{"as_of":"2026-08-18T18:33:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:fb8c92c0121da3c3d76d790eed08cecfcf6eb1c3d2549f8fa4237cf948189dbf","coverage":[{"denominator":29,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":29,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-05T11:58:17.861583Z","state":"measured"},{"denominator":30,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":30,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-18T06:34:40.430872+00:00","state":"measured"},{"denominator":1,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":1,"source":"paper_references, paper_reference_links","source_observed_at":"2026-06-26T20:41:53.557398Z","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":"2026-07-04T01:09:18.818026Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2509.02211","last_updated":"2025-09-03T09:34:57Z","snapshot_observed_at":"2026-08-13T16:49:25.688844Z","submitted_at":"2025-09-02T11:27:25Z","title":"Invariants in Linear Optics","version":2},"cited_work":{"arxiv_id":"2509.02211","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2509.02211","snapshot_observed_at":"2026-07-04T01:09:18.818026Z","title":"Draux, S","venue":null,"work_id":"eb0494ea-b034-431e-9ec1-c7c407c7653c","year":2025},"citing_paper":{"arxiv_id":"2606.19470","last_updated":"2026-06-17T18:04:29Z","snapshot_observed_at":"2026-08-08T02:01:46.824058Z","submitted_at":"2026-06-17T18:04:29Z","title":"Local controllability of heralded quantum linear optics","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-06-26T20:41:53.557398Z"},"links":{"cited_paper":"/paper/2509.02211","citing_paper":"/paper/2606.19470"},"observation_digest":"sha256:bbf4b0b980479d6e5421e2c1abaaf45f7597f032e17a851f772116aa74612d8c","observation_id":"39d9d543-6280-4a9f-ad18-2e38f6bbdd56","resolution":{"observed_at":"2026-07-04T01:09:18.819653Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}}],"links":{"evidence":"/evidence","html":"/paper/2509.02211/citation-record","integrity":"/paper/2509.02211/integrity","json":"/paper/2509.02211/citation-record.json","paper":"/paper/2509.02211"},"outbound":[{"citation":{"cited_paper":{"arxiv_id":"quant-ph/0512071","last_updated":"2006-03-14T11:41:15Z","snapshot_observed_at":"2026-08-09T13:37:55.928772Z","submitted_at":"2005-12-09T11:59:00Z","title":"Review article: Linear optical quantum computing","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"quant-ph/0512071","snapshot_observed_at":"2026-08-05T11:58:15.753949Z","title":"Linear optical quantum computing,","venue":null,"work_id":null,"year":2007},"citing_paper":{"arxiv_id":"2509.02211","last_updated":"2025-09-03T09:34:57Z","snapshot_observed_at":"2026-08-13T16:49:25.688844Z","submitted_at":"2025-09-02T11:27:25Z","title":"Invariants in Linear Optics","version":2},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-05T11:58:15.753949Z"},"links":{"cited_paper":"/paper/quant-ph/0512071","citing_paper":"/paper/2509.02211"},"observation_digest":"sha256:fde4ad744ae9568523e1b170e2ed7868a56709d9e109cf0cf87d50d1adb598e7","observation_id":"31f07d62-ece8-4b49-90e6-7761e70a9acb","resolution":{"observed_at":"2026-08-05T11:58:15.753949Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2409.08229","last_updated":"2024-09-12T17:16:38Z","snapshot_observed_at":"2026-08-17T01:44:36.954668Z","submitted_at":"2024-09-12T17:16:38Z","title":"Photonic Quantum Computers","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2409.08229","snapshot_observed_at":"2026-08-05T11:58:15.816838Z","title":"Photonic quantum computers,","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2509.02211","last_updated":"2025-09-03T09:34:57Z","snapshot_observed_at":"2026-08-13T16:49:25.688844Z","submitted_at":"2025-09-02T11:27:25Z","title":"Invariants