{"as_of":"2026-08-23T11:23:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:e3c3d2dc4e7ed51ceb09f905280f718eca3af6a1a72f9a11aadba93a3a4ade28","coverage":[{"denominator":32,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":32,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-11T10:27:11.857077Z","state":"measured"},{"denominator":32,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":32,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-23T06:30:58.430688+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/2412.16756/citation-record","integrity":"/paper/2412.16756/integrity","json":"/paper/2412.16756/citation-record.json","paper":"/paper/2412.16756"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T10:27:12.424475Z","title":null,"venue":null,"work_id":"62b962d1-34d8-437b-91c0-8278c9c3c65c","year":2013},"citing_paper":{"arxiv_id":"2412.16756","last_updated":"2024-12-21T20:09:22Z","snapshot_observed_at":"2026-08-18T18:01:50.177493Z","submitted_at":"2024-12-21T20:09:22Z","title":"Resolvent and spectrum for discrete symplectic systems in the limit point case","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-11T10:27:11.674852Z"},"links":{"citing_paper":"/paper/2412.16756"},"observation_digest":"sha256:03dc69331759ec2628b4f06eab637bb964637b5b6b945aa4acb81259f5349c6c","observation_id":"06b63197-d289-48a0-bb70-73e70cc591e5","resolution":{"observed_at":"2026-08-11T10:27:12.429822Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-08-11T10:27:12.404004Z","title":"Behncke, Spectral theory of Hamiltonian difference systems with almost constant coefﬁcients , J","venue":null,"work_id":"24e503e3-08ce-4599-bc55-99acfbe359ba","year":2013},"citing_paper":{"arxiv_id":"2412.16756","last_updated":"2024-12-21T20:09:22Z","snapshot_observed_at":"2026-08-18T18:01:50.177493Z","submitted_at":"2024-12-21T20:09:22Z","title":"Resolvent and spectrum for discrete symplectic systems in the limit point case","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-11T10:27:11.681365Z"},"links":{"citing_paper":"/paper/2412.16756"},"observation_digest":"sha256:10e95c679caab69a746011955a816a4f61b7c1e03ac14aa0fe6fd493c6d53cec","observation_id":"534cdee6-ff87-4bc2-b7bf-926917afefac","resolution":{"observed_at":"2026-08-11T10:27:12.409568Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-08-11T10:27:12.385099Z","title":"Behrndt, S","venue":null,"work_id":"7a71fef2-58f6-4da9-89eb-52bda9d14e46","year":null},"citing_paper":{"arxiv_id":"2412.16756","last_updated":"2024-12-21T20:09:22Z","snapshot_observed_at":"2026-08-18T18:01:50.177493Z","submitted_at":"2024-12-21T20:09:22Z","title":"Resolvent and spectrum for discrete symplectic systems in the limit point case","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-11T10:27:11.687954Z"},"links":{"citing_paper":"/paper/2412.16756"},"observation_digest":"sha256:9760b6cd3881345ffd22fa468f0769ad7234079fcef6dcf5ad59bae7416da697","observation_id":"c3a51b49-4897-40c6-afcb-0ba983771b4f","resolution":{"observed_at":"2026-08-11T10:27:12.391411Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-08-11T10:27:12.365259Z","title":"Brunnhuber, J","venue":null,"work_id":"0e60481f-9437-4fa2-bfa5-3eb06deff2d7","year":2014},"citing_paper":{"arxiv_id":"2412.16756","last_updated":"2024-12-21T20:09:22Z","snapshot_observed_at":"2026-08-18T18:01:50.177493Z","submitted_at":"2024-12-21T20:09:22Z","title":"Resolvent and spectrum for discrete symplectic systems in the limit point case","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-11T10:27:11.693525Z"},"links":{"citing_paper":"/paper/2412.16756"},"observation_digest":"sha256:000b4bf6da0711fea4dd18607688e2b5f5d1dd2cb683f2dc8d7f2f0e342e5327","observation_id":"c26e070c-4a9d-4201-ba58-821e1deefa63","resolution":{"observed_at":"2026-08-11T10:27:12.372361Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-08-11T10:27:12.345097Z","title":"Chaudhuri