{"as_of":"2026-08-15T19:12:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:79fcde6526e358605c4a07e6ae95c12451f805a8ff09c7f98bf2c81e1eb32066","coverage":[{"denominator":10,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":10,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-01T16:24:29.463424Z","state":"measured"},{"denominator":10,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":10,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-15T06:32:42.880941+00:00","state":"measured"},{"denominator":0,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":0,"source":"paper_references, paper_reference_links","source_observed_at":null,"state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"cited_works","source_observed_at":null,"state":"measured"}],"external_citation_measurements":[],"inbound":[],"links":{"evidence":"/evidence","html":"/paper/2607.18012/citation-record","integrity":"/paper/2607.18012/integrity","json":"/paper/2607.18012/citation-record.json","paper":"/paper/2607.18012"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T16:24:28.653650Z","title":"A practical algorithm for the determination of phase from image and diffraction plane pic- tures,","venue":null,"work_id":null,"year":1972},"citing_paper":{"arxiv_id":"2607.18012","last_updated":"2026-07-22T01:18:40Z","snapshot_observed_at":"2026-08-07T15:08:37.884216Z","submitted_at":"2026-07-20T14:45:55Z","title":"Physics-Informed Neural Networks for Optimal Beam Shaping in Flat Optics","version":2},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-01T16:24:28.653650Z"},"links":{"citing_paper":"/paper/2607.18012"},"observation_digest":"sha256:45a283f1a106ec9a0e4ae997a69285e314baabdd8545bc20d9a4d2594daf4576","observation_id":"57c4654d-2ba4-4bef-8be7-443f25443d03","resolution":{"observed_at":"2026-08-01T16:24:28.653650Z","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":"2026-08-01T16:24:28.726573Z","title":"Design and simulation of structured beams using phase profiles,","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.18012","last_updated":"2026-07-22T01:18:40Z","snapshot_observed_at":"2026-08-07T15:08:37.884216Z","submitted_at":"2026-07-20T14:45:55Z","title":"Physics-Informed Neural Networks for Optimal Beam Shaping in Flat Optics","version":2},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-01T16:24:28.726573Z"},"links":{"citing_paper":"/paper/2607.18012"},"observation_digest":"sha256:9e48eee4fd2a0c12ba0fac735d62aabff4b78b1eb11f9f78f998729c7acc7ba0","observation_id":"7b9b30a8-d1f8-4fb8-8c86-51e9c9866f2f","resolution":{"observed_at":"2026-08-01T16:24:28.726573Z","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":"2026-08-01T16:24:28.790396Z","title":null,"venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2607.18012","last_updated":"2026-07-22T01:18:40Z","snapshot_observed_at":"2026-08-07T15:08:37.884216Z","submitted_at":"2026-07-20T14:45:55Z","title":"Physics-Informed Neural Networks for Optimal Beam Shaping in Flat Optics","version":2},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-01T16:24:28.790396Z"},"links":{"citing_paper":"/paper/2607.18012"},"observation_digest":"sha256:c301091f76534f2c08f6c0d3dbb2be53ab5da537e04eb21d938265479812002b","observation_id":"250c81ff-f0af-4585-9e0b-213009ce8006","resolution":{"observed_at":"2026-08-01T16:24:28.790396Z","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":"2026-08-01T16:24:28.918812Z","title":"Physics- informed neural networks: A deep learning framework for solv- ing forward and inverse problems involving nonlinear partial differential equations,","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2607.18012","last_updated":"2026-07-22T01:18:40Z","snapshot_observed_at":"2026-08-07T15:08:37.884216Z","submitted_at":"2026-07-20T14:45:55Z","title":"Physics-Informed Neural Networks for Optimal Beam Shaping in Flat Optics","version":2},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-01T16:24:28.918812Z"},"links":{"citing_paper":"/paper/2607.18012"},"observation_digest":"sha256:a766797cff910f726f651ab148c78f20aad637a79bc1381c0b2c8eb3fd6fbd96","observation_id":"13225c23-c64f-4789-a604-1bc643c28434","resolution":{"observed_at":"2026-08-01T16:24:28.918812Z","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":"2026-08-01T16:24:29.001477Z","title":"Physics-informed neural networks for inverse problems in nano-optics and metamaterials,","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2607.18012","last_updated":"2026-07-22T01:18:40Z","snapshot_observed_at":"2026-08-07T15:08:37.884216Z","submitted_at":"2026-07-20T14:45:55Z","title":"Physics-Informed Neural Networks for Optimal Beam Shaping in Flat Optics","version":2},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-01T16:24:29.001477Z"},"links":{"citing_paper":"/paper/2607.18012"},"observation_digest":"sha256:4f322629f95b843b0d7c09471b41322a2fc4d216fe11fb9d45eb487cbf9befb4","observation_id":"a62596bf-5a4f-4cf9-86d0-811269c6c8c3","resolution":{"observed_at":"2026-08-01T16:24:29.001477Z","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":"10.1117/12.3027738","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Cylindrically-symmetric