{"as_of":"2026-08-14T00:11:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:b9854960ca4111a2db8ef9551b294da048dec271fb04a95ec402ee4eabe84576","coverage":[{"denominator":46,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":46,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-08T19:20:22.230304Z","state":"measured"},{"denominator":46,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":46,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-13T06:32:02.005865+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/2608.04357/citation-record","integrity":"/paper/2608.04357/integrity","json":"/paper/2608.04357/citation-record.json","paper":"/paper/2608.04357"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-08T19:20:23.579253Z","title":"Alphonse and N","venue":null,"work_id":"40c83f40-e0c3-4f67-9c05-750d28c97663","year":2025},"citing_paper":{"arxiv_id":"2608.04357","last_updated":"2026-08-05T01:56:32Z","snapshot_observed_at":"2026-08-10T02:44:45.055534Z","submitted_at":"2026-08-05T01:56:32Z","title":"Controllable subspaces and real-part observability for Schr\\\"odinger equations on $\\mathbb T^d$","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-08T19:20:22.027239Z"},"links":{"citing_paper":"/paper/2608.04357"},"observation_digest":"sha256:ccbac6545366058f25eda9597d92444343ea87a661660e3c46827c8d902f7fef","observation_id":"8615252a-5603-44f8-a2b6-171d4b1b56fd","resolution":{"observed_at":"2026-08-08T19:20:23.583625Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-08T19:20:23.565469Z","title":"Ammar-Khodja, A","venue":null,"work_id":"d7686138-d528-47f8-91e3-eaaace2d2724","year":2011},"citing_paper":{"arxiv_id":"2608.04357","last_updated":"2026-08-05T01:56:32Z","snapshot_observed_at":"2026-08-10T02:44:45.055534Z","submitted_at":"2026-08-05T01:56:32Z","title":"Controllable subspaces and real-part observability for Schr\\\"odinger equations on $\\mathbb T^d$","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-08T19:20:22.032421Z"},"links":{"citing_paper":"/paper/2608.04357"},"observation_digest":"sha256:44144d0cc7959eaa57836fd4ec2f8987fa6eb26e3094280082d64201faf384c3","observation_id":"00faf21b-56de-4e94-bf96-8669304b1f3a","resolution":{"observed_at":"2026-08-08T19:20:23.569821Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-08T19:20:23.551837Z","title":"Anantharaman and F","venue":null,"work_id":"84ad72a4-eb93-42d3-bb2f-91c8a7ae6d52","year":2014},"citing_paper":{"arxiv_id":"2608.04357","last_updated":"2026-08-05T01:56:32Z","snapshot_observed_at":"2026-08-10T02:44:45.055534Z","submitted_at":"2026-08-05T01:56:32Z","title":"Controllable subspaces and real-part observability for Schr\\\"odinger equations on $\\mathbb T^d$","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-08T19:20:22.036900Z"},"links":{"citing_paper":"/paper/2608.04357"},"observation_digest":"sha256:1d38e0ba8fe69cb805adeff4d4491131ab2708ee4b144f519284030fddec381b","observation_id":"9dc4dca1-f307-4dd3-aa89-6dd29167a762","resolution":{"observed_at":"2026-08-08T19:20:23.556251Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-08T19:20:23.538549Z","title":null,"venue":null,"work_id":"eda57fb9-ac74-47be-8dbb-27c2fb9a5f50","year":2016},"citing_paper":{"arxiv_id":"2608.04357","last_updated":"2026-08-05T01:56:32Z","snapshot_observed_at":"2026-08-10T02:44:45.055534Z","submitted_at":"2026-08-05T01:56:32Z","title":"Controllable subspaces and real-part observability for Schr\\\"odinger equations on $\\mathbb T^d$","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-08T19:20:22.041415Z"},"links":{"citing_paper":"/paper/2608.04357"},"observation_digest":"sha256:13544f7de7dc4d78953ac3c9a6feee0c6ae00fc3761f8ff6381190d5b0fc4be4","observation_id":"02e7204d-311f-4838-a9be-46603c1f4219","resolution":{"observed_at":"2026-08-08T19:20:23.542837Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-08T19:20:23.524651Z","title":"Bardos, G","venue":null,"work_id":"a3b13341-8fda-4dd8-98a1-a50663b91214","year":1992},"citing_paper":{"arxiv_id":"2608.04357","last_updated":"2026-08-05T01:56:32Z","snapshot_observed_at":"2026-08-10T02:44:45.055534Z","submitted_at":"2026-08-05T01:56:32Z","title":"Controllable subspaces and real-part observability for Schr\\\"odinger equations on $\\mathbb T^d$","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-08T19:20:22.046290Z"},"links":{"citing_paper":"/paper/2608.04357"},"observation_digest":"sha256:50e4ada653aecd29285a5b77ed909f32e41f6444ea6e39d62c736c267acfc315","observation_id":"4fc8949f-6f51-4254-aede-596a148e5a5a","resolution":{"observed_at":"2026-08-08T19:20:23.529373Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-08T19:20:23.511056Z","title":"Beauchard and C","venue":null,"work_id":"9aa87026-b95a-4aca-92b0-b8b23d187f9f","year":2010},"citing_paper":{"arxiv_id":"2608.04357","last_updated":"2026-08-05T01:56:32Z","snapshot_observed_at":"2026-08-10T02:44:45.055534Z","submitted_at":"2026-08-05T01:56:32Z","title":"Controllable subspaces and real-part observability for