in Linear Optics","version":2},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-05T11:58:15.816838Z"},"links":{"cited_paper":"/paper/2409.08229","citing_paper":"/paper/2509.02211"},"observation_digest":"sha256:b906dd997af4e85d3d52846dad84377700397f35f03464436499ab4a3614fbad","observation_id":"a95e9604-13f9-495e-adca-6bb306d2baf8","resolution":{"observed_at":"2026-08-05T11:58:15.816838Z","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":"2026-08-05T11:58:22.657648Z","title":"A spin-optical quantum computing architecture,","venue":null,"work_id":"dbd3ec7d-8783-4d70-9bf9-25a73ac65f82","year":2024},"citing_paper":{"arxiv_id":"2509.02211","last_updated":"2025-09-03T09:34:57Z","snapshot_observed_at":"2026-08-13T16:49:25.688844Z","submitted_at":"2025-09-02T11:27:25Z","title":"Invariants in Linear Optics","version":2},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-05T11:58:15.876016Z"},"links":{"citing_paper":"/paper/2509.02211"},"observation_digest":"sha256:a2eaf08849e0037aa0b2a75d91ad2c2733ae113e49f46de70f3bbff210408c6c","observation_id":"2b280e96-067a-4d14-8719-7a9ddda0dd74","resolution":{"observed_at":"2026-08-05T11:58:22.662646Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-05T11:58:15.931044Z","title":"Enhanced fault-tolerance in photonic quantum computing: Floquet code outperforms surface code in tailored architecture,","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2509.02211","last_updated":"2025-09-03T09:34:57Z","snapshot_observed_at":"2026-08-13T16:49:25.688844Z","submitted_at":"2025-09-02T11:27:25Z","title":"Invariants in Linear Optics","version":2},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-05T11:58:15.931044Z"},"links":{"citing_paper":"/paper/2509.02211"},"observation_digest":"sha256:4cd222b28da45c8211906059e2602fab773a9bce678326baed3b50db01d74c50","observation_id":"22daaa3f-a021-4119-a665-802b7ef68f1d","resolution":{"observed_at":"2026-08-05T11:58:15.931044Z","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":"2026-08-05T11:58:22.642237Z","title":"Fusion-based quantum computation,","venue":null,"work_id":"ff6ad812-f634-44f4-a97f-66aa090c6b7e","year":2023},"citing_paper":{"arxiv_id":"2509.02211","last_updated":"2025-09-03T09:34:57Z","snapshot_observed_at":"2026-08-13T16:49:25.688844Z","submitted_at":"2025-09-02T11:27:25Z","title":"Invariants in Linear Optics","version":2},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-05T11:58:16.020452Z"},"links":{"citing_paper":"/paper/2509.02211"},"observation_digest":"sha256:14fdfa51e86bcbc4415398f82b7e420df59650345f5d33440e00ee3dbd52598d","observation_id":"439e46f2-ac1d-4654-a2e6-fdae6ff9c87a","resolution":{"observed_at":"2026-08-05T11:58:22.647231Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-05T11:58:22.625857Z","title":"Re- cent progress in quantum photonic chips for quantum communication and internet,","venue":null,"work_id":"d6204680-610c-482e-a7c9-ea697dce259c","year":2023},"citing_paper":{"arxiv_id":"2509.02211","last_updated":"2025-09-03T09:34:57Z","snapshot_observed_at":"2026-08-13T16:49:25.688844Z","submitted_at":"2025-09-02T11:27:25Z","title":"Invariants in Linear Optics","version":2},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-05T11:58:16.078786Z"},"links":{"citing_paper":"/paper/2509.02211"},"observation_digest":"sha256:83a44bc64362339e43987101b880253efaf41978f65ac7ec965405645ddfebc7","observation_id":"8b1dc053-4c55-4685-ae18-f9f8f8c95424","resolution":{"observed_at":"2026-08-05T11:58:22.631086Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-05T11:58:22.544680Z","title":"A versatile single- photon-based quantum computing