{"as_of":"2026-08-14T01:22:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:8bde3a5f995c0f10e77f95abcdb88ce1d608ad628e7384c912081aae4d9ff065","coverage":[{"denominator":36,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":36,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-10T23:10:24.119619Z","state":"measured"},{"denominator":36,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":36,"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/2501.00121/citation-record","integrity":"/paper/2501.00121/integrity","json":"/paper/2501.00121/citation-record.json","paper":"/paper/2501.00121"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T23:10:24.666651Z","title":"Inverse scattering transform for the integrable discrete nonlinear Schr¨ odinger equation with non-vanishing boundary conditions","venue":null,"work_id":"6f5ea1a6-f074-430d-9b6e-0f6bffb9e9cd","year":2007},"citing_paper":{"arxiv_id":"2501.00121","last_updated":"2024-12-30T19:41:20Z","snapshot_observed_at":"2026-08-13T18:21:12.428826Z","submitted_at":"2024-12-30T19:41:20Z","title":"On the discrete Kuznetsov-Ma solutions for the defocusing Ablowitz-Ladik equation with large background amplitude","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-10T23:10:23.971031Z"},"links":{"citing_paper":"/paper/2501.00121"},"observation_digest":"sha256:3a745edf417b91a22cb031a4a01f1d6b80d04b43899f940d5a655ec64c336208","observation_id":"89a54a87-b5a9-4ddf-9e5b-3c4dd39855a1","resolution":{"observed_at":"2026-08-10T23:10:24.670872Z","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":"2026-08-10T23:10:24.653097Z","title":"Nonlinear differential-difference equations","venue":null,"work_id":"d801e658-c97e-44b6-9ca8-c0d997fd4209","year":1975},"citing_paper":{"arxiv_id":"2501.00121","last_updated":"2024-12-30T19:41:20Z","snapshot_observed_at":"2026-08-13T18:21:12.428826Z","submitted_at":"2024-12-30T19:41:20Z","title":"On the discrete Kuznetsov-Ma solutions for the defocusing Ablowitz-Ladik equation with large background amplitude","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-10T23:10:23.975874Z"},"links":{"citing_paper":"/paper/2501.00121"},"observation_digest":"sha256:1d277638fc7ebd0fd37fa3f4c1b9d4fe3738180a47b42bd64306b47f9c2b7894","observation_id":"7663cc94-cbe3-47be-8a81-7ded791eb5d0","resolution":{"observed_at":"2026-08-10T23:10:24.657280Z","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":"2026-08-10T23:10:24.639576Z","title":"Nonlinear differential-difference equations and Fourier analysis","venue":null,"work_id":"4a597663-c668-45f2-8d6d-d2d63bc0d13f","year":1976},"citing_paper":{"arxiv_id":"2501.00121","last_updated":"2024-12-30T19:41:20Z","snapshot_observed_at":"2026-08-13T18:21:12.428826Z","submitted_at":"2024-12-30T19:41:20Z","title":"On the discrete Kuznetsov-Ma solutions for the defocusing Ablowitz-Ladik equation with large background amplitude","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-10T23:10:23.980162Z"},"links":{"citing_paper":"/paper/2501.00121"},"observation_digest":"sha256:f2c50845c6e7bd79977eba72f0cf24080a254f1a38758f779c96215408e4acd8","observation_id":"c3f194df-b75f-4e48-88f5-28cd949bce13","resolution":{"observed_at":"2026-08-10T23:10:24.643801Z","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":"2026-08-10T23:10:24.624880Z","title":null,"venue":null,"work_id":"30cdeada-6a7b-459c-8f33-57f14958d095","year":2004},"citing_paper":{"arxiv_id":"2501.00121","last_updated":"2024-12-30T19:41:20Z","snapshot_observed_at":"2026-08-13T18:21:12.428826Z","submitted_at":"2024-12-30T19:41:20Z","title":"On