and W","venue":null,"work_id":"9e0eea9c-0821-494f-9d03-0d873576922a","year":1969},"citing_paper":{"arxiv_id":"2412.16756","last_updated":"2024-12-21T20:09:22Z","snapshot_observed_at":"2026-08-18T18:01:50.177493Z","submitted_at":"2024-12-21T20:09:22Z","title":"Resolvent and spectrum for discrete symplectic systems in the limit point case","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-11T10:27:11.699300Z"},"links":{"citing_paper":"/paper/2412.16756"},"observation_digest":"sha256:723e880e2fbbbf293a13e4370597ca2a449945542ef53844f66366ebd4065279","observation_id":"6eed148f-15f3-402e-93d2-d85521d41258","resolution":{"observed_at":"2026-08-11T10:27:12.351831Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-08-11T10:27:12.324887Z","title":null,"venue":null,"work_id":"db73508c-2f98-4771-8f23-5d788f620aa3","year":2010},"citing_paper":{"arxiv_id":"2412.16756","last_updated":"2024-12-21T20:09:22Z","snapshot_observed_at":"2026-08-18T18:01:50.177493Z","submitted_at":"2024-12-21T20:09:22Z","title":"Resolvent and spectrum for discrete symplectic systems in the limit point case","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-11T10:27:11.704855Z"},"links":{"citing_paper":"/paper/2412.16756"},"observation_digest":"sha256:ef742a92b046ab25af1a764d1145384aaf532aa7cc9278fa519a4c91d5c8ecac","observation_id":"70548e4d-2722-4e51-8bb2-c7d24f59ab1a","resolution":{"observed_at":"2026-08-11T10:27:12.330526Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-08-11T10:27:11.710191Z","title":null,"venue":null,"work_id":null,"year":2015},"citing_paper":{"arxiv_id":"2412.16756","last_updated":"2024-12-21T20:09:22Z","snapshot_observed_at":"2026-08-18T18:01:50.177493Z","submitted_at":"2024-12-21T20:09:22Z","title":"Resolvent and spectrum for discrete symplectic systems in the limit point case","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-11T10:27:11.710191Z"},"links":{"citing_paper":"/paper/2412.16756"},"observation_digest":"sha256:02f910b9189bb86f9cf90ae702dbb8ec09746475b9d500214847a62227fd62e9","observation_id":"f464bfaf-787c-4013-afac-634de22554dc","resolution":{"observed_at":"2026-08-11T10:27:11.710191Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T10:27:11.715858Z","title":"Došlý, J","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2412.16756","last_updated":"2024-12-21T20:09:22Z","snapshot_observed_at":"2026-08-18T18:01:50.177493Z","submitted_at":"2024-12-21T20:09:22Z","title":"Resolvent and spectrum for discrete symplectic systems in the limit point case","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-11T10:27:11.715858Z"},"links":{"citing_paper":"/paper/2412.16756"},"observation_digest":"sha256:948309b92d58a1c22998d56d81ddc9755b28650cc79c802c7cdef7904fd3985d","observation_id":"409c7200-a952-4861-ba79-e3407d1d63dc","resolution":{"observed_at":"2026-08-11T10:27:11.715858Z","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":"2026-08-11T10:27:12.282152Z","title":"Advances in Difference Equations, IV","venue":null,"work_id":"63b25d0f-8a3c-44c3-abac-c48ecd80459d","year":2003},"citing_paper":{"arxiv_id":"2412.16756","last_updated":"2024-12-21T20:09:22Z","snapshot_observed_at":"2026-08-18T18:01:50.177493Z","submitted_at":"2024-12-21T20:09:22Z","title":"Resolvent and spectrum for discrete symplectic systems in the limit point case","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-11T10:27:11.721166Z"},"links":{"citing_paper":"/paper/2412.16756"},"observation_digest":"sha256:e024a14678b60815c92f1bf18065e340a26902f7d5572f4eee1870c03cc7d907","observation_id":"9b774ae6-a1ee-4b73-8ca4-bdb957f1f8c2","resolution":{"observed_at":"2026-08-11T10:27:12.288183Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-08-11T10:27:11.726260Z","title":"Gesztesy