at":"2026-08-14T15:49:27.555722Z","submitted_at":"2024-12-27T18:19:26Z","title":"Symbolic Approximations to Ricci-flat Metrics Via Extrinsic Symmetries of Calabi-Yau Hypersurfaces","version":2},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-10T23:59:51.180011Z"},"links":{"citing_paper":"/paper/2412.19778"},"observation_digest":"sha256:fecd55484e6abb97c51d4dd468d6f808e03ea6c39919a48e27d58fede5065ef2","observation_id":"64a2fc0d-20c0-4c2d-8604-6759df8092bf","resolution":{"observed_at":"2026-08-10T23:59:52.711805Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T23:59:52.675504Z","title":"H¨ ubsch.Calabi-Yau Manifolds: A Bestiary for Physicists","venue":null,"work_id":"b56e7907-a1bf-46fe-99b2-0ca595cb5fa5","year":1994},"citing_paper":{"arxiv_id":"2412.19778","last_updated":"2025-03-12T13:38:59Z","snapshot_observed_at":"2026-08-14T15:49:27.555722Z","submitted_at":"2024-12-27T18:19:26Z","title":"Symbolic Approximations to Ricci-flat Metrics Via Extrinsic Symmetries of Calabi-Yau Hypersurfaces","version":2},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-10T23:59:51.186900Z"},"links":{"citing_paper":"/paper/2412.19778"},"observation_digest":"sha256:e28484701dcb15a1b4a32615f03ac046536ad05f06d32a3ff90e669d988df050","observation_id":"d1697994-a1d6-4490-bcce-22b5fa53bd90","resolution":{"observed_at":"2026-08-10T23:59:52.683260Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T23:59:51.192729Z","title":"Numerical Calabi-Yau metrics","venue":null,"work_id":null,"year":2008},"citing_paper":{"arxiv_id":"2412.19778","last_updated":"2025-03-12T13:38:59Z","snapshot_observed_at":"2026-08-14T15:49:27.555722Z","submitted_at":"2024-12-27T18:19:26Z","title":"Symbolic Approximations to Ricci-flat Metrics Via Extrinsic Symmetries of Calabi-Yau Hypersurfaces","version":2},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-10T23:59:51.192729Z"},"links":{"citing_paper":"/paper/2412.19778"},"observation_digest":"sha256:1650042abc945188c1ee6bf74b130805771ea4ea392127216c403455b8aad2a9","observation_id":"28440286-851a-4d1d-acda-507e7d1bf062","resolution":{"observed_at":"2026-08-10T23:59:51.192729Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1088/1126-6708/2007/12/083","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T23:59:51.846937Z","title":"Numerical solution to the hermitian Yang-Mills equation on the Fermat quintic","venue":null,"work_id":"1f0f3973-2547-4a1d-bc01-c6bb738dda39","year":2007},"citing_paper":{"arxiv_id":"2412.19778","last_updated":"2025-03-12T13:38:59Z","snapshot_observed_at":"2026-08-14T15:49:27.555722Z","submitted_at":"2024-12-27T18:19:26Z","title":"Symbolic Approximations to Ricci-flat Metrics Via Extrinsic Symmetries of Calabi-Yau Hypersurfaces","version":2},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-10T23:59:51.199046Z"},"links":{"citing_paper":"/paper/2412.19778"},"observation_digest":"sha256:004af00de51f37237b59485c000581361057a672760fe55f351c1c8d01859d2e","observation_id":"bc2e3969-ce50-40ab-9780-1ae13e97e06b","resolution":{"observed_at":"2026-08-10T23:59:51.853487Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T23:59:52.655139Z","title":"Larfors, A","venue":null,"work_id":"0c4ba194-00e8-48d4-89ff-6556ab643fe3","year":2021},"citing_paper":{"arxiv_id":"2412.19778","last_updated":"2025-03-12T13:38:59Z","snapshot_observed_at":"2026-08-14T15:49:27.555722Z","submitted_at":"2024-12-27T18:19:26Z","title":"Symbolic Approximations to Ricci-flat Metrics Via Extrinsic Symmetries of Calabi-Yau Hypersurfaces","version":2},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-08-10T23:59:51.204819Z"},"links":{"citing_paper":"/paper/2412.19778"},"observation_digest":"sha256:8a0ed1dc1303ec7232686b0dbfd657ce67aabdbf4608bbf573a28cf952ad817c","observation_id":"df529da2-4da2-436b-8e73-7e069ed56402","resolution":{"observed_at":"2026-08-10T23:59:52.661238Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T23:59:52.635916Z","title":"Hendi, M","venue":null,"work_id":"509d5819-b2b4-44df-b53b-b1a944e2c23a","year":2024},"citing_paper":{"arxiv_id":"2412.19778","last_updated":"2025-03-12T13:38:59Z","snapshot_observed_at":"2026-08-14T15:49:27.555722Z","submitted_at":"2024-12-27T18:19:26Z","title":"Symbolic