the discrete Kuznetsov-Ma solutions for the defocusing Ablowitz-Ladik equation with large background amplitude","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-10T23:10:23.984731Z"},"links":{"citing_paper":"/paper/2501.00121"},"observation_digest":"sha256:f949b708b0ab6a2378342d67f73f4a6b4736179a8d01effd14c8422452557b52","observation_id":"b289be8a-d2ca-421c-bbf1-8d55af72393b","resolution":{"observed_at":"2026-08-10T23:10:24.629642Z","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":"2026-08-10T23:10:24.610112Z","title":"Rogue waves and rational solutions of the nonlinear Schr¨ odinger equation","venue":null,"work_id":"3ae7c23f-f95e-4085-b125-b9394839c4b3","year":2009},"citing_paper":{"arxiv_id":"2501.00121","last_updated":"2024-12-30T19:41:20Z","snapshot_observed_at":"2026-08-13T18:21:12.428826Z","submitted_at":"2024-12-30T19:41:20Z","title":"On the discrete Kuznetsov-Ma solutions for the defocusing Ablowitz-Ladik equation with large background amplitude","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-10T23:10:23.988952Z"},"links":{"citing_paper":"/paper/2501.00121"},"observation_digest":"sha256:63cd0e48ece61a96342554457c1d0d3f51d11245d96b653599df3ab5bc932276","observation_id":"29b96245-b451-4963-9e3c-f417195ced37","resolution":{"observed_at":"2026-08-10T23:10:24.615062Z","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":"2026-08-10T23:10:24.595377Z","title":"Waves that appear from nowhere and disappear without a trace","venue":null,"work_id":"119e1449-5543-424a-95d7-ab024ed91409","year":2009},"citing_paper":{"arxiv_id":"2501.00121","last_updated":"2024-12-30T19:41:20Z","snapshot_observed_at":"2026-08-13T18:21:12.428826Z","submitted_at":"2024-12-30T19:41:20Z","title":"On the discrete Kuznetsov-Ma solutions for the defocusing Ablowitz-Ladik equation with large background amplitude","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-10T23:10:23.993840Z"},"links":{"citing_paper":"/paper/2501.00121"},"observation_digest":"sha256:75c96c6783e65fe25a00d975dd6fc12161ebab8b0f99e2ecdff09af8820cd8ee","observation_id":"22290d99-669a-4e52-aa9a-ad81f45c0c95","resolution":{"observed_at":"2026-08-10T23:10:24.600482Z","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":"2026-08-10T23:10:24.581837Z","title":"Generation of a periodic sequence of picosecond pulses in an optical fiber. Exact solutions","venue":null,"work_id":"10c5df07-0c5c-4c8a-afcf-c0693f25f27d","year":1985},"citing_paper":{"arxiv_id":"2501.00121","last_updated":"2024-12-30T19:41:20Z","snapshot_observed_at":"2026-08-13T18:21:12.428826Z","submitted_at":"2024-12-30T19:41:20Z","title":"On the discrete Kuznetsov-Ma solutions for the defocusing Ablowitz-Ladik equation with large background amplitude","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-10T23:10:23.998837Z"},"links":{"citing_paper":"/paper/2501.00121"},"observation_digest":"sha256:572be96c2d0874531f52e92242bb4bce6a12ec7ba60522a859f95c638d061736","observation_id":"85220c6d-6033-47ea-b303-9e98912ecbec","resolution":{"observed_at":"2026-08-10T23:10:24.586035Z","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":"2026-08-10T23:10:24.568188Z","title":"Modulational instability and periodic solutions of the nonlinear Schr¨ odinger equation","venue":null,"work_id":"3e1e101f-304e-424d-b72c-56e86eb1d929","year":1987},"citing_paper":{"arxiv_id":"2501.00121","last_updated":"2024-12-30T19:41:20Z","snapshot_observed_at":"2026-08-13T18:21:12.428826Z","submitted_at":"2024-12-30T19:41:20Z","title":"On the discrete