and E","venue":null,"work_id":null,"year":2000},"citing_paper":{"arxiv_id":"2412.16756","last_updated":"2024-12-21T20:09:22Z","snapshot_observed_at":"2026-08-18T18:01:50.177493Z","submitted_at":"2024-12-21T20:09:22Z","title":"Resolvent and spectrum for discrete symplectic systems in the limit point case","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-11T10:27:11.726260Z"},"links":{"citing_paper":"/paper/2412.16756"},"observation_digest":"sha256:2be5d1865fc2e5cdc4649431bb70fee1c78ed32cdb607eb717b10127e07be076","observation_id":"c009c953-2c70-4f82-9ad7-24d5001b8f68","resolution":{"observed_at":"2026-08-11T10:27:11.726260Z","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":"2026-08-11T10:27:12.239996Z","title":null,"venue":null,"work_id":"9a20f214-0ac4-404e-8317-2ee6847efb25","year":1975},"citing_paper":{"arxiv_id":"2412.16756","last_updated":"2024-12-21T20:09:22Z","snapshot_observed_at":"2026-08-18T18:01:50.177493Z","submitted_at":"2024-12-21T20:09:22Z","title":"Resolvent and spectrum for discrete symplectic systems in the limit point case","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-11T10:27:11.731645Z"},"links":{"citing_paper":"/paper/2412.16756"},"observation_digest":"sha256:65ac69989e061bf6509c0a064fdd8db80f65c4e3000ad09984d1829e537f066e","observation_id":"7c5deaa6-2ef6-40ab-9474-cd01003c2298","resolution":{"observed_at":"2026-08-11T10:27:12.246420Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-08-11T10:27:12.222157Z","title":null,"venue":null,"work_id":"d82f8af8-04db-4cbc-a3e9-04f710a77fa4","year":1978},"citing_paper":{"arxiv_id":"2412.16756","last_updated":"2024-12-21T20:09:22Z","snapshot_observed_at":"2026-08-18T18:01:50.177493Z","submitted_at":"2024-12-21T20:09:22Z","title":"Resolvent and spectrum for discrete symplectic systems in the limit point case","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-11T10:27:11.737451Z"},"links":{"citing_paper":"/paper/2412.16756"},"observation_digest":"sha256:1e6960e2a82625e1f3266041213bfafa078708dd2d6888ca773efb79dfb66658","observation_id":"46d149d4-ad3c-4d2f-b21f-e921cece7537","resolution":{"observed_at":"2026-08-11T10:27:12.227689Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-08-11T10:27:12.203576Z","title":null,"venue":null,"work_id":"8adb42dd-f7b0-41e3-b356-7267fa78f9c8","year":1979},"citing_paper":{"arxiv_id":"2412.16756","last_updated":"2024-12-21T20:09:22Z","snapshot_observed_at":"2026-08-18T18:01:50.177493Z","submitted_at":"2024-12-21T20:09:22Z","title":"Resolvent and spectrum for discrete symplectic systems in the limit point case","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-11T10:27:11.742989Z"},"links":{"citing_paper":"/paper/2412.16756"},"observation_digest":"sha256:7b8e87f21b3fb00a6d49c987ac17c61636822c03f7923e6a2607119201bf8375","observation_id":"95ba255c-176e-431d-93f9-b3cc2662abf1","resolution":{"observed_at":"2026-08-11T10:27:12.208905Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-08-11T10:27:12.183126Z","title":null,"venue":null,"work_id":"1b7d8b7c-9b31-4619-aa72-3daeb1536ab4","year":1982},"citing_paper":{"arxiv_id":"2412.16756","last_updated":"2024-12-21T20:09:22Z","snapshot_observed_at":"2026-08-18T18:01:50.177493Z","submitted_at":"2024-12-21T20:09:22Z","title":"Resolvent and spectrum for discrete symplectic systems in the limit point