Approximations to Ricci-flat Metrics Via Extrinsic Symmetries of Calabi-Yau Hypersurfaces","version":2},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-08-10T23:59:51.212768Z"},"links":{"citing_paper":"/paper/2412.19778"},"observation_digest":"sha256:b39f58423c5ef52b6163e0313cb62dbf7c4894af06f3af4c8df5f44277e1ba17","observation_id":"90e08649-83f2-4cc5-a253-8b9a4d657b85","resolution":{"observed_at":"2026-08-10T23:59:52.641730Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2211.09801","last_updated":"2023-06-06T15:06:15Z","snapshot_observed_at":"2026-08-16T16:15:18.290994Z","submitted_at":"2022-11-17T18:59:03Z","title":"Machine Learned Calabi-Yau Metrics and Curvature","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2211.09801","snapshot_observed_at":"2026-08-10T23:59:51.218379Z","title":"Berglund, G","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2412.19778","last_updated":"2025-03-12T13:38:59Z","snapshot_observed_at":"2026-08-14T15:49:27.555722Z","submitted_at":"2024-12-27T18:19:26Z","title":"Symbolic Approximations to Ricci-flat Metrics Via Extrinsic Symmetries of Calabi-Yau Hypersurfaces","version":2},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-08-10T23:59:51.218379Z"},"links":{"cited_paper":"/paper/2211.09801","citing_paper":"/paper/2412.19778"},"observation_digest":"sha256:643b6cf9777c3e787508e4a13b2fb2a498abf0163cd56f1b807531d205db6fe5","observation_id":"85092cea-f38b-4253-af93-5180ad98f863","resolution":{"observed_at":"2026-08-10T23:59:51.218379Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T23:59:51.226470Z","title":"Machine learning Calabi-Yau metrics","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2412.19778","last_updated":"2025-03-12T13:38:59Z","snapshot_observed_at":"2026-08-14T15:49:27.555722Z","submitted_at":"2024-12-27T18:19:26Z","title":"Symbolic Approximations to Ricci-flat Metrics Via Extrinsic Symmetries of Calabi-Yau Hypersurfaces","version":2},"reference_index":38,"source":"pdf_text","source_observed_at":"2026-08-10T23:59:51.226470Z"},"links":{"citing_paper":"/paper/2412.19778"},"observation_digest":"sha256:fd701199bf5133fccededca33a0d0a95db51dfdc576fe86ce1959538ee384d83","observation_id":"9da442e7-2818-4769-9ff1-b07b3ea94b66","resolution":{"observed_at":"2026-08-10T23:59:51.226470Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2211.12520","last_updated":"2023-07-12T11:37:33Z","snapshot_observed_at":"2026-08-16T16:14:05.229105Z","submitted_at":"2022-11-22T19:00:01Z","title":"CYJAX: A package for Calabi-Yau metrics with JAX","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2211.12520","snapshot_observed_at":"2026-08-10T23:59:51.231779Z","title":"Gerdes and S","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2412.19778","last_updated":"2025-03-12T13:38:59Z","snapshot_observed_at":"2026-08-14T15:49:27.555722Z","submitted_at":"2024-12-27T18:19:26Z","title":"Symbolic Approximations to Ricci-flat Metrics Via Extrinsic Symmetries of Calabi-Yau Hypersurfaces","version":2},"reference_index":39,"source":"pdf_text","source_observed_at":"2026-08-10T23:59:51.231779Z"},"links":{"cited_paper":"/paper/2211.12520","citing_paper":"/paper/2412.19778"},"observation_digest":"sha256:f7b1897e861c38d167d97d5dd186681a35868e38cc6e6924d9f8d24dba10d1ce","observation_id":"5d875bd1-f4cf-4b1b-bae6-173f9a0f2df1","resolution":{"observed_at":"2026-08-10T23:59:51.231779Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T23:59:51.238192Z","title":"Numerical Ricci-flat metrics on K3","venue":null,"work_id":null,"year":2005},"citing_paper":{"arxiv_id":"2412.19778","last_updated":"2025-03-12T13:38:59Z","snapshot_observed_at":"2026-08-14T15:49:27.555722Z","submitted_at":"2024-12-27T18:19:26Z","title":"Symbolic Approximations to Ricci-flat Metrics Via Extrinsic Symmetries of Calabi-Yau