Schr\\\"odinger equations on $\\mathbb T^d$","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-08T19:20:22.050765Z"},"links":{"citing_paper":"/paper/2608.04357"},"observation_digest":"sha256:f4bb45af3dec3eebeee3289eb34d062db1f809a30ad1c0b7a7f3230c5f5baf5c","observation_id":"b89cc6f1-6e6b-4c2c-b681-9527c78c3f16","resolution":{"observed_at":"2026-08-08T19:20:23.515459Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-08T19:20:23.497826Z","title":"Benabdallah, P","venue":null,"work_id":"df44f105-09a4-4e30-911b-53edd079e631","year":2009},"citing_paper":{"arxiv_id":"2608.04357","last_updated":"2026-08-05T01:56:32Z","snapshot_observed_at":"2026-08-10T02:44:45.055534Z","submitted_at":"2026-08-05T01:56:32Z","title":"Controllable subspaces and real-part observability for Schr\\\"odinger equations on $\\mathbb T^d$","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-08T19:20:22.055868Z"},"links":{"citing_paper":"/paper/2608.04357"},"observation_digest":"sha256:69da0a0851a62236a409fa9ac87a8b6cb10f5fad08a9c57d9536c7c0d064f2c0","observation_id":"3a34d83d-514c-4d8c-ad9f-dfb88aec3794","resolution":{"observed_at":"2026-08-08T19:20:23.502100Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-08T19:20:23.483918Z","title":"Bonami and B","venue":null,"work_id":"5ebd9402-3a67-4d29-82e0-f899c638d5e5","year":2006},"citing_paper":{"arxiv_id":"2608.04357","last_updated":"2026-08-05T01:56:32Z","snapshot_observed_at":"2026-08-10T02:44:45.055534Z","submitted_at":"2026-08-05T01:56:32Z","title":"Controllable subspaces and real-part observability for Schr\\\"odinger equations on $\\mathbb T^d$","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-08T19:20:22.060394Z"},"links":{"citing_paper":"/paper/2608.04357"},"observation_digest":"sha256:04daaa447c1746317d2328c2b42cb8516c8475a257d3a9c248e67fde65700c77","observation_id":"a842ae4a-df6d-4f53-8cbf-14f6ed873e8e","resolution":{"observed_at":"2026-08-08T19:20:23.488287Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-08T19:20:23.469967Z","title":"Boscain, M","venue":null,"work_id":"916fb433-49e4-45f7-8fd4-b9e6f85676ac","year":2012},"citing_paper":{"arxiv_id":"2608.04357","last_updated":"2026-08-05T01:56:32Z","snapshot_observed_at":"2026-08-10T02:44:45.055534Z","submitted_at":"2026-08-05T01:56:32Z","title":"Controllable subspaces and real-part observability for Schr\\\"odinger equations on $\\mathbb T^d$","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-08T19:20:22.064972Z"},"links":{"citing_paper":"/paper/2608.04357"},"observation_digest":"sha256:1a0fbd41a5fa257b62285b00fa958ced88c4f6d8129b27d4f2482cf5b8a2fd45","observation_id":"f007db22-c7d6-4cd0-b4ae-3c39419aa711","resolution":{"observed_at":"2026-08-08T19:20:23.474506Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-08T19:20:23.456353Z","title":"Bourgain, On the control problem for Schr¨ odinger operators on tori, inGeometric aspects of functional analysis, Springer, Cham, 2014, 97–105","venue":null,"work_id":"b4c2fe85-6c78-43db-9cfe-44874c0a2e40","year":2014},"citing_paper":{"arxiv_id":"2608.04357","last_updated":"2026-08-05T01:56:32Z","snapshot_observed_at":"2026-08-10T02:44:45.055534Z","submitted_at":"2026-08-05T01:56:32Z","title":"Controllable subspaces and real-part observability for Schr\\\"odinger equations on $\\mathbb T^d$","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-08T19:20:22.069261Z"},"links":{"citing_paper":"/paper/2608.04357"},"observation_digest":"sha256:c56ca3559dfdf786d9c909a294b7953cdeb909019526e98098d7e71217c274ec","observation_id":"24c8e574-e354-4bfd-8f15-8bba5eb5503e","resolution":{"observed_at":"2026-08-08T19:20:23.460708Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-08T19:20:23.442403Z","title":"Bourgain, N","venue":null,"work_id":"9e4793e6-75ac-4c82-b927-bb67bae86f25","year":2013},"citing_paper":{"arxiv_id":"2608.04357","last_updated":"2026-08-05T01:56:32Z","snapshot_observed_at":"2026-08-10T02:44:45.055534Z","submitted_at":"2026-08-05T01:56:32Z","title":"Controllable subspaces and real-part observability for Schr\\\"odinger equations on $\\mathbb T^d$","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-08T19:20:22.073722Z"},"links":{"citing_paper":"/paper/2608.04357"},"observation_digest":"sha256:4f2ca40f262c89e5b0cff7e7ac1c46f19e5fc910232229e99079c611dd03baa2","observation_id":"40c315b9-49e6-400d-8eb0-84036043de6a","resolution":{"observed_at":"2026-08-08T19:20:23.446893Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-08T19:20:23.428379Z","title":"Burq and M","venue":null,"work_id":"00286eb2-54ba-4693-a45a-eccae3bc6f36","year":2012},"citing_paper":{"arxiv_id":"2608.04357","last_updated":"2026-08-05T01:56:32Z","snapshot_observed_at":"2026-08-10T02:44:45.055534Z","submitted_at":"2026-08-05T01:56:32Z","title":"Controllable subspaces and real-part observability for Schr\\\"odinger equations on $\\mathbb