case","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-11T10:27:11.749006Z"},"links":{"citing_paper":"/paper/2412.16756"},"observation_digest":"sha256:62df54e0ce5a167d46bce73d9439c603d7ea61559f9a0f077c6667d35304090f","observation_id":"668209be-8eba-4329-a787-bba2e0cab156","resolution":{"observed_at":"2026-08-11T10:27:12.190351Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-08-11T10:27:12.163054Z","title":null,"venue":null,"work_id":"97694ce1-4337-44e6-8b87-360db04ce1de","year":2019},"citing_paper":{"arxiv_id":"2412.16756","last_updated":"2024-12-21T20:09:22Z","snapshot_observed_at":"2026-08-18T18:01:50.177493Z","submitted_at":"2024-12-21T20:09:22Z","title":"Resolvent and spectrum for discrete symplectic systems in the limit point case","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-11T10:27:11.754323Z"},"links":{"citing_paper":"/paper/2412.16756"},"observation_digest":"sha256:9eeba8a31db0d5283bc794260f506d70f3990cb4eb532e01a41daf43c8c62836","observation_id":"a8e0840f-5c3e-4c93-a13f-2b99713d3bc4","resolution":{"observed_at":"2026-08-11T10:27:12.168925Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-08-11T10:27:12.143238Z","title":null,"venue":null,"work_id":"1fbe0679-75fe-4c4d-bcd8-d96caf90dd51","year":2017},"citing_paper":{"arxiv_id":"2412.16756","last_updated":"2024-12-21T20:09:22Z","snapshot_observed_at":"2026-08-18T18:01:50.177493Z","submitted_at":"2024-12-21T20:09:22Z","title":"Resolvent and spectrum for discrete symplectic systems in the limit point case","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-11T10:27:11.760583Z"},"links":{"citing_paper":"/paper/2412.16756"},"observation_digest":"sha256:4579764cb6be805171fabb28a7f8b87a8bab9584908ef995354ecead76a4160a","observation_id":"6a2b3cf8-cad0-41de-864d-2f5dabb7ade5","resolution":{"observed_at":"2026-08-11T10:27:12.150473Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-08-11T10:27:12.122789Z","title":"Rudin, Principles of Mathematical Analysis , third edition, McGraw–Hill Book, New Y ork,","venue":null,"work_id":"365c0545-5f90-4391-8522-4770260ae95e","year":null},"citing_paper":{"arxiv_id":"2412.16756","last_updated":"2024-12-21T20:09:22Z","snapshot_observed_at":"2026-08-18T18:01:50.177493Z","submitted_at":"2024-12-21T20:09:22Z","title":"Resolvent and spectrum for discrete symplectic systems in the limit point case","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-11T10:27:11.766522Z"},"links":{"citing_paper":"/paper/2412.16756"},"observation_digest":"sha256:c77fee413697bb2849157ceb2af189ede4500d4e436a1904a9319ad8e904de92","observation_id":"2cd01e24-cd00-45e8-af7b-889bfc9200b4","resolution":{"observed_at":"2026-08-11T10:27:12.128892Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-08-11T10:27:11.779650Z","title":"Shi, Weyl–Titchmarsh theory for a class of discrete linear Hamil tonian systems, Linear Alge- bra Appl","venue":null,"work_id":null,"year":2006},"citing_paper":{"arxiv_id":"2412.16756","last_updated":"2024-12-21T20:09:22Z","snapshot_observed_at":"2026-08-18T18:01:50.177493Z","submitted_at":"2024-12-21T20:09:22Z","title":"Resolvent and spectrum for discrete symplectic systems in the limit point case","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-11T10:27:11.779650Z"},"links":{"citing_paper":"/paper/2412.16756"},"observation_digest":"sha256:9ea8f4b7c3151f19ad525161eebf16cd1c070785a7381c3c9f7a1726872bb81f","observation_id":"c16e5850-49e2-4c8b-b4b7-af906c1207c0","resolution":{"observed_at":"2026-08-11T10:27:11.779650Z","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":"2026-08-11T10:27:12.080930Z","title":"Theory and Applications of Difference – 26 – REFERENCES Equations and Discrete Dynamical Systems","venue":null,"work_id":"12965269-83da-4ee7-895d-4b1d6f38f63a","year":2014},"citing_paper":{"arxiv_id":"2412.16756","last_updated":"2024-12-21T20:09:22Z","snapshot_observed_at":"2026-08-18T18:01:50.177493Z","submitted_at":"2024-12-21T20:09:22Z","title":"Resolvent