Hypersurfaces","version":2},"reference_index":40,"source":"pdf_text","source_observed_at":"2026-08-10T23:59:51.238192Z"},"links":{"citing_paper":"/paper/2412.19778"},"observation_digest":"sha256:d6ebeb472d4a2aa0cf39e5c003cb4a43b4a1352acae5f67ee1ca8262175ad24e","observation_id":"035618a5-a4d9-47e0-85c3-a1bc3c0233f7","resolution":{"observed_at":"2026-08-10T23:59:51.238192Z","resolver_source":null,"status":"malformed_identifier"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2312.17125","last_updated":"2023-12-29T16:42:21Z","snapshot_observed_at":"2026-08-16T14:31:07.794365Z","submitted_at":"2023-12-28T17:03:58Z","title":"Lectures on Numerical and Machine Learning Methods for Approximating Ricci-flat Calabi-Yau Metrics","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2312.17125","snapshot_observed_at":"2026-08-10T23:59:51.244104Z","title":null,"venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2412.19778","last_updated":"2025-03-12T13:38:59Z","snapshot_observed_at":"2026-08-14T15:49:27.555722Z","submitted_at":"2024-12-27T18:19:26Z","title":"Symbolic Approximations to Ricci-flat Metrics Via Extrinsic Symmetries of Calabi-Yau Hypersurfaces","version":2},"reference_index":41,"source":"pdf_text","source_observed_at":"2026-08-10T23:59:51.244104Z"},"links":{"cited_paper":"/paper/2312.17125","citing_paper":"/paper/2412.19778"},"observation_digest":"sha256:90471ee8453d1f12d336ae187a9df0c3272ab8fd872d675820e61edc6a45bfab","observation_id":"9862fb02-e585-4ead-bc78-aa89cce7f43e","resolution":{"observed_at":"2026-08-10T23:59:51.244104Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2401.15078","last_updated":"2024-05-01T16:27:39Z","snapshot_observed_at":"2026-08-16T14:24:08.997087Z","submitted_at":"2024-01-26T18:59:30Z","title":"Physical Yukawa Couplings in Heterotic String Compactifications","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2401.15078","snapshot_observed_at":"2026-08-10T23:59:51.250893Z","title":"Butbaia, D","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2412.19778","last_updated":"2025-03-12T13:38:59Z","snapshot_observed_at":"2026-08-14T15:49:27.555722Z","submitted_at":"2024-12-27T18:19:26Z","title":"Symbolic Approximations to Ricci-flat Metrics Via Extrinsic Symmetries of Calabi-Yau Hypersurfaces","version":2},"reference_index":42,"source":"pdf_text","source_observed_at":"2026-08-10T23:59:51.250893Z"},"links":{"cited_paper":"/paper/2401.15078","citing_paper":"/paper/2412.19778"},"observation_digest":"sha256:0a0ba11c7246bcf8b87f8bce861f73ffe55e2767dc581fd3c332c217fe0f3037","observation_id":"6ab19974-7869-45a1-bb19-1160bf53d132","resolution":{"observed_at":"2026-08-10T23:59:51.250893Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T23:59:51.257391Z","title":"Symmetry breaking patterns in superstring models","venue":null,"work_id":null,"year":1985},"citing_paper":{"arxiv_id":"2412.19778","last_updated":"2025-03-12T13:38:59Z","snapshot_observed_at":"2026-08-14T15:49:27.555722Z","submitted_at":"2024-12-27T18:19:26Z","title":"Symbolic Approximations to Ricci-flat Metrics Via Extrinsic Symmetries of Calabi-Yau Hypersurfaces","version":2},"reference_index":43,"source":"pdf_text","source_observed_at":"2026-08-10T23:59:51.257391Z"},"links":{"citing_paper":"/paper/2412.19778"},"observation_digest":"sha256:c8f8ecf5fdf8e028bac8849ff35269a3409245f4e6c4a39ecbfaa073ba70e206","observation_id":"65e16410-4d61-4e59-8156-3fbf1d4d1229","resolution":{"observed_at":"2026-08-10T23:59:51.257391Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T23:59:52.612550Z","title":"Moduli-dependent Calabi-Yau and SU(3)-structure metrics from machine learning","venue":null,"work_id":"3662f5d9-69d4-4c37-8dac-839dc18ca327","year":2021},"citing_paper":{"arxiv_id":"2412.19778","last_updated":"2025-03-12T13:38:59Z","snapshot_observed_at":"2026-08-14T15:49:27.555722Z","submitted_at":"2024-12-27T18:19:26Z","title":"Symbolic Approximations to Ricci-flat Metrics Via Extrinsic Symmetries of Calabi-Yau Hypersurfaces","version":2},"reference_index":44,"source":"pdf_text","source_observed_at":"2026-08-10T23:59:51.264619Z"},"links":{"citing_paper":"/paper/2412.19778"},"observation_digest":"sha256:a434a0b89a8798fe62699db5c51060c9c6d42e9462434f3cba644a7b729a8cd2","observation_id":"8bcf853f-5932-4dd2-ba16-3b87de70f2fa","resolution":{"observed_at":"2026-08-10T23:59:52.620219Z","resolver_source":"raw_fallback","status":"malformed_identifier"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2006.02435","last_updated":"2020-10-06T02:34:54Z","snapshot_observed_at":"2026-08-12T16:12:33.655452Z","submitted_at":"2020-06-03T18:00:00Z","title":"K3 