platform,","venue":null,"work_id":"f61191dc-f138-4f8a-a781-98c5b5279667","year":2024},"citing_paper":{"arxiv_id":"2509.02211","last_updated":"2025-09-03T09:34:57Z","snapshot_observed_at":"2026-08-13T16:49:25.688844Z","submitted_at":"2025-09-02T11:27:25Z","title":"Invariants in Linear Optics","version":2},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-05T11:58:16.123991Z"},"links":{"citing_paper":"/paper/2509.02211"},"observation_digest":"sha256:e7fdd8f077d4091599136d79df69703c03e6cad25ad58f270435250f8c683a1d","observation_id":"5a8a24a5-a5aa-455c-ac95-1b07f985de5f","resolution":{"observed_at":"2026-08-05T11:58:22.614484Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-05T11:58:22.263734Z","title":"A scheme for efficient quantum computation with linear optics,","venue":null,"work_id":"9815acfb-17ac-4fc5-abce-658dff273a1d","year":2001},"citing_paper":{"arxiv_id":"2509.02211","last_updated":"2025-09-03T09:34:57Z","snapshot_observed_at":"2026-08-13T16:49:25.688844Z","submitted_at":"2025-09-02T11:27:25Z","title":"Invariants in Linear Optics","version":2},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-05T11:58:16.208963Z"},"links":{"citing_paper":"/paper/2509.02211"},"observation_digest":"sha256:d27d99e0131163c34c9b3e0028357eff10897fc68cd3a746886ec3b61e1d8c81","observation_id":"7c5e306f-79f0-4b3d-8116-4dcff821941a","resolution":{"observed_at":"2026-08-05T11:58:22.366904Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-05T11:58:22.050342Z","title":"Quantum gates using linear optics and postselection,","venue":null,"work_id":"b62e51e0-6800-4c55-8c27-3b8489cc67c6","year":2002},"citing_paper":{"arxiv_id":"2509.02211","last_updated":"2025-09-03T09:34:57Z","snapshot_observed_at":"2026-08-13T16:49:25.688844Z","submitted_at":"2025-09-02T11:27:25Z","title":"Invariants in Linear Optics","version":2},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-05T11:58:16.293799Z"},"links":{"citing_paper":"/paper/2509.02211"},"observation_digest":"sha256:3c9b5f82537641cfac48ed39b1628b1b0e723f09f950f34cfac27f014dfb22ae","observation_id":"293d845e-ffe7-47e3-b4c5-223c3a08889d","resolution":{"observed_at":"2026-08-05T11:58:22.133413Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-05T11:58:21.850431Z","title":"Efficient toffoli gates using qudits,","venue":null,"work_id":"5278c1d1-af87-4a4f-a761-82a095e604a6","year":2007},"citing_paper":{"arxiv_id":"2509.02211","last_updated":"2025-09-03T09:34:57Z","snapshot_observed_at":"2026-08-13T16:49:25.688844Z","submitted_at":"2025-09-02T11:27:25Z","title":"Invariants in Linear Optics","version":2},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-05T11:58:16.368442Z"},"links":{"citing_paper":"/paper/2509.02211"},"observation_digest":"sha256:c6ccd0cfc65bc545e3229f49b0c8b21a745536cd21c2fd6d1249e5e7a057e567","observation_id":"71602663-0e87-4099-84b2-cc12a02916f4","resolution":{"observed_at":"2026-08-05T11:58:21.909916Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1901.06178","last_updated":"2023-09-29T13:59:07Z","snapshot_observed_at":"2026-08-16T07:47:44.248870Z","submitted_at":"2019-01-18T11:00:52Z","title":"A method to determine which quantum operations can be realized with linear optics with a constructive implementation recipe","version":3},"cited_work":{"arxiv_id":"1901.06178","doi":null,"metadata_source":"pith","pith_arxiv_id":"1901.06178","snapshot_observed_at":"2026-08-05T11:58:18.123233Z","title":"A method to determine which quantum operations can be realized with linear optics with a constructive implementation recipe","venue":"quant-ph","work_id":"651983b4-067b-40b4-a52d-c99adc1d72d9","year":2019},"citing_paper":{"arxiv_id":"2509.02211","last_updated":"2025-09-03T09:34:57Z","snapshot_observed_at":"2026-08-13T16:49:25.688844Z","submitted_at":"2025-09-02T11:27:25Z","title":"Invariants