and spectrum for discrete symplectic systems in the limit point case","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-11T10:27:11.785107Z"},"links":{"citing_paper":"/paper/2412.16756"},"observation_digest":"sha256:810c101dcb9f91913e3d90d1700f1ba035f77aec82c83c3bcd95f5b4b7de1f86","observation_id":"95dc9e9b-a382-456f-8539-f36d93237cea","resolution":{"observed_at":"2026-08-11T10:27:12.087187Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-08-11T10:27:11.790438Z","title":"Šimon Hilscher and P","venue":null,"work_id":null,"year":2014},"citing_paper":{"arxiv_id":"2412.16756","last_updated":"2024-12-21T20:09:22Z","snapshot_observed_at":"2026-08-18T18:01:50.177493Z","submitted_at":"2024-12-21T20:09:22Z","title":"Resolvent and spectrum for discrete symplectic systems in the limit point case","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-11T10:27:11.790438Z"},"links":{"citing_paper":"/paper/2412.16756"},"observation_digest":"sha256:3bc172dca84bda41727c34b305d853cc6f02df4397b74339011bbbe5b5974add","observation_id":"52094e35-13df-4680-946f-54155b52f731","resolution":{"observed_at":"2026-08-11T10:27:11.790438Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T10:27:11.797724Z","title":"Šimon Hilscher and P","venue":null,"work_id":null,"year":2014},"citing_paper":{"arxiv_id":"2412.16756","last_updated":"2024-12-21T20:09:22Z","snapshot_observed_at":"2026-08-18T18:01:50.177493Z","submitted_at":"2024-12-21T20:09:22Z","title":"Resolvent and spectrum for discrete symplectic systems in the limit point case","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-11T10:27:11.797724Z"},"links":{"citing_paper":"/paper/2412.16756"},"observation_digest":"sha256:f24818177047f08dceebb44cced7a85d5977fe611cad15f048d4c776726dd2a9","observation_id":"6a0ca888-fdea-4dec-9351-179b90c7af76","resolution":{"observed_at":"2026-08-11T10:27:11.797724Z","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":"2026-08-11T10:27:12.037799Z","title":null,"venue":null,"work_id":"5561b2c0-66f8-4ef7-a32d-736f26676e65","year":1991},"citing_paper":{"arxiv_id":"2412.16756","last_updated":"2024-12-21T20:09:22Z","snapshot_observed_at":"2026-08-18T18:01:50.177493Z","submitted_at":"2024-12-21T20:09:22Z","title":"Resolvent and spectrum for discrete symplectic systems in the limit point case","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-11T10:27:11.802849Z"},"links":{"citing_paper":"/paper/2412.16756"},"observation_digest":"sha256:cd80811abd454cec99e4e2259dc42714ca3d52c5f5690e170600a683e54f057e","observation_id":"dc9f7ee7-abf1-4b7e-9b15-494dd3823c5c","resolution":{"observed_at":"2026-08-11T10:27:12.043962Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-08-11T10:27:12.020837Z","title":null,"venue":null,"work_id":"ef20067a-d3e5-42c5-a10b-e02bdbd2d0e0","year":2016},"citing_paper":{"arxiv_id":"2412.16756","last_updated":"2024-12-21T20:09:22Z","snapshot_observed_at":"2026-08-18T18:01:50.177493Z","submitted_at":"2024-12-21T20:09:22Z","title":"Resolvent and spectrum for discrete symplectic systems in the limit point case","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-11T10:27:11.807684Z"},"links":{"citing_paper":"/paper/2412.16756"},"observation_digest":"sha256:61ff2c6c9c5a2e1feb583a0e0fecd837c843a3accc6516d8921c5456fb11705b","observation_id":"f4e7af79-16eb-44f0-947f-21d55baedaf0","resolution":{"observed_at":"2026-08-11T10:27:12.026250Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-08-11T10:27:12.002572Z","title":"Sun and Y","venue":null,"work_id":"99010382-f185-4fb2-9ffd-0ef11882d8d7","year":2014},"citing_paper":{"arxiv_id":"2412.16756","last_updated":"2024-12-21T20:09:22Z","snapshot_observed_at":"2026-08-18T18:01:50.177493Z","submitted_at":"2024-12-21T20:09:22Z","title":"Resolvent