metrics","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2006.02435","snapshot_observed_at":"2026-08-10T23:59:51.270935Z","title":"Kachru, A","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2412.19778","last_updated":"2025-03-12T13:38:59Z","snapshot_observed_at":"2026-08-14T15:49:27.555722Z","submitted_at":"2024-12-27T18:19:26Z","title":"Symbolic Approximations to Ricci-flat Metrics Via Extrinsic Symmetries of Calabi-Yau Hypersurfaces","version":2},"reference_index":45,"source":"pdf_text","source_observed_at":"2026-08-10T23:59:51.270935Z"},"links":{"cited_paper":"/paper/2006.02435","citing_paper":"/paper/2412.19778"},"observation_digest":"sha256:f2c9a0b243085aa2415316d4bf3e62f37feead8a2214a97d1635cefc6f56340f","observation_id":"831dd4c6-67b3-4634-9c0e-3fdc509019d4","resolution":{"observed_at":"2026-08-10T23:59:51.270935Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2410.19728","last_updated":"2024-10-25T17:55:01Z","snapshot_observed_at":"2026-08-16T13:05:52.629694Z","submitted_at":"2024-10-25T17:55:01Z","title":"cymyc -- Calabi-Yau Metrics, Yukawas, and Curvature","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2410.19728","snapshot_observed_at":"2026-08-10T23:59:51.277479Z","title":"Berglund, G","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2412.19778","last_updated":"2025-03-12T13:38:59Z","snapshot_observed_at":"2026-08-14T15:49:27.555722Z","submitted_at":"2024-12-27T18:19:26Z","title":"Symbolic Approximations to Ricci-flat Metrics Via Extrinsic Symmetries of Calabi-Yau Hypersurfaces","version":2},"reference_index":46,"source":"pdf_text","source_observed_at":"2026-08-10T23:59:51.277479Z"},"links":{"cited_paper":"/paper/2410.19728","citing_paper":"/paper/2412.19778"},"observation_digest":"sha256:509efd3dc0e626c388e770a19b2a20e96ce6f7975a83bccba5eaf9d0cb91201d","observation_id":"121656f4-ffc0-438c-af78-54c3d1363b41","resolution":{"observed_at":"2026-08-10T23:59:51.277479Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2404.19756","last_updated":"2025-02-09T21:09:09Z","snapshot_observed_at":"2026-08-15T02:33:31.807561Z","submitted_at":"2024-04-30T17:58:29Z","title":"KAN: Kolmogorov-Arnold Networks","version":5},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2404.19756","snapshot_observed_at":"2026-08-10T23:59:51.282924Z","title":null,"venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2412.19778","last_updated":"2025-03-12T13:38:59Z","snapshot_observed_at":"2026-08-14T15:49:27.555722Z","submitted_at":"2024-12-27T18:19:26Z","title":"Symbolic Approximations to Ricci-flat Metrics Via Extrinsic Symmetries of Calabi-Yau Hypersurfaces","version":2},"reference_index":47,"source":"pdf_text","source_observed_at":"2026-08-10T23:59:51.282924Z"},"links":{"cited_paper":"/paper/2404.19756","citing_paper":"/paper/2412.19778"},"observation_digest":"sha256:2ccbc083c8516988c020c994be812825c0b835c5ee1d2613d6adf14455481ba9","observation_id":"fc78d043-b27c-4ac6-a240-b6fa0cc97dc7","resolution":{"observed_at":"2026-08-10T23:59:51.282924Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T23:59:52.592064Z","title":"On the Representation of Continuous Functions of Several Variables by Superposition of Continuous Functions of One Variable and Addition","venue":null,"work_id":"a7260084-366f-4188-a72e-9c2ea2a13a81","year":1957},"citing_paper":{"arxiv_id":"2412.19778","last_updated":"2025-03-12T13:38:59Z","snapshot_observed_at":"2026-08-14T15:49:27.555722Z","submitted_at":"2024-12-27T18:19:26Z","title":"Symbolic Approximations to Ricci-flat Metrics Via Extrinsic Symmetries of Calabi-Yau Hypersurfaces","version":2},"reference_index":48,"source":"pdf_text","source_observed_at":"2026-08-10T23:59:51.289661Z"},"links":{"citing_paper":"/paper/2412.19778"},"observation_digest":"sha256:981a31dc57b450349da5b36d8433f4bcbaf74329e0e3f2db9aa31077cfb15611","observation_id":"cc707b40-fde4-4b3a-bda8-ec38c5c5323a","resolution":{"observed_at":"2026-08-10T23:59:52.598970Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T23:59:51.295564Z","title":"Representation