T^d$","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-08T19:20:22.078373Z"},"links":{"citing_paper":"/paper/2608.04357"},"observation_digest":"sha256:7c6bbbd90c9f8b1f8da2330adf3b841a44cd2de828ca8a7d3a8854cd2ebe7af3","observation_id":"9ef0ce6c-c135-40de-ae2c-79c27b6355b2","resolution":{"observed_at":"2026-08-08T19:20:23.432811Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-08T19:20:23.414493Z","title":"Burq and M","venue":null,"work_id":"b10f6ccb-9341-411c-8352-005b2d4e88f4","year":2019},"citing_paper":{"arxiv_id":"2608.04357","last_updated":"2026-08-05T01:56:32Z","snapshot_observed_at":"2026-08-10T02:44:45.055534Z","submitted_at":"2026-08-05T01:56:32Z","title":"Controllable subspaces and real-part observability for Schr\\\"odinger equations on $\\mathbb T^d$","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-08T19:20:22.083255Z"},"links":{"citing_paper":"/paper/2608.04357"},"observation_digest":"sha256:af66670d29ac655fc0151e9f4e346b2f64c003b8eb53a965de0dded4d3aa9e5d","observation_id":"31331976-6fc3-44c0-afbd-8a3c134eeb19","resolution":{"observed_at":"2026-08-08T19:20:23.419046Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-08T19:20:22.087617Z","title":"Burq and H","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2608.04357","last_updated":"2026-08-05T01:56:32Z","snapshot_observed_at":"2026-08-10T02:44:45.055534Z","submitted_at":"2026-08-05T01:56:32Z","title":"Controllable subspaces and real-part observability for Schr\\\"odinger equations on $\\mathbb T^d$","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-08T19:20:22.087617Z"},"links":{"citing_paper":"/paper/2608.04357"},"observation_digest":"sha256:d6994d838417026233e5dfba837f912b98d2ec985a07d18745480f66564381e5","observation_id":"1514041e-2bce-4f93-8d57-b82184e29205","resolution":{"observed_at":"2026-08-08T19:20:22.087617Z","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":"2510.24517","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-08T19:20:22.822606Z","title":"Burq and H","venue":null,"work_id":"ed2cc2d0-3e32-45cd-bc28-235a06484212","year":2025},"citing_paper":{"arxiv_id":"2608.04357","last_updated":"2026-08-05T01:56:32Z","snapshot_observed_at":"2026-08-10T02:44:45.055534Z","submitted_at":"2026-08-05T01:56:32Z","title":"Controllable subspaces and real-part observability for Schr\\\"odinger equations on $\\mathbb T^d$","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-08T19:20:22.092076Z"},"links":{"citing_paper":"/paper/2608.04357"},"observation_digest":"sha256:15fa0ca46743ad51e6a0a880f165d5f2f8dbb198c77291f0dc66ff6ab483eb49","observation_id":"9bec635b-6a0f-4caf-9b32-76f7878c095b","resolution":{"observed_at":"2026-08-08T19:20:22.829690Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-08T19:20:23.400427Z","title":"Chambrion, P","venue":null,"work_id":"a30ee847-9ba7-4808-a3da-f08817c46eba","year":2009},"citing_paper":{"arxiv_id":"2608.04357","last_updated":"2026-08-05T01:56:32Z","snapshot_observed_at":"2026-08-10T02:44:45.055534Z","submitted_at":"2026-08-05T01:56:32Z","title":"Controllable subspaces and real-part observability for Schr\\\"odinger equations on $\\mathbb T^d$","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-08T19:20:22.096613Z"},"links":{"citing_paper":"/paper/2608.04357"},"observation_digest":"sha256:c91cea59159e1a5ed8c32cce27483b3bce06349acb9cb1342ec4f5ca76372fe3","observation_id":"d8257b58-2d95-40f2-bf46-3bd181194f7f","resolution":{"observed_at":"2026-08-08T19:20:23.404805Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-08T19:20:23.385818Z","title":"Coron,Control and nonlinearity, Mathematical Surveys and Monographs, vol","venue":null,"work_id":"e6205170-2599-43ff-84f4-bd0ef63608e9","year":2007},"citing_paper":{"arxiv_id":"2608.04357","last_updated":"2026-08-05T01:56:32Z","snapshot_observed_at":"2026-08-10T02:44:45.055534Z","submitted_at":"2026-08-05T01:56:32Z","title":"Controllable subspaces and real-part observability for Schr\\\"odinger equations on $\\mathbb T^d$","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-08T19:20:22.101075Z"},"links":{"citing_paper":"/paper/2608.04357"},"observation_digest":"sha256:81803e55bcf97c75e9d9956288c5e75277a0135e1ecb4b2bf46b7216bbae8bf6","observation_id":"2e0009da-cf11-435f-9fd1-8aa576f04453","resolution":{"observed_at":"2026-08-08T19:20:23.390456Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-08T19:20:23.371660Z","title":"Dard´ e and S","venue":null,"work_id":"fc687fee-3e10-43f1-a8c4-41875bb185df","year":2018},"citing_paper":{"arxiv_id":"2608.04357","last_updated":"2026-08-05T01:56:32Z","snapshot_observed_at":"2026-08-10T02:44:45.055534Z","submitted_at":"2026-08-05T01:56:32Z","title":"Controllable subspaces and real-part observability for Schr\\\"odinger equations on $\\mathbb T^d$","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-08T19:20:22.105657Z"},"links":{"citing_paper":"/paper/2608.04357"},"observation_digest":"sha256:07c5bba9a1beb875d7b0cb4ceb1fb037c51b1d8790fa00b8b0669eeaaf0387e0","observation_id":"35887b51-a201-48cd-96bb-744e98fe1f69","resolution":{"observed_at":"2026-08-08T19:20:23.376146Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-08T19:20:23.357249Z","title":"Fern´ andez-Cara, M","venue":null,"work_id":"bbb5fbb7-170f-479a-9baa-d5a38cc610d1","year":2010},"citing_paper":{"arxiv_id":"2608.04357","last_updated":"2026-08-05T01:56:32Z","snapshot_observed_at":"2026-08-10T02:44:45.055534Z","submitted_at":"2026-08-05T01:56:32Z","title":"Controllable subspaces and real-part observability for Schr\\\"odinger equations on $\\mathbb T^d$","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-08T19:20:22.109911Z"},"links":{"citing_paper":"/paper/2608.04357"},"observation_digest":"sha256:61c6bd7358927d058adb45c1da48bfdd0c0c79231ec6a22a30561f4892976066","observation_id":"664a02d4-755a-45e2-972b-af074dcae239","resolution":{"observed_at":"2026-08-08T19:20:23.361838Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-08T19:20:23.342888Z","title":"Fontes-Merz, A multidimensional version of Tur´ an’s lemma,J","venue":null,"work_id":"2f1ba973-db23-48eb-8238-5472ac2d7961","year":2006},"citing_paper":{"arxiv_id":"2608.04357","last_updated":"2026-08-05T01:56:32Z","snapshot_observed_at":"2026-08-10T02:44:45.055534Z","submitted_at":"2026-08-05T01:56:32Z","title":"Controllable subspaces and real-part observability for Schr\\\"odinger equations on $\\mathbb T^d$","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-08T19:20:22.114237Z"},"links":{"citing_paper":"/paper/2608.04357"},"observation_digest":"sha256:48a1e43935d242cdcf855d44d91e3d412d47fcb485f822dc6538662aeec3dd68","observation_id":"4616202f-0bac-4529-afd8-b168b45809b9","resolution":{"observed_at":"2026-08-08T19:20:23.347359Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2604.13599","last_updated":"2026-04-15T08:08:44Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2026-04-15T08:08:44Z","title":"Observability from measurable sets for strongly coupled parabolic systems via single-component observation","version":1},"cited_work":{"arxiv_id":"2604.13599","doi":null,"metadata_source":"pith","pith_arxiv_id":"2604.13599","snapshot_observed_at":"2026-08-08T19:20:22.597913Z","title":"Observability from measurable sets for strongly coupled parabolic systems via single-component observation","venue":"math.OC","work_id":"a750d27c-2ddb-4b75-a0a6-9384fed3cee4","year":2026},"citing_paper":{"arxiv_id":"2608.04357","last_updated":"2026-08-05T01:56:32Z","snapshot_observed_at":"2026-08-10T02:44:45.055534Z","submitted_at":"2026-08-05T01:56:32Z","title":"Controllable subspaces and real-part observability for Schr\\\"odinger equations on $\\mathbb T^d$","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-08T19:20:22.118945Z"},"links":{"cited_paper":"/paper/2604.13599","citing_paper":"/paper/2608.04357"},"observation_digest":"sha256:4f0a46f7be055470d54e34aa4fa05152623f8a3a2c37a85a26329f933ac65f8b","observation_id":"b616852f-3413-492a-9516-44b9687d293e","resolution":{"observed_at":"2026-08-08T19:20:22.603725Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-08T19:20:23.328633Z","title":"Guerrero, Null controllability of some systems of two parabolic equations with one control force,SIAM J","venue":null,"work_id":"eb6988dd-d425-47c5-82c3-5c960ed9f844","year":2007},"citing_paper":{"arxiv_id":"2608.04357","last_updated":"2026-08-05T01:56:32Z","snapshot_observed_at":"2026-08-10T02:44:45.055534Z","submitted_at":"2026-08-05T01:56:32Z","title":"Controllable subspaces and real-part observability for Schr\\\"odinger equations on $\\mathbb T^d$","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-08T19:20:22.123670Z"},"links":{"citing_paper":"/paper/2608.04357"},"observation_digest":"sha256:fc18539b942a9f61e9f3b485a819e031f8b68bc175aa3b1fd101e1225d888e0c","observation_id":"351a976a-9652-4b67-a86f-960cd0d91cac","resolution":{"observed_at":"2026-08-08T19:20:23.333261Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":"2603.15193","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-08T19:20:22.574179Z","title":null,"venue":null,"work_id":"fb63355a-c18c-4e22-96e0-1023e97515b6","year":2026},"citing_paper":{"arxiv_id":"2608.04357","last_updated":"2026-08-05T01:56:32Z","snapshot_observed_at":"2026-08-10T02:44:45.055534Z","submitted_at":"2026-08-05T01:56:32Z","title":"Controllable subspaces and real-part observability for Schr\\\"odinger equations on $\\mathbb T^d$","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-08T19:20:22.127888Z"},"links":{"citing_paper":"/paper/2608.04357"},"observation_digest":"sha256:e96c6ca83434dd32499b6f289e131d607b096db793749c3d5ab1c9bd4887f60b","observation_id":"9ec5f061-56ad-4876-98e2-ebda0bbf9c01","resolution":{"observed_at":"2026-08-08T19:20:22.582404Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-08T19:20:23.314719Z","title":"Haraux, S´ eries lacunaires et contrˆ ole semi-interne des vibrations d’une plaque rectangulaire,J","venue":null,"work_id":"b534283c-0447-4b4f-aeb5-3813a05d004e","year":1989},"citing_paper":{"arxiv_id":"2608.04357","last_updated":"2026-08-05T01:56:32Z","snapshot_observed_at":"2026-08-10T02:44:45.055534Z","submitted_at":"2026-08-05T01:56:32Z","title":"Controllable