and spectrum for discrete symplectic systems in the limit point case","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-11T10:27:11.813491Z"},"links":{"citing_paper":"/paper/2412.16756"},"observation_digest":"sha256:bb23eaa9b41298752e1b504316cc47881c654472f5d825860ff159993e0822b7","observation_id":"674621f8-549e-4ff3-bf3a-07b2f4f94e5d","resolution":{"observed_at":"2026-08-11T10:27:12.008413Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-08-11T10:27:11.984651Z","title":"Sun and Y","venue":null,"work_id":"4c5463d4-b802-454d-8d62-610f1ba5463d","year":2015},"citing_paper":{"arxiv_id":"2412.16756","last_updated":"2024-12-21T20:09:22Z","snapshot_observed_at":"2026-08-18T18:01:50.177493Z","submitted_at":"2024-12-21T20:09:22Z","title":"Resolvent and spectrum for discrete symplectic systems in the limit point case","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-11T10:27:11.819032Z"},"links":{"citing_paper":"/paper/2412.16756"},"observation_digest":"sha256:0e334b3206499dbee8eaeed98928ade6a38e245b517f482ce06b238a039964fd","observation_id":"e995d84d-a321-4bba-9c8b-ee8ac6373eee","resolution":{"observed_at":"2026-08-11T10:27:11.989731Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-08-11T10:27:11.967193Z","title":null,"venue":null,"work_id":"50a7d31b-05be-4156-8fe8-cdef8894d141","year":1951},"citing_paper":{"arxiv_id":"2412.16756","last_updated":"2024-12-21T20:09:22Z","snapshot_observed_at":"2026-08-18T18:01:50.177493Z","submitted_at":"2024-12-21T20:09:22Z","title":"Resolvent and spectrum for discrete symplectic systems in the limit point case","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-11T10:27:11.825375Z"},"links":{"citing_paper":"/paper/2412.16756"},"observation_digest":"sha256:aa3dc613ddebbcd33da2dbd1b4ddd3382efac96fdd303d6d69c741c734b3d191","observation_id":"888e1796-93ab-4ce8-9dd2-65551ced3a1c","resolution":{"observed_at":"2026-08-11T10:27:11.972866Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-08-11T10:27:11.830902Z","title":"Progress on Difference Equations and Discrete Dynamic al Systems","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2412.16756","last_updated":"2024-12-21T20:09:22Z","snapshot_observed_at":"2026-08-18T18:01:50.177493Z","submitted_at":"2024-12-21T20:09:22Z","title":"Resolvent and spectrum for discrete symplectic systems in the limit point case","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-11T10:27:11.830902Z"},"links":{"citing_paper":"/paper/2412.16756"},"observation_digest":"sha256:cfed99c72accacd2682a147a629f82e670b032b5c1add7c6c1e827c613f51ecf","observation_id":"17da9a21-f964-402f-9692-f20466ccf2ee","resolution":{"observed_at":"2026-08-11T10:27:11.830902Z","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":"2026-08-11T10:27:11.938512Z","title":"Zemánek, Eigenfunctions expansion for discrete symplectic systems with general linear de- pendence on spectral parameter , J","venue":null,"work_id":"37a369a7-a725-4f17-950f-52b5b67868a7","year":2021},"citing_paper":{"arxiv_id":"2412.16756","last_updated":"2024-12-21T20:09:22Z","snapshot_observed_at":"2026-08-18T18:01:50.177493Z","submitted_at":"2024-12-21T20:09:22Z","title":"Resolvent and spectrum for discrete symplectic systems in the limit point case","version":1},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-11T10:27:11.836861Z"},"links":{"citing_paper":"/paper/2412.16756"},"observation_digest":"sha256:d86e32a50f390a6638ff6b84144423e4b32ec365e1b72f825569b30c18e88f1e","observation_id":"9b9aaf8a-ba52-4207-b856-846d78c04bed","resolution":{"observed_at":"2026-08-11T10:27:11.944398Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-08-11T10:27:11.917562Z","title":"Zemánek, Non-limit-circle