in Linear Optics","version":2},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-05T11:58:16.473875Z"},"links":{"cited_paper":"/paper/1901.06178","citing_paper":"/paper/2509.02211"},"observation_digest":"sha256:4f60f5e6dc1414810b520a499f1163250537eeb4dca395ca2e6ba44d0fd89f7f","observation_id":"dc5afd0d-522d-4851-b8e9-d0dc83ce120e","resolution":{"observed_at":"2026-08-05T11:58:18.217986Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-05T11:58:21.500153Z","title":"Linear optics quantum computing - con- struction of small networks and asymptotic scaling,","venue":null,"work_id":"37fb9edc-0c38-416c-a236-9e7cc0eca2f3","year":null},"citing_paper":{"arxiv_id":"2509.02211","last_updated":"2025-09-03T09:34:57Z","snapshot_observed_at":"2026-08-13T16:49:25.688844Z","submitted_at":"2025-09-02T11:27:25Z","title":"Invariants in Linear Optics","version":2},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-05T11:58:16.547213Z"},"links":{"citing_paper":"/paper/2509.02211"},"observation_digest":"sha256:d7a8ec2e6c2dc001a0edc87cb074bbd84c09510d9399da1eb4087c0f564c0d81","observation_id":"888e2425-72d7-450c-85e8-a3f77733527f","resolution":{"observed_at":"2026-08-05T11:58:21.685770Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-05T11:58:20.852967Z","title":"Simple rules for two-photon state preparation with linear optics,","venue":null,"work_id":"03cffea4-373a-4e9a-893d-16faecd81692","year":2024},"citing_paper":{"arxiv_id":"2509.02211","last_updated":"2025-09-03T09:34:57Z","snapshot_observed_at":"2026-08-13T16:49:25.688844Z","submitted_at":"2025-09-02T11:27:25Z","title":"Invariants in Linear Optics","version":2},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-05T11:58:16.693201Z"},"links":{"citing_paper":"/paper/2509.02211"},"observation_digest":"sha256:47176d6f2b01bcbdd516fd08173e2e13b7bb10629f3845213f08fafcda0e2922","observation_id":"34dfa715-9009-4f8c-aed9-5d45483bbdbe","resolution":{"observed_at":"2026-08-05T11:58:20.988247Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-05T11:58:20.584581Z","title":"No-go theorems for photon state transformations in quantum linear optics,","venue":null,"work_id":"c4853596-3bc6-4f14-9e3e-5ee03283a51e","year":2023},"citing_paper":{"arxiv_id":"2509.02211","last_updated":"2025-09-03T09:34:57Z","snapshot_observed_at":"2026-08-13T16:49:25.688844Z","submitted_at":"2025-09-02T11:27:25Z","title":"Invariants in Linear Optics","version":2},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-05T11:58:16.737276Z"},"links":{"citing_paper":"/paper/2509.02211"},"observation_digest":"sha256:d4e8055ecd5bef1ba3eb4d9938452c80022982501a9654b1e752b78709dd97ad","observation_id":"3ac2f2da-a44a-4f06-aa99-22409fa9b238","resolution":{"observed_at":"2026-08-05T11:58:20.693389Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1007/978-3-211-77417-5","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T05:30:23.456663Z","title":"Sturmfels, Algorithms in Invariant Theory , ser","venue":"Texts & monographs in symbolic computation/Texts and monographs in symbolic computation","work_id":"15d5f39a-6021-4d79-9cdb-175e4982ea97","year":2008},"citing_paper":{"arxiv_id":"2509.02211","last_updated":"2025-09-03T09:34:57Z","snapshot_observed_at":"2026-08-13T16:49:25.688844Z","submitted_at":"2025-09-02T11:27:25Z","title":"Invariants in Linear Optics","version":2},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-05T11:58:16.844622Z"},"links":{"citing_paper":"/paper/2509.02211"},"observation_digest":"sha256:60318f95e9c996d48b0281fb4ac5aa0f0ea7f2c9e3eceddbfb982cc107521936","observation_id":"6762ccd1-9a85-4080-9848-69e4c2184913","resolution":{"observed_at":"2026-08-05T11:58:18.045628Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-05T11:58:20.315883Z","title":"An