of continuous functions of three variables by the superposition of continuous functions of two variables","venue":null,"work_id":null,"year":1957},"citing_paper":{"arxiv_id":"2412.19778","last_updated":"2025-03-12T13:38:59Z","snapshot_observed_at":"2026-08-14T15:49:27.555722Z","submitted_at":"2024-12-27T18:19:26Z","title":"Symbolic Approximations to Ricci-flat Metrics Via Extrinsic Symmetries of Calabi-Yau Hypersurfaces","version":2},"reference_index":49,"source":"pdf_text","source_observed_at":"2026-08-10T23:59:51.295564Z"},"links":{"citing_paper":"/paper/2412.19778"},"observation_digest":"sha256:eb6dc7598a5256d9d20903dda7a4895593860ad434629b7374ff52e53feb963d","observation_id":"f0385ca6-719b-4377-888d-00ef779fe73b","resolution":{"observed_at":"2026-08-10T23:59:51.295564Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T23:59:52.565142Z","title":"Discovering Symbolic Models from Deep Learning with Inductive Biases","venue":null,"work_id":"1bd342bf-2ff9-47e9-9ae5-dc63da27ca84","year":2020},"citing_paper":{"arxiv_id":"2412.19778","last_updated":"2025-03-12T13:38:59Z","snapshot_observed_at":"2026-08-14T15:49:27.555722Z","submitted_at":"2024-12-27T18:19:26Z","title":"Symbolic Approximations to Ricci-flat Metrics Via Extrinsic Symmetries of Calabi-Yau Hypersurfaces","version":2},"reference_index":50,"source":"pdf_text","source_observed_at":"2026-08-10T23:59:51.301874Z"},"links":{"citing_paper":"/paper/2412.19778"},"observation_digest":"sha256:04b24f139bbad8052bfff779430dd1f31cc86f625a3b6922cbad60e050821cfc","observation_id":"ebaa94b9-b545-4f67-ac93-b43bf504f2ff","resolution":{"observed_at":"2026-08-10T23:59:52.576236Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2305.01582","last_updated":"2023-05-05T17:44:07Z","snapshot_observed_at":"2026-08-15T03:20:28.565133Z","submitted_at":"2023-05-02T16:31:35Z","title":"Interpretable Machine Learning for Science with PySR and SymbolicRegression.jl","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2305.01582","snapshot_observed_at":"2026-08-10T23:59:51.307384Z","title":null,"venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2412.19778","last_updated":"2025-03-12T13:38:59Z","snapshot_observed_at":"2026-08-14T15:49:27.555722Z","submitted_at":"2024-12-27T18:19:26Z","title":"Symbolic Approximations to Ricci-flat Metrics Via Extrinsic Symmetries of Calabi-Yau Hypersurfaces","version":2},"reference_index":51,"source":"pdf_text","source_observed_at":"2026-08-10T23:59:51.307384Z"},"links":{"cited_paper":"/paper/2305.01582","citing_paper":"/paper/2412.19778"},"observation_digest":"sha256:118e7c790b6df18c7ccbbf07cf219c6d6adc9ddf083794a86964570a288bebd8","observation_id":"6dc8e0ff-10a5-4560-bb53-4f9042e93bcb","resolution":{"observed_at":"2026-08-10T23:59:51.307384Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T23:59:52.541905Z","title":"Axiomatic attribution for deep networks","venue":null,"work_id":"748a7db0-7888-4ee6-9b42-3d2e697ecdec","year":null},"citing_paper":{"arxiv_id":"2412.19778","last_updated":"2025-03-12T13:38:59Z","snapshot_observed_at":"2026-08-14T15:49:27.555722Z","submitted_at":"2024-12-27T18:19:26Z","title":"Symbolic Approximations to Ricci-flat Metrics Via Extrinsic Symmetries of Calabi-Yau Hypersurfaces","version":2},"reference_index":52,"source":"pdf_text","source_observed_at":"2026-08-10T23:59:51.314903Z"},"links":{"citing_paper":"/paper/2412.19778"},"observation_digest":"sha256:85c7ca605ce6b50a9a5983394444a9bca352171a8081907da094b308c3f94046","observation_id":"3a7a33f6-0112-445f-a738-fd3e7b25c74e","resolution":{"observed_at":"2026-08-10T23:59:52.549965Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T23:59:52.492430Z","title":"Layer-Wise Relevance Propagation: An Overview","venue":null,"work_id":"6951a29b-a537-4135-802a-31cc242d168a","year":2019},"citing_paper":{"arxiv_id":"2412.19778","last_updated":"2025-03-12T13:38:59Z","snapshot_observed_at":"2026-08-14T15:49:27.555722Z","submitted_at":"2024-12-27T18:19:26Z","title":"Symbolic