subspaces and real-part observability for Schr\\\"odinger equations on $\\mathbb T^d$","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-08T19:20:22.132365Z"},"links":{"citing_paper":"/paper/2608.04357"},"observation_digest":"sha256:0243af8ba28f74ea83d10b24edad9fd5de9592aa7e4bb1c0d695998e9e407fe1","observation_id":"f92896c7-f9e1-4ec4-aa6c-13d6baeecb1e","resolution":{"observed_at":"2026-08-08T19:20:23.319298Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-08T19:20:23.300706Z","title":"Hartmann, K","venue":null,"work_id":"da121416-d77a-424e-a586-66a9d72f0f8c","year":2020},"citing_paper":{"arxiv_id":"2608.04357","last_updated":"2026-08-05T01:56:32Z","snapshot_observed_at":"2026-08-10T02:44:45.055534Z","submitted_at":"2026-08-05T01:56:32Z","title":"Controllable subspaces and real-part observability for Schr\\\"odinger equations on $\\mathbb T^d$","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-08T19:20:22.136649Z"},"links":{"citing_paper":"/paper/2608.04357"},"observation_digest":"sha256:ddcfc5ebd4ebf284fd135e678e4e2eafdb424e7fe4a956267cb786f85a408b7f","observation_id":"e4b688f2-300b-4d85-9615-cbe61dc0bdae","resolution":{"observed_at":"2026-08-08T19:20:23.305402Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-08T19:20:23.286853Z","title":"Havin and B","venue":null,"work_id":"9ac0fd67-beb4-47de-bb5f-48817b8f5cef","year":1994},"citing_paper":{"arxiv_id":"2608.04357","last_updated":"2026-08-05T01:56:32Z","snapshot_observed_at":"2026-08-10T02:44:45.055534Z","submitted_at":"2026-08-05T01:56:32Z","title":"Controllable subspaces and real-part observability for Schr\\\"odinger equations on $\\mathbb T^d$","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-08T19:20:22.141145Z"},"links":{"citing_paper":"/paper/2608.04357"},"observation_digest":"sha256:4ee04dd008f58ebc59868f1da130958e10aea81320b3a0a8ba43255bc66b9805","observation_id":"a97c18b2-7b3e-4ad2-97b9-5a7375da9982","resolution":{"observed_at":"2026-08-08T19:20:23.291272Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-08T19:20:23.273239Z","title":"Huang and C","venue":null,"work_id":"28bb160c-e938-41f1-8876-544a7ef0d722","year":2021},"citing_paper":{"arxiv_id":"2608.04357","last_updated":"2026-08-05T01:56:32Z","snapshot_observed_at":"2026-08-10T02:44:45.055534Z","submitted_at":"2026-08-05T01:56:32Z","title":"Controllable subspaces and real-part observability for Schr\\\"odinger equations on $\\mathbb T^d$","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-08T19:20:22.145566Z"},"links":{"citing_paper":"/paper/2608.04357"},"observation_digest":"sha256:2b49c09885d50c3f6b2b830e6c353b0d0870f782aa21dd6a7f41a2ab645a8eb1","observation_id":"09d184b6-cbf7-4970-a4e2-53d2b098c870","resolution":{"observed_at":"2026-08-08T19:20:23.277663Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-08T19:20:23.258971Z","title":null,"venue":null,"work_id":"df18a863-a80d-47d2-8185-aaed39352b62","year":1936},"citing_paper":{"arxiv_id":"2608.04357","last_updated":"2026-08-05T01:56:32Z","snapshot_observed_at":"2026-08-10T02:44:45.055534Z","submitted_at":"2026-08-05T01:56:32Z","title":"Controllable subspaces and real-part observability for Schr\\\"odinger equations on $\\mathbb T^d$","version":1},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-08T19:20:22.149753Z"},"links":{"citing_paper":"/paper/2608.04357"},"observation_digest":"sha256:be3ee173bdf026bcf7337f501bfd20bd41fdd1451db73f9477b3e6a8377a50db","observation_id":"ec68076a-8fab-45ad-9295-d9f12abb13d1","resolution":{"observed_at":"2026-08-08T19:20:23.263313Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-08T19:20:23.244952Z","title":"Jaffard, Contrˆ ole interne exact des vibrations d’une plaque rectangulaire,Port","venue":null,"work_id":"36fcf607-753b-4fc8-8432-03e0ec2e0a17","year":1990},"citing_paper":{"arxiv_id":"2608.04357","last_updated":"2026-08-05T01:56:32Z","snapshot_observed_at":"2026-08-10T02:44:45.055534Z","submitted_at":"2026-08-05T01:56:32Z","title":"Controllable subspaces and real-part observability for Schr\\\"odinger equations on $\\mathbb T^d$","version":1},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-08T19:20:22.154513Z"},"links":{"citing_paper":"/paper/2608.04357"},"observation_digest":"sha256:0261a716d57ac00936c77fa91463b12979e12c46028d9f4917c54b01f3e37730","observation_id":"15df72ba-e94d-4bc1-9d5f-13effebaac19","resolution":{"observed_at":"2026-08-08T19:20:23.249413Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-08T19:20:23.230906Z","title":"Kahane, Pseudo-p´ eriodicit´ e et s´ eries de Fourier lacunaires,Ann","venue":null,"work_id":"3d0ad557-32e9-4c45-a396-4f2f5cde70f5","year":1962},"citing_paper":{"arxiv_id":"2608.04357","last_updated":"2026-08-05T01:56:32Z","snapshot_observed_at":"2026-08-10T02:44:45.055534Z","submitted_at":"2026-08-05T01:56:32Z","title":"Controllable subspaces and real-part observability for Schr\\\"odinger equations on $\\mathbb