introduction to invariants and moduli,","venue":null,"work_id":"e73476a6-bf5b-4b70-815e-a772ac5965a1","year":2003},"citing_paper":{"arxiv_id":"2509.02211","last_updated":"2025-09-03T09:34:57Z","snapshot_observed_at":"2026-08-13T16:49:25.688844Z","submitted_at":"2025-09-02T11:27:25Z","title":"Invariants in Linear Optics","version":2},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-05T11:58:16.959362Z"},"links":{"citing_paper":"/paper/2509.02211"},"observation_digest":"sha256:3022d142c91f28f7d00db0db776ac9bd68071ba3ae9de6160e25fef736dbe881","observation_id":"d4282e34-8b90-4a90-ae3a-f67d474fe267","resolution":{"observed_at":"2026-08-05T11:58:20.425928Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-05T11:58:17.023396Z","title":"Derksen and G","venue":null,"work_id":null,"year":2015},"citing_paper":{"arxiv_id":"2509.02211","last_updated":"2025-09-03T09:34:57Z","snapshot_observed_at":"2026-08-13T16:49:25.688844Z","submitted_at":"2025-09-02T11:27:25Z","title":"Invariants in Linear Optics","version":2},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-05T11:58:17.023396Z"},"links":{"citing_paper":"/paper/2509.02211"},"observation_digest":"sha256:24eae2d1f8bc94dddfa7c9bd07062f4f1f83a72f0ae439dde3d2169d3672b4af","observation_id":"91dab127-2334-404d-ad68-afb3086f8795","resolution":{"observed_at":"2026-08-05T11:58:17.023396Z","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":"2026-08-05T11:58:20.002479Z","title":"Dolgachev, Lectures on Invariant Theory , ser","venue":null,"work_id":"77c5ae08-52d0-4c02-b652-8f00b20c22a2","year":2003},"citing_paper":{"arxiv_id":"2509.02211","last_updated":"2025-09-03T09:34:57Z","snapshot_observed_at":"2026-08-13T16:49:25.688844Z","submitted_at":"2025-09-02T11:27:25Z","title":"Invariants in Linear Optics","version":2},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-05T11:58:17.134358Z"},"links":{"citing_paper":"/paper/2509.02211"},"observation_digest":"sha256:e40da6d17ed7ba3d57ecf1083406413a9321d600518438aef508a8f3cb390b13","observation_id":"770a2f5e-825c-49a2-89a3-dd0bc9797814","resolution":{"observed_at":"2026-08-05T11:58:20.124171Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-05T11:58:17.209249Z","title":null,"venue":null,"work_id":null,"year":2007},"citing_paper":{"arxiv_id":"2509.02211","last_updated":"2025-09-03T09:34:57Z","snapshot_observed_at":"2026-08-13T16:49:25.688844Z","submitted_at":"2025-09-02T11:27:25Z","title":"Invariants in Linear Optics","version":2},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-05T11:58:17.209249Z"},"links":{"citing_paper":"/paper/2509.02211"},"observation_digest":"sha256:c01817af23eac6f10d5d615a8f35d22489efd732207fb1950ca07cb4aa80ec70","observation_id":"ba167999-336a-4e75-ac3c-57640e83b0cf","resolution":{"observed_at":"2026-08-05T11:58:17.209249Z","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":"2026-08-05T11:58:19.847873Z","title":"Integration with respect to the haar measure on unitary, orthogonal and symplectic group,","venue":null,"work_id":"8f643c95-93c7-4ccd-a2f5-4281b1322d0a","year":2006},"citing_paper":{"arxiv_id":"2509.02211","last_updated":"2025-09-03T09:34:57Z","snapshot_observed_at":"2026-08-13T16:49:25.688844Z","submitted_at":"2025-09-02T11:27:25Z","title":"Invariants in Linear Optics","version":2},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-05T11:58:17.246718Z"},"links":{"citing_paper":"/paper/2509.02211"},"observation_digest":"sha256:d947ef5107fc360a1619921a07507b6f058a781fcc329833122e61eb03c5e3de","observation_id":"69cdf256-fadf-4d04-a05c-76abf40a425a","resolution":{"observed_at":"2026-08-05T11:58:19.941018Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-05T11:58:19.598043Z","title":"Ueber die theorie der