Approximations to Ricci-flat Metrics Via Extrinsic Symmetries of Calabi-Yau Hypersurfaces","version":2},"reference_index":53,"source":"pdf_text","source_observed_at":"2026-08-10T23:59:51.326705Z"},"links":{"citing_paper":"/paper/2412.19778"},"observation_digest":"sha256:f9410010e4a577490dae0cae870a448c449872cd52fe3b0526706b920f891fb2","observation_id":"8332a38d-0d1b-4f54-b4c9-fbf3108ef84f","resolution":{"observed_at":"2026-08-10T23:59:52.501344Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T23:59:51.339587Z","title":"Advancing mathematics by guiding human intuition with AI","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2412.19778","last_updated":"2025-03-12T13:38:59Z","snapshot_observed_at":"2026-08-14T15:49:27.555722Z","submitted_at":"2024-12-27T18:19:26Z","title":"Symbolic Approximations to Ricci-flat Metrics Via Extrinsic Symmetries of Calabi-Yau Hypersurfaces","version":2},"reference_index":54,"source":"pdf_text","source_observed_at":"2026-08-10T23:59:51.339587Z"},"links":{"citing_paper":"/paper/2412.19778"},"observation_digest":"sha256:129f41837f882452afa9afb7cdab231d0f07ae33559ba3a4d898c7f2bdfba5c5","observation_id":"bbe25db2-3c9a-4d0c-b53c-741a50e5e0c6","resolution":{"observed_at":"2026-08-10T23:59:51.339587Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T23:59:52.472978Z","title":"Villar, D","venue":null,"work_id":"a35d5086-8571-46ec-a00f-b684abc5ac8c","year":2023},"citing_paper":{"arxiv_id":"2412.19778","last_updated":"2025-03-12T13:38:59Z","snapshot_observed_at":"2026-08-14T15:49:27.555722Z","submitted_at":"2024-12-27T18:19:26Z","title":"Symbolic Approximations to Ricci-flat Metrics Via Extrinsic Symmetries of Calabi-Yau Hypersurfaces","version":2},"reference_index":55,"source":"pdf_text","source_observed_at":"2026-08-10T23:59:51.345524Z"},"links":{"citing_paper":"/paper/2412.19778"},"observation_digest":"sha256:6015b14372133c2dbdb5af1437e118f1d8aba161691a7354ce922ac0a81a94cd","observation_id":"f8ace113-b629-4563-8b2c-572264687f70","resolution":{"observed_at":"2026-08-10T23:59:52.479023Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T23:59:52.439247Z","title":null,"venue":null,"work_id":"c4f7238c-e5b2-4067-8991-9995ff273f02","year":1946},"citing_paper":{"arxiv_id":"2412.19778","last_updated":"2025-03-12T13:38:59Z","snapshot_observed_at":"2026-08-14T15:49:27.555722Z","submitted_at":"2024-12-27T18:19:26Z","title":"Symbolic Approximations to Ricci-flat Metrics Via Extrinsic Symmetries of Calabi-Yau Hypersurfaces","version":2},"reference_index":56,"source":"pdf_text","source_observed_at":"2026-08-10T23:59:51.353434Z"},"links":{"citing_paper":"/paper/2412.19778"},"observation_digest":"sha256:839923e9c6e6e5bd0a3e7bab65e20008a08512d51397f836381c47126517363c","observation_id":"ec724058-73d0-4961-aa23-99d3e5224fb0","resolution":{"observed_at":"2026-08-10T23:59:52.451189Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T23:59:52.417583Z","title":"Herstellung von Graphen mit vorgegebener abstrakter Gruppe","venue":null,"work_id":"7baeb60c-7de0-4437-b560-1b729ca10341","year":1938},"citing_paper":{"arxiv_id":"2412.19778","last_updated":"2025-03-12T13:38:59Z","snapshot_observed_at":"2026-08-14T15:49:27.555722Z","submitted_at":"2024-12-27T18:19:26Z","title":"Symbolic Approximations to Ricci-flat Metrics Via Extrinsic Symmetries of Calabi-Yau Hypersurfaces","version":2},"reference_index":57,"source":"pdf_text","source_observed_at":"2026-08-10T23:59:51.360945Z"},"links":{"citing_paper":"/paper/2412.19778"},"observation_digest":"sha256:70dc3261f7593267c772ff760041b8833c8b16664257184a638601b8049dd4cb","observation_id":"3eae16b7-94cd-4d68-a5de-1ccf03ab430c","resolution":{"observed_at":"2026-08-10T23:59:52.424119Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1007/978-3-030-46040-2_18","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T11:03:20.376878Z","title":"Isometries, Local Isometries, Riemannian Coverings and Submersions, and Killing Vector Fields","venue":"Geometry and