T^d$","version":1},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-08T19:20:22.158675Z"},"links":{"citing_paper":"/paper/2608.04357"},"observation_digest":"sha256:f4cd425505c6f5f671e208ed6b70b6d732abef68d7f3ab58ae35ee70571c6faa","observation_id":"383cdce3-7551-430a-8ceb-ee73428c1952","resolution":{"observed_at":"2026-08-08T19:20:23.235380Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-08T19:20:23.216931Z","title":"Komornik, On the exact internal controllability of a Petrowsky system,J","venue":null,"work_id":"ad45aa09-53bf-484d-a342-5eef23eeefd2","year":1992},"citing_paper":{"arxiv_id":"2608.04357","last_updated":"2026-08-05T01:56:32Z","snapshot_observed_at":"2026-08-10T02:44:45.055534Z","submitted_at":"2026-08-05T01:56:32Z","title":"Controllable subspaces and real-part observability for Schr\\\"odinger equations on $\\mathbb T^d$","version":1},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-08T19:20:22.163156Z"},"links":{"citing_paper":"/paper/2608.04357"},"observation_digest":"sha256:0e2bfb92fbaca9f01e95b616e194de9bc6f7c7f8d21e4e341115c578502153a4","observation_id":"aef54cc8-283b-41c5-9286-0b3c94dd3e19","resolution":{"observed_at":"2026-08-08T19:20:23.221302Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-08T19:20:23.203643Z","title":"Laurent, Internal control of the Schr¨ odinger equation,Math","venue":null,"work_id":"056a3502-f792-448e-848b-54b0c0c91e0e","year":2014},"citing_paper":{"arxiv_id":"2608.04357","last_updated":"2026-08-05T01:56:32Z","snapshot_observed_at":"2026-08-10T02:44:45.055534Z","submitted_at":"2026-08-05T01:56:32Z","title":"Controllable subspaces and real-part observability for Schr\\\"odinger equations on $\\mathbb T^d$","version":1},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-08T19:20:22.167657Z"},"links":{"citing_paper":"/paper/2608.04357"},"observation_digest":"sha256:990afc5b9627cacca6a9bcca6db35aa9ad6f2846503d030109cdc4f0e0f3bfd6","observation_id":"943fb9a8-e2f6-48c5-b370-61f07476a464","resolution":{"observed_at":"2026-08-08T19:20:23.207857Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2304.08050","last_updated":"2023-04-17T08:10:38Z","snapshot_observed_at":"2026-08-13T18:01:21.419029Z","submitted_at":"2023-04-17T08:10:38Z","title":"Observability estimates for the Schr{\\\"o}dinger equation in the plane with periodic bounded potentials from measurable sets","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2304.08050","snapshot_observed_at":"2026-08-08T19:20:22.172050Z","title":"Le Balc’h and J","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2608.04357","last_updated":"2026-08-05T01:56:32Z","snapshot_observed_at":"2026-08-10T02:44:45.055534Z","submitted_at":"2026-08-05T01:56:32Z","title":"Controllable subspaces and real-part observability for Schr\\\"odinger equations on $\\mathbb T^d$","version":1},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-08T19:20:22.172050Z"},"links":{"cited_paper":"/paper/2304.08050","citing_paper":"/paper/2608.04357"},"observation_digest":"sha256:ec35adcee520b3d9ba178b5308b96d9314c81c3ce7a24263c55b28cdb2d1b541","observation_id":"84b3be4a-c854-47a8-98a7-8ef625ae018d","resolution":{"observed_at":"2026-08-08T19:20:22.172050Z","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":"2026-08-08T19:20:23.189995Z","title":"Li and J","venue":null,"work_id":"6b041f96-23d8-423c-af3e-6d935bfec0ec","year":1995},"citing_paper":{"arxiv_id":"2608.04357","last_updated":"2026-08-05T01:56:32Z","snapshot_observed_at":"2026-08-10T02:44:45.055534Z","submitted_at":"2026-08-05T01:56:32Z","title":"Controllable subspaces and real-part observability for Schr\\\"odinger equations on $\\mathbb T^d$","version":1},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-08T19:20:22.176668Z"},"links":{"citing_paper":"/paper/2608.04357"},"observation_digest":"sha256:ba4d1f90f7758a9e110d168a89929478e2889e75980d847026c785428a14b2ae","observation_id":"126db110-5bc2-45df-bd42-646f228d8f3e","resolution":{"observed_at":"2026-08-08T19:20:23.194536Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-08T19:20:23.176208Z","title":"Lions,Contrˆ olabilit´ e exacte, perturbations et stabilisation de syst` emes distribu´ es","venue":null,"work_id":"01bd709c-d8bf-49ab-86db-3bcbe6916ee8","year":1988},"citing_paper":{"arxiv_id":"2608.04357","last_updated":"2026-08-05T01:56:32Z","snapshot_observed_at":"2026-08-10T02:44:45.055534Z","submitted_at":"2026-08-05T01:56:32Z","title":"Controllable subspaces and real-part observability for Schr\\\"odinger equations on $\\mathbb T^d$","version":1},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-08-08T19:20:22.181206Z"},"links":{"citing_paper":"/paper/2608.04357"},"observation_digest":"sha256:f34aedc2da63caf31a36771d8da4f8d42cccdf2028820349b5b04c0e6833121a","observation_id":"994467d8-b8ac-4446-bd4b-946007797bc4","resolution":{"observed_at":"2026-08-08T19:20:23.180735Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-08T19:20:23.162523Z","title":"Lissy and