algebraischen formen,","venue":null,"work_id":"3bcd3188-a0de-4b20-bd7f-4388c80c2c35","year":null},"citing_paper":{"arxiv_id":"2509.02211","last_updated":"2025-09-03T09:34:57Z","snapshot_observed_at":"2026-08-13T16:49:25.688844Z","submitted_at":"2025-09-02T11:27:25Z","title":"Invariants in Linear Optics","version":2},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-05T11:58:17.336040Z"},"links":{"citing_paper":"/paper/2509.02211"},"observation_digest":"sha256:dc508917ac5bd8f0a928741ca65284257e09fcef65746386c00294159096d9c2","observation_id":"48d2e68b-2e45-4810-b53d-0d25661ea3d8","resolution":{"observed_at":"2026-08-05T11:58:19.739966Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-05T11:58:19.426121Z","title":"The noether number in invariant theory","venue":null,"work_id":"621eb0b9-d336-4990-9e53-c382ff8954b2","year":null},"citing_paper":{"arxiv_id":"2509.02211","last_updated":"2025-09-03T09:34:57Z","snapshot_observed_at":"2026-08-13T16:49:25.688844Z","submitted_at":"2025-09-02T11:27:25Z","title":"Invariants in Linear Optics","version":2},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-05T11:58:17.449173Z"},"links":{"citing_paper":"/paper/2509.02211"},"observation_digest":"sha256:f17e43e84b8d9c9f0971db186639c8110971ebf056847c023e2e2261807ca953","observation_id":"61c1e468-7ebb-4af7-bcd9-f8dccf42e941","resolution":{"observed_at":"2026-08-05T11:58:19.495350Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-05T11:58:19.229434Z","title":"Polynomial bounds for rings of invariants,","venue":null,"work_id":"72ae2047-d3be-47ec-b3fd-f8e1d0e71219","year":2001},"citing_paper":{"arxiv_id":"2509.02211","last_updated":"2025-09-03T09:34:57Z","snapshot_observed_at":"2026-08-13T16:49:25.688844Z","submitted_at":"2025-09-02T11:27:25Z","title":"Invariants in Linear Optics","version":2},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-05T11:58:17.549448Z"},"links":{"citing_paper":"/paper/2509.02211"},"observation_digest":"sha256:dbc88f499587302f68b7e3fec81a8a9d5dd9b7ebcfbebe595939ebc5b3f71c15","observation_id":"206b33d7-cb52-44b5-8a5f-f9768309c31f","resolution":{"observed_at":"2026-08-05T11:58:19.325569Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-05T11:58:18.997347Z","title":"On the castelnuovo-mumford regularity of rings of polynomial invariants,","venue":null,"work_id":"f10425d0-ff85-48fd-a234-3d6020567523","year":2011},"citing_paper":{"arxiv_id":"2509.02211","last_updated":"2025-09-03T09:34:57Z","snapshot_observed_at":"2026-08-13T16:49:25.688844Z","submitted_at":"2025-09-02T11:27:25Z","title":"Invariants in Linear Optics","version":2},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-05T11:58:17.593835Z"},"links":{"citing_paper":"/paper/2509.02211"},"observation_digest":"sha256:a245762ced08c5a01288034af2b578f8080a2e9645342cd3383496a8fc795016","observation_id":"708bc73e-e6ff-4ed9-9dca-43b488a6757d","resolution":{"observed_at":"2026-08-05T11:58:19.141928Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-05T11:58:18.867015Z","title":"Molien, ¨Uber die Invarianten der linearen Substitutionsgruppen , ser","venue":null,"work_id":"c6081eda-ec20-489a-a44c-085a23513f28","year":null},"citing_paper":{"arxiv_id":"2509.02211","last_updated":"2025-09-03T09:34:57Z","snapshot_observed_at":"2026-08-13T16:49:25.688844Z","submitted_at":"2025-09-02T11:27:25Z","title":"Invariants in Linear Optics","version":2},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-05T11:58:17.656408Z"},"links":{"citing_paper":"/paper/2509.02211"},"observation_digest":"sha256:e7e8a7ba7ad09482fb1f915d71caf73442decbe017833c8677374afd4ae8ca00","observation_id":"c7a82ffe-832f-4f31-8029-73c72836d678","resolution":{"observed_at":"2026-08-05T11:58:18.911376Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-05T11:58:18.726103Z","title":"Invariant