computing","work_id":"63eef333-d1a3-4bf3-96c2-8dddc487e780","year":2020},"citing_paper":{"arxiv_id":"2412.19778","last_updated":"2025-03-12T13:38:59Z","snapshot_observed_at":"2026-08-14T15:49:27.555722Z","submitted_at":"2024-12-27T18:19:26Z","title":"Symbolic Approximations to Ricci-flat Metrics Via Extrinsic Symmetries of Calabi-Yau Hypersurfaces","version":2},"reference_index":58,"source":"pdf_text","source_observed_at":"2026-08-10T23:59:51.367402Z"},"links":{"citing_paper":"/paper/2412.19778"},"observation_digest":"sha256:eff4cb6759b72be5c130e0635a956d749016837120071b4ddd607bf81014571b","observation_id":"8105aec1-9270-4834-8dda-925dc76530aa","resolution":{"observed_at":"2026-08-10T23:59:51.570061Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T23:59:52.388607Z","title":"Bradbury, R","venue":null,"work_id":"fce3fb1e-35d9-4d76-8531-da3b8af54c28","year":2018},"citing_paper":{"arxiv_id":"2412.19778","last_updated":"2025-03-12T13:38:59Z","snapshot_observed_at":"2026-08-14T15:49:27.555722Z","submitted_at":"2024-12-27T18:19:26Z","title":"Symbolic Approximations to Ricci-flat Metrics Via Extrinsic Symmetries of Calabi-Yau Hypersurfaces","version":2},"reference_index":59,"source":"pdf_text","source_observed_at":"2026-08-10T23:59:51.380667Z"},"links":{"citing_paper":"/paper/2412.19778"},"observation_digest":"sha256:fc3168c7656d388737faf755884c15f7b9c9c8d1e3547b3644f4bc7c911161bf","observation_id":"2cdbdaed-53b5-4ad1-9e7b-e69bfba8dd96","resolution":{"observed_at":"2026-08-10T23:59:52.394690Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2012.04797","last_updated":"2021-05-05T17:13:41Z","snapshot_observed_at":"2026-08-16T18:59:57.596916Z","submitted_at":"2020-12-09T00:15:56Z","title":"Numerical Calabi-Yau metrics from holomorphic networks","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2012.04797","snapshot_observed_at":"2026-08-10T23:59:51.388479Z","title":null,"venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2412.19778","last_updated":"2025-03-12T13:38:59Z","snapshot_observed_at":"2026-08-14T15:49:27.555722Z","submitted_at":"2024-12-27T18:19:26Z","title":"Symbolic Approximations to Ricci-flat Metrics Via Extrinsic Symmetries of Calabi-Yau Hypersurfaces","version":2},"reference_index":60,"source":"pdf_text","source_observed_at":"2026-08-10T23:59:51.388479Z"},"links":{"cited_paper":"/paper/2012.04797","citing_paper":"/paper/2412.19778"},"observation_digest":"sha256:b82cbb52a6574e954569dc6e1c38b83444c5e87e6fccfc12bab426564cb68af3","observation_id":"453765aa-1fb9-4faa-874c-77e66ebe357d","resolution":{"observed_at":"2026-08-10T23:59:51.388479Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"hep-th/0702063","last_updated":"2007-02-08T18:36:43Z","snapshot_observed_at":"2026-08-15T10:48:16.645187Z","submitted_at":"2007-02-08T18:36:43Z","title":"Lectures on complex geometry, Calabi-Yau manifolds and toric geometry","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"hep-th/0702063","snapshot_observed_at":"2026-08-10T23:59:51.395368Z","title":"Bouchard","venue":null,"work_id":null,"year":2007},"citing_paper":{"arxiv_id":"2412.19778","last_updated":"2025-03-12T13:38:59Z","snapshot_observed_at":"2026-08-14T15:49:27.555722Z","submitted_at":"2024-12-27T18:19:26Z","title":"Symbolic Approximations to Ricci-flat Metrics Via Extrinsic Symmetries of Calabi-Yau Hypersurfaces","version":2},"reference_index":61,"source":"pdf_text","source_observed_at":"2026-08-10T23:59:51.395368Z"},"links":{"cited_paper":"/paper/hep-th/0702063","citing_paper":"/paper/2412.19778"},"observation_digest":"sha256:5286a896c17aff5868046e49445abb875a0a6509124f5d36877cefcb24e30357","observation_id":"20dca3cf-edb4-41fc-950b-07892545cab0","resolution":{"observed_at":"2026-08-10T23:59:51.395368Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2101.10501","last_updated":"2021-05-24T10:59:07Z","snapshot_observed_at":"2026-08-16T18:50:02.596762Z","submitted_at":"2021-01-26T00:51:58Z","title":"Kummer quartic surfaces, strict self-duality, and more","version":2},"cited_work":{"arxiv_id":"2101.10501","doi":"10.48550/arxiv.2101.10501","metadata_source":"pith","pith_arxiv_id":"2101.10501","snapshot_observed_at":"2026-08-11T00:16:15.729268Z","title":"Kummer