and limit-point criteria for symplectic dynamic systems on time scales, Math","venue":null,"work_id":"1e6415da-b3db-45cc-8c7f-c01e11a7095a","year":null},"citing_paper":{"arxiv_id":"2412.16756","last_updated":"2024-12-21T20:09:22Z","snapshot_observed_at":"2026-08-18T18:01:50.177493Z","submitted_at":"2024-12-21T20:09:22Z","title":"Resolvent and spectrum for discrete symplectic systems in the limit point case","version":1},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-11T10:27:11.842439Z"},"links":{"citing_paper":"/paper/2412.16756"},"observation_digest":"sha256:25dc3933a295e13ecbadc2057796b4cf419ec24f4d708b4442870b10191e19c1","observation_id":"360b231c-4231-4657-98c6-fad706bfeb10","resolution":{"observed_at":"2026-08-11T10:27:11.925484Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-08-11T10:27:11.851772Z","title":"Zemánek and S","venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2412.16756","last_updated":"2024-12-21T20:09:22Z","snapshot_observed_at":"2026-08-18T18:01:50.177493Z","submitted_at":"2024-12-21T20:09:22Z","title":"Resolvent and spectrum for discrete symplectic systems in the limit point case","version":1},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-11T10:27:11.851772Z"},"links":{"citing_paper":"/paper/2412.16756"},"observation_digest":"sha256:ca49ca8ef91b47514f5718d2b0f2211b46bc51a57fd78095911720d0f151411a","observation_id":"ff4d5546-1df6-4b21-8344-be6d3a98ac3c","resolution":{"observed_at":"2026-08-11T10:27:11.851772Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T10:27:11.857077Z","title":"Zemánek and S","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2412.16756","last_updated":"2024-12-21T20:09:22Z","snapshot_observed_at":"2026-08-18T18:01:50.177493Z","submitted_at":"2024-12-21T20:09:22Z","title":"Resolvent and spectrum for discrete symplectic systems in the limit point case","version":1},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-11T10:27:11.857077Z"},"links":{"citing_paper":"/paper/2412.16756"},"observation_digest":"sha256:9be21bb7a51675542632dbeeb17f721a7b8a0d13a631d2f6a819a098fa85e924","observation_id":"98f467ab-552a-4f21-b50b-977d0f50fd17","resolution":{"observed_at":"2026-08-11T10:27:11.857077Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T10:27:11.773537Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2412.16756","last_updated":"2024-12-21T20:09:22Z","snapshot_observed_at":"2026-08-18T18:01:50.177493Z","submitted_at":"2024-12-21T20:09:22Z","title":"Resolvent and spectrum for discrete symplectic systems in the limit point case","version":1},"reference_index":1976,"source":"pdf_text","source_observed_at":"2026-08-11T10:27:11.773537Z"},"links":{"citing_paper":"/paper/2412.16756"},"observation_digest":"sha256:7f3f1fda4070ceaa724d7653daa1e3c1d8a39bbcb36eba5682f47ddd40ee7cfc","observation_id":"a867b638-6c1a-4b7c-968e-ced226571639","resolution":{"observed_at":"2026-08-11T10:27:11.773537Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2412.16756","last_updated":"2024-12-21T20:09:22Z","latest_version":1,"primary_category":"math.SP","snapshot_observed_at":"2026-08-18T18:01:50.177493Z","submitted_at":"2024-12-21T20:09:22Z","title":"Resolvent and spectrum for discrete symplectic systems in the limit point case"},"reference_resolution":{"displayed":32,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":21,"verified_exact":0,"verified_fuzzy":11},"total_outbound_references":32},"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":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"thesis":"As of 23 August 2026, this Paper Citation Record lists 32 of 32 outbound references and 0 inbound Pith citation observations for arXiv:2412.16756."}