E","venue":null,"work_id":"8b29a47b-1f9c-40a4-9310-cdeeaf08a4a2","year":2019},"citing_paper":{"arxiv_id":"2608.04357","last_updated":"2026-08-05T01:56:32Z","snapshot_observed_at":"2026-08-10T02:44:45.055534Z","submitted_at":"2026-08-05T01:56:32Z","title":"Controllable subspaces and real-part observability for Schr\\\"odinger equations on $\\mathbb T^d$","version":1},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-08-08T19:20:22.185769Z"},"links":{"citing_paper":"/paper/2608.04357"},"observation_digest":"sha256:8415f5e201ab48cb2a29f06443bf958191300e3491f33e0de20d7822d92faeb2","observation_id":"230ae6b9-ff49-403d-a275-4d0a138b999f","resolution":{"observed_at":"2026-08-08T19:20:23.167003Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-08T19:20:23.148573Z","title":null,"venue":null,"work_id":"38dc7c7d-13f0-411d-a80e-0725423770f8","year":2020},"citing_paper":{"arxiv_id":"2608.04357","last_updated":"2026-08-05T01:56:32Z","snapshot_observed_at":"2026-08-10T02:44:45.055534Z","submitted_at":"2026-08-05T01:56:32Z","title":"Controllable subspaces and real-part observability for Schr\\\"odinger equations on $\\mathbb T^d$","version":1},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-08-08T19:20:22.190727Z"},"links":{"citing_paper":"/paper/2608.04357"},"observation_digest":"sha256:78942e1fe40e0815a8966edc3b44ef102a88af67cbeeb7decc4cc6b8390ce3b3","observation_id":"88d51a13-1822-4e58-9963-3d2c34ee010b","resolution":{"observed_at":"2026-08-08T19:20:23.152918Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-08T19:20:23.134730Z","title":"Maci` a, High-frequency propagation for the Schr¨ odinger equation on the torus,J","venue":null,"work_id":"8407b49f-6360-4dd1-9f5e-5207b1f310ce","year":2010},"citing_paper":{"arxiv_id":"2608.04357","last_updated":"2026-08-05T01:56:32Z","snapshot_observed_at":"2026-08-10T02:44:45.055534Z","submitted_at":"2026-08-05T01:56:32Z","title":"Controllable subspaces and real-part observability for Schr\\\"odinger equations on $\\mathbb T^d$","version":1},"reference_index":38,"source":"pdf_text","source_observed_at":"2026-08-08T19:20:22.195192Z"},"links":{"citing_paper":"/paper/2608.04357"},"observation_digest":"sha256:cec989a9dcf692af61631bb3d86e2ef0bc943fb1532ebefc3bb16c6c34dbf277","observation_id":"0bd97fb7-c868-429a-b45f-70c6fff5c6d0","resolution":{"observed_at":"2026-08-08T19:20:23.139214Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-08T19:20:23.121051Z","title":null,"venue":null,"work_id":"6629fe27-7e33-4df3-8fbd-dd114004e258","year":2026},"citing_paper":{"arxiv_id":"2608.04357","last_updated":"2026-08-05T01:56:32Z","snapshot_observed_at":"2026-08-10T02:44:45.055534Z","submitted_at":"2026-08-05T01:56:32Z","title":"Controllable subspaces and real-part observability for Schr\\\"odinger equations on $\\mathbb T^d$","version":1},"reference_index":39,"source":"pdf_text","source_observed_at":"2026-08-08T19:20:22.199513Z"},"links":{"citing_paper":"/paper/2608.04357"},"observation_digest":"sha256:cf3b3d89f2d0629468839316c1086cd04a04a088549b1ba970816e43aef73ccf","observation_id":"01694dc8-8ad8-4a91-8bcf-243c19d9eafb","resolution":{"observed_at":"2026-08-08T19:20:23.125284Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-08T19:20:23.107530Z","title":"Rauch and M","venue":null,"work_id":"6f61efbd-d3e4-4593-b523-c5c8482216a9","year":1975},"citing_paper":{"arxiv_id":"2608.04357","last_updated":"2026-08-05T01:56:32Z","snapshot_observed_at":"2026-08-10T02:44:45.055534Z","submitted_at":"2026-08-05T01:56:32Z","title":"Controllable subspaces and real-part observability for Schr\\\"odinger equations on $\\mathbb T^d$","version":1},"reference_index":40,"source":"pdf_text","source_observed_at":"2026-08-08T19:20:22.203834Z"},"links":{"citing_paper":"/paper/2608.04357"},"observation_digest":"sha256:512ea9fef8f602acad5d300e939e6aebad8cb5ba4351ebddb9b4f8a7eba65f98","observation_id":"de51b585-559f-431b-ab33-b164d7c5f5d8","resolution":{"observed_at":"2026-08-08T19:20:23.111750Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-08T19:20:23.092917Z","title":"Schechter and B","venue":null,"work_id":"9d09a131-d2a5-4047-86dc-a0666af3eacb","year":1980},"citing_paper":{"arxiv_id":"2608.04357","last_updated":"2026-08-05T01:56:32Z","snapshot_observed_at":"2026-08-10T02:44:45.055534Z","submitted_at":"2026-08-05T01:56:32Z","title":"Controllable subspaces and real-part observability for Schr\\\"odinger equations on $\\mathbb T^d$","version":1},"reference_index":41,"source":"pdf_text","source_observed_at":"2026-08-08T19:20:22.208352Z"},"links":{"citing_paper":"/paper/2608.04357"},"observation_digest":"sha256:6a7e0dd431e5e8850409efc1501efa2f2b69fa7d0d9334a8de5afa7e54dccb90","observation_id":"005d2d26-139a-41c7-9afc-b3ea35fb5b96","resolution":{"observed_at":"2026-08-08T19:20:23.097777Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-08T19:20:23.077401Z","title":"Tao, Exact control for the Schr¨ odinger equation on the torus from small balls,Pure Appl","venue":null,"work_id":"e7c55e84-7eff-4cce-a003-346e52be51e0","year":2021},"citing_paper":{"arxiv_id":"2608.04357","last_updated":"2026-08-05T01:56:32Z","snapshot_observed_at":"2026-08-10T02:44:45.055534Z","submitted_at":"2026-08-05T01:56:32Z","title":"Controllable