quartic surfaces, strict self-duality, and more","venue":"math.AG","work_id":"ca49fe74-34f5-4c83-8ebe-d760aff3d432","year":2021},"citing_paper":{"arxiv_id":"2412.19778","last_updated":"2025-03-12T13:38:59Z","snapshot_observed_at":"2026-08-14T15:49:27.555722Z","submitted_at":"2024-12-27T18:19:26Z","title":"Symbolic Approximations to Ricci-flat Metrics Via Extrinsic Symmetries of Calabi-Yau Hypersurfaces","version":2},"reference_index":62,"source":"pdf_text","source_observed_at":"2026-08-10T23:59:51.403342Z"},"links":{"cited_paper":"/paper/2101.10501","citing_paper":"/paper/2412.19778"},"observation_digest":"sha256:8d827fc67c527fb9dd8798f028648d79adb475d4217a628cf449dc802bab1510","observation_id":"24c2ce02-d0b3-4d79-bba3-9bc2facac130","resolution":{"observed_at":"2026-08-10T23:59:51.495904Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T23:59:51.411022Z","title":"IEEE Standard for Floating-Point Arithmetic","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2412.19778","last_updated":"2025-03-12T13:38:59Z","snapshot_observed_at":"2026-08-14T15:49:27.555722Z","submitted_at":"2024-12-27T18:19:26Z","title":"Symbolic Approximations to Ricci-flat Metrics Via Extrinsic Symmetries of Calabi-Yau Hypersurfaces","version":2},"reference_index":63,"source":"pdf_text","source_observed_at":"2026-08-10T23:59:51.411022Z"},"links":{"citing_paper":"/paper/2412.19778"},"observation_digest":"sha256:29c44a8a4aad8b2a91fb931769f18d43e9ff3c1b152c599b8243509f60218369","observation_id":"676d427d-c024-464f-b34a-bbd49c649944","resolution":{"observed_at":"2026-08-10T23:59:51.411022Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T23:59:52.518896Z","title":"Sydney, NSW, Australia: JMLR.org, Aug","venue":null,"work_id":"9fe97d04-2273-47bb-8eb2-509b756a51af","year":2017},"citing_paper":{"arxiv_id":"2412.19778","last_updated":"2025-03-12T13:38:59Z","snapshot_observed_at":"2026-08-14T15:49:27.555722Z","submitted_at":"2024-12-27T18:19:26Z","title":"Symbolic Approximations to Ricci-flat Metrics Via Extrinsic Symmetries of Calabi-Yau Hypersurfaces","version":2},"reference_index":70,"source":"pdf_text","source_observed_at":"2026-08-10T23:59:51.320740Z"},"links":{"citing_paper":"/paper/2412.19778"},"observation_digest":"sha256:0a15afa10be7a97f81df1bfc3ee183e359b73896cc5ac9a7875b471a84e30174","observation_id":"d925d2ff-d4e5-4789-bba9-3b14b5b71cdb","resolution":{"observed_at":"2026-08-10T23:59:52.526927Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T23:59:51.333178Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2412.19778","last_updated":"2025-03-12T13:38:59Z","snapshot_observed_at":"2026-08-14T15:49:27.555722Z","submitted_at":"2024-12-27T18:19:26Z","title":"Symbolic Approximations to Ricci-flat Metrics Via Extrinsic Symmetries of Calabi-Yau Hypersurfaces","version":2},"reference_index":209,"source":"pdf_text","source_observed_at":"2026-08-10T23:59:51.333178Z"},"links":{"citing_paper":"/paper/2412.19778"},"observation_digest":"sha256:595ffdbe666ed364399c1155041ecb0a8ea746be7fe2e6df18b8cf5d59165c32","observation_id":"91f5b70d-4ef2-471f-8c8c-71fef949deb3","resolution":{"observed_at":"2026-08-10T23:59:51.333178Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2412.19778","last_updated":"2025-03-12T13:38:59Z","latest_version":2,"primary_category":"hep-th","snapshot_observed_at":"2026-08-14T15:49:27.555722Z","submitted_at":"2024-12-27T18:19:26Z","title":"Symbolic Approximations to Ricci-flat Metrics Via Extrinsic Symmetries of Calabi-Yau Hypersurfaces"},"reference_resolution":{"displayed":65,"state_counts":{"malformed_identifier":4,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":33,"verified_exact":8,"verified_fuzzy":20},"total_outbound_references":65},"refusal":"A citation records a reference. It does not transfer a finding from one paper to another.","schema":"pith.paper-citation-record.v1","standing_sources":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"thesis":"As of 18 August 2026, this Paper Citation Record lists 65 of 65 outbound references and 4 inbound Pith citation observations for arXiv:2412.19778."}