Kuznetsov-Ma solutions for the defocusing Ablowitz-Ladik equation with large background amplitude","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-10T23:10:24.002896Z"},"links":{"citing_paper":"/paper/2501.00121"},"observation_digest":"sha256:21cdf05de2af7caa22f4396f96d44c83c9c650ef9ed1b68a7c5bed220bade275","observation_id":"3331cb85-f457-40b7-8ccb-70d8af21a0e4","resolution":{"observed_at":"2026-08-10T23:10:24.572660Z","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":"2026-08-10T23:10:24.553828Z","title":"Discrete rogue waves of the Ablowitz-Ladik and Hirota equations","venue":null,"work_id":"083c3215-05cf-40be-be1a-6f79d71d3103","year":2010},"citing_paper":{"arxiv_id":"2501.00121","last_updated":"2024-12-30T19:41:20Z","snapshot_observed_at":"2026-08-13T18:21:12.428826Z","submitted_at":"2024-12-30T19:41:20Z","title":"On the discrete Kuznetsov-Ma solutions for the defocusing Ablowitz-Ladik equation with large background amplitude","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-10T23:10:24.006849Z"},"links":{"citing_paper":"/paper/2501.00121"},"observation_digest":"sha256:c9cc2495de3910ae7e311b98156eaa49deb7ccb8758487f6dfc663fcac094d50","observation_id":"654e7e74-3eb6-4313-ab5c-310287bb721e","resolution":{"observed_at":"2026-08-10T23:10:24.558554Z","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":"2026-08-10T23:10:24.539628Z","title":"Rogue waves and other solutions of single and coupled Ablowitz-Ladik and nonlinear Schr¨ odinger equations","venue":null,"work_id":"2600b0b9-505e-4e50-9e46-03f86152e655","year":2013},"citing_paper":{"arxiv_id":"2501.00121","last_updated":"2024-12-30T19:41:20Z","snapshot_observed_at":"2026-08-13T18:21:12.428826Z","submitted_at":"2024-12-30T19:41:20Z","title":"On the discrete Kuznetsov-Ma solutions for the defocusing Ablowitz-Ladik equation with large background amplitude","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-10T23:10:24.010753Z"},"links":{"citing_paper":"/paper/2501.00121"},"observation_digest":"sha256:909f6009a1ec61f5ca9431a0a364db140e9b6daa8b191de9448ac474cc824d6d","observation_id":"e279a267-ff70-4a90-80d0-7be786f4877d","resolution":{"observed_at":"2026-08-10T23:10:24.544296Z","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":"2026-08-10T23:10:24.525811Z","title":null,"venue":null,"work_id":"aaa4f4c7-877e-4a77-8be5-ee71c37cef7a","year":1996},"citing_paper":{"arxiv_id":"2501.00121","last_updated":"2024-12-30T19:41:20Z","snapshot_observed_at":"2026-08-13T18:21:12.428826Z","submitted_at":"2024-12-30T19:41:20Z","title":"On the discrete Kuznetsov-Ma solutions for the defocusing Ablowitz-Ladik equation with large background amplitude","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-10T23:10:24.014927Z"},"links":{"citing_paper":"/paper/2501.00121"},"observation_digest":"sha256:8873c5efdc7622b4a8d769146366fc9ffc8c70d2b293b538df35a1df0e14c3b8","observation_id":"a5e8a4aa-2678-4da4-b477-9ebd8e94eb3f","resolution":{"observed_at":"2026-08-10T23:10:24.530215Z","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":"2026-08-10T23:10:24.510816Z","title":"Existence, stability and spatio-temporal dynamics of time-quasiperiodic solutions on a finite back- ground in discrete nonlinear Schr¨ odinger models","venue":null,"work_id":"4695d050-1fc7-461a-9d9e-55577fd1b92a","year":2024},"citing_paper":{"arxiv_id":"2501.00121","last_updated":"2024-12-30T19:41:20Z","snapshot_observed_at":"2026-08-13T18:21:12.428826Z","submitted_at":"2024-12-30T19:41:20Z","title":"On the discrete Kuznetsov-Ma solutions for the