subspaces and real-part observability for Schr\\\"odinger equations on $\\mathbb T^d$","version":1},"reference_index":42,"source":"pdf_text","source_observed_at":"2026-08-08T19:20:22.212837Z"},"links":{"citing_paper":"/paper/2608.04357"},"observation_digest":"sha256:cb9e0da4851633ae2ef50f4465135a603ef019fd27ff85f04bc9d4115808568b","observation_id":"2dbd350e-3161-4d6c-bd15-013c6d2b589b","resolution":{"observed_at":"2026-08-08T19:20:23.082440Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-08T19:20:23.063613Z","title":"T¨ aufer, Controllability of the Schr¨ odinger equation on unbounded domains without geometric control condition,ESAIM Control Optim","venue":null,"work_id":"9a4afb8f-207b-4608-b54e-b5155bc675f9","year":2023},"citing_paper":{"arxiv_id":"2608.04357","last_updated":"2026-08-05T01:56:32Z","snapshot_observed_at":"2026-08-10T02:44:45.055534Z","submitted_at":"2026-08-05T01:56:32Z","title":"Controllable subspaces and real-part observability for Schr\\\"odinger equations on $\\mathbb T^d$","version":1},"reference_index":43,"source":"pdf_text","source_observed_at":"2026-08-08T19:20:22.217319Z"},"links":{"citing_paper":"/paper/2608.04357"},"observation_digest":"sha256:ce2170159a9244b751c2bbbcb1d2fd00865e6ade77dfffd85d6668663f493f4d","observation_id":"9b96ca9b-6a9b-4298-9b09-47c3c76028fd","resolution":{"observed_at":"2026-08-08T19:20:23.068140Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-08T19:20:23.049524Z","title":"Tucsnak, Reachable states for infinite-dimensional linear systems: old and new, inProceedings of the International Congress of Mathematicians 2022, Vol","venue":null,"work_id":"98248328-fe0c-4f04-b87a-828f8c1cfd0e","year":2022},"citing_paper":{"arxiv_id":"2608.04357","last_updated":"2026-08-05T01:56:32Z","snapshot_observed_at":"2026-08-10T02:44:45.055534Z","submitted_at":"2026-08-05T01:56:32Z","title":"Controllable subspaces and real-part observability for Schr\\\"odinger equations on $\\mathbb T^d$","version":1},"reference_index":44,"source":"pdf_text","source_observed_at":"2026-08-08T19:20:22.221617Z"},"links":{"citing_paper":"/paper/2608.04357"},"observation_digest":"sha256:094b20104afeebf17fc3ca0a168f617891bb3c82db9857569768213f8b267cda","observation_id":"6a6775be-2f3a-4dc5-b381-88767af9148a","resolution":{"observed_at":"2026-08-08T19:20:23.054083Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-08T19:20:23.035134Z","title":"Wunsch, Periodic damping gives polynomial energy decay,Math","venue":null,"work_id":"0963d8e3-bbc5-4a5d-aa0e-21bb29b8d54a","year":2017},"citing_paper":{"arxiv_id":"2608.04357","last_updated":"2026-08-05T01:56:32Z","snapshot_observed_at":"2026-08-10T02:44:45.055534Z","submitted_at":"2026-08-05T01:56:32Z","title":"Controllable subspaces and real-part observability for Schr\\\"odinger equations on $\\mathbb T^d$","version":1},"reference_index":45,"source":"pdf_text","source_observed_at":"2026-08-08T19:20:22.226030Z"},"links":{"citing_paper":"/paper/2608.04357"},"observation_digest":"sha256:add596439e6ab29fd746c51ca2dc5612fd20181d2de14b5b7288869ec4e398f6","observation_id":"c3fc8a9f-665b-4ea3-a98b-06a7e409a29d","resolution":{"observed_at":"2026-08-08T19:20:23.039819Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-08T19:20:23.020673Z","title":"Zygmund, A Cantor–Lebesgue theorem for double trigonometric series,Studia Math.43 (1972), 173–178","venue":null,"work_id":"b7897871-0c89-451a-a4fb-79e2e05733ed","year":1972},"citing_paper":{"arxiv_id":"2608.04357","last_updated":"2026-08-05T01:56:32Z","snapshot_observed_at":"2026-08-10T02:44:45.055534Z","submitted_at":"2026-08-05T01:56:32Z","title":"Controllable subspaces and real-part observability for Schr\\\"odinger equations on $\\mathbb T^d$","version":1},"reference_index":46,"source":"pdf_text","source_observed_at":"2026-08-08T19:20:22.230304Z"},"links":{"citing_paper":"/paper/2608.04357"},"observation_digest":"sha256:a1cf4918e7df448c31a1ff26fae35e61e9bcae167b70ba1e8222b7f94c2ef877","observation_id":"b4fbda65-0d3d-41ff-94f8-824f83a5a413","resolution":{"observed_at":"2026-08-08T19:20:23.025285Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2608.04357","last_updated":"2026-08-05T01:56:32Z","latest_version":1,"primary_category":"math.AP","snapshot_observed_at":"2026-08-10T02:44:45.055534Z","submitted_at":"2026-08-05T01:56:32Z","title":"Controllable subspaces and real-part observability for Schr\\\"odinger equations on $\\mathbb T^d$"},"reference_resolution":{"displayed":46,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":6,"verified_exact":3,"verified_fuzzy":37},"total_outbound_references":46},"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":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"thesis":"As of 14 August 2026, this Paper Citation Record lists 46 of 46 outbound references and 0 inbound Pith citation observations for arXiv:2608.04357."}