collimated beam shaping using non- imaging metasurfaces,","venue":null,"work_id":"8cf21fc2-5e49-4123-ba5e-f9e2e1fadde7","year":2024},"citing_paper":{"arxiv_id":"2607.18012","last_updated":"2026-07-22T01:18:40Z","snapshot_observed_at":"2026-08-07T15:08:37.884216Z","submitted_at":"2026-07-20T14:45:55Z","title":"Physics-Informed Neural Networks for Optimal Beam Shaping in Flat Optics","version":2},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-01T16:24:29.036268Z"},"links":{"citing_paper":"/paper/2607.18012"},"observation_digest":"sha256:be3caf3854c0cff9c611496f293d82b484c259c386cd4377788398cac4298e48","observation_id":"761c445b-3409-40f8-b44e-0e0e1541f05b","resolution":{"observed_at":"2026-08-01T16:28:37.795857Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1364/oe.559542","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Experimental demonstration of a beam shaping non- imaging metasurface,","venue":"Optics Express","work_id":"25da0328-b1d9-4339-9324-62f8263bd04d","year":2025},"citing_paper":{"arxiv_id":"2607.18012","last_updated":"2026-07-22T01:18:40Z","snapshot_observed_at":"2026-08-07T15:08:37.884216Z","submitted_at":"2026-07-20T14:45:55Z","title":"Physics-Informed Neural Networks for Optimal Beam Shaping in Flat Optics","version":2},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-01T16:24:29.145367Z"},"links":{"citing_paper":"/paper/2607.18012"},"observation_digest":"sha256:72ef57b0bd725c64ba28c022b9e59bd4547b18f4d00514036238675faac65a6e","observation_id":"64d1f9f2-1d19-41fb-951a-8bb9e88eb801","resolution":{"observed_at":"2026-08-01T16:28:37.560913Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-01T16:24:29.285425Z","title":"Light propagation with phase discon- tinuities: generalized laws of reflection and refraction,","venue":null,"work_id":null,"year":2011},"citing_paper":{"arxiv_id":"2607.18012","last_updated":"2026-07-22T01:18:40Z","snapshot_observed_at":"2026-08-07T15:08:37.884216Z","submitted_at":"2026-07-20T14:45:55Z","title":"Physics-Informed Neural Networks for Optimal Beam Shaping in Flat Optics","version":2},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-01T16:24:29.285425Z"},"links":{"citing_paper":"/paper/2607.18012"},"observation_digest":"sha256:a1f73591fc4cb7069cdaa2d12a2234de5c784e720c4c494341e4ccc719252e51","observation_id":"c8ecca8f-128d-4677-93ff-0812d8d6248b","resolution":{"observed_at":"2026-08-01T16:24:29.285425Z","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":"10.5281/zenodo.6147771","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"diffractsim: A flex- ible Python diffraction simulator,","venue":"Zenodo (CERN European Organization for Nuclear Research)","work_id":"e365d18b-e150-4a9b-a158-b39149e37555","year":2022},"citing_paper":{"arxiv_id":"2607.18012","last_updated":"2026-07-22T01:18:40Z","snapshot_observed_at":"2026-08-07T15:08:37.884216Z","submitted_at":"2026-07-20T14:45:55Z","title":"Physics-Informed Neural Networks for Optimal Beam Shaping in Flat Optics","version":2},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-01T16:24:29.397172Z"},"links":{"citing_paper":"/paper/2607.18012"},"observation_digest":"sha256:07fd749cb72ef2122bb5aaaa05fde6f53045fd3f918229eb58679cc5a6ecdf14","observation_id":"2d165eb3-fb75-45e8-8b47-0ad1fd12930f","resolution":{"observed_at":"2026-08-01T16:28:37.272351Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1506.02025","last_updated":"2016-02-04T18:08:46Z","snapshot_observed_at":"2026-08-15T13:44:02.183786Z","submitted_at":"2015-06-05T19:54:26Z","title":"Spatial Transformer Networks","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1506.02025","snapshot_observed_at":"2026-08-01T16:24:29.463424Z","title":"Spatial Transformer Networks,","venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2607.18012","last_updated":"2026-07-22T01:18:40Z","snapshot_observed_at":"2026-08-07T15:08:37.884216Z","submitted_at":"2026-07-20T14:45:55Z","title":"Physics-Informed Neural Networks for Optimal Beam Shaping in Flat Optics","version":2},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-01T16:24:29.463424Z"},"links":{"cited_paper":"/paper/1506.02025","citing_paper":"/paper/2607.18012"},"observation_digest":"sha256:948a076cfb26fc60ece9a882ff1af4bcbd5cdaa87c19dcfdcc17fde97c1c5fc0","observation_id":"50604cb4-bac1-454f-b264-ee419d087fa5","resolution":{"observed_at":"2026-08-01T16:24:29.463424Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2607.18012","last_updated":"2026-07-22T01:18:40Z","latest_version":2,"primary_category":"physics.optics","snapshot_observed_at":"2026-08-07T15:08:37.884216Z","submitted_at":"2026-07-20T14:45:55Z","title":"Physics-Informed Neural Networks for Optimal Beam Shaping in Flat Optics"},"reference_resolution":{"displayed":10,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":7,"verified_exact":3,"verified_fuzzy":0},"total_outbound_references":10},"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":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"thesis":"As of 15 August 2026, this Paper Citation Record lists 10 of 10 outbound references and 0 inbound Pith citation observations for arXiv:2607.18012."}