polynomials and molien functions,","venue":null,"work_id":"9982d185-3640-4716-8e1c-a909ffe4b23c","year":1998},"citing_paper":{"arxiv_id":"2509.02211","last_updated":"2025-09-03T09:34:57Z","snapshot_observed_at":"2026-08-13T16:49:25.688844Z","submitted_at":"2025-09-02T11:27:25Z","title":"Invariants in Linear Optics","version":2},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-05T11:58:17.733084Z"},"links":{"citing_paper":"/paper/2509.02211"},"observation_digest":"sha256:d54cd7049f405da67eac72aaeebaeeae6f3f9330a3536b79fe3ed4e8984bbb60","observation_id":"5f385b97-b362-44b6-8cbc-f25112817779","resolution":{"observed_at":"2026-08-05T11:58:18.788964Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-05T11:58:18.557883Z","title":null,"venue":null,"work_id":"aa1ed156-ffa7-4110-b829-00ee16f339c0","year":1985},"citing_paper":{"arxiv_id":"2509.02211","last_updated":"2025-09-03T09:34:57Z","snapshot_observed_at":"2026-08-13T16:49:25.688844Z","submitted_at":"2025-09-02T11:27:25Z","title":"Invariants in Linear Optics","version":2},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-05T11:58:17.807190Z"},"links":{"citing_paper":"/paper/2509.02211"},"observation_digest":"sha256:e14a1e1e105ca830c4f4120d7d0b2f1ddeec820b00b0b4470b4d890919983950","observation_id":"f3fef21f-148a-4380-8e92-7a5747177ac5","resolution":{"observed_at":"2026-08-05T11:58:18.658596Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-05T11:58:18.449286Z","title":null,"venue":null,"work_id":"ef9e7195-ebfd-4cf8-8779-ef95e4ac7159","year":2015},"citing_paper":{"arxiv_id":"2509.02211","last_updated":"2025-09-03T09:34:57Z","snapshot_observed_at":"2026-08-13T16:49:25.688844Z","submitted_at":"2025-09-02T11:27:25Z","title":"Invariants in Linear Optics","version":2},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-05T11:58:17.861583Z"},"links":{"citing_paper":"/paper/2509.02211"},"observation_digest":"sha256:8d3ff290c922059f9eac62dfd753d21dfa1a387d1b6878f2a45013899cbf6c9b","observation_id":"ddc30dde-77a5-4023-a96d-dde12e560af9","resolution":{"observed_at":"2026-08-05T11:58:18.497759Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-05T11:58:21.225354Z","title":"Available: https://www.semanticscholar.org/ paper/Linear-optics-quantum-computing-construction-of-and-Kieling/ 11490cfeb0c2f5efca748d836c2c6f2f025540a3","venue":null,"work_id":"f08d29a4-29ef-4c7c-8ef5-4b3cb39c0562","year":null},"citing_paper":{"arxiv_id":"2509.02211","last_updated":"2025-09-03T09:34:57Z","snapshot_observed_at":"2026-08-13T16:49:25.688844Z","submitted_at":"2025-09-02T11:27:25Z","title":"Invariants in Linear Optics","version":2},"reference_index":2008,"source":"pdf_text","source_observed_at":"2026-08-05T11:58:16.634465Z"},"links":{"citing_paper":"/paper/2509.02211"},"observation_digest":"sha256:236f81ff86a3499e2ab56a440f7b29b93f930a21f4d67c5e47e3e443830ae5b6","observation_id":"22057744-2afa-4225-97b0-b4b791cb5f9d","resolution":{"observed_at":"2026-08-05T11:58:21.332705Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2509.02211","last_updated":"2025-09-03T09:34:57Z","latest_version":2,"primary_category":"quant-ph","snapshot_observed_at":"2026-08-13T16:49:25.688844Z","submitted_at":"2025-09-02T11:27:25Z","title":"Invariants in Linear Optics"},"reference_resolution":{"displayed":29,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":7,"verified_exact":2,"verified_fuzzy":20},"total_outbound_references":29},"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":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"thesis":"As of 18 August 2026, this Paper Citation Record lists 29 of 29 outbound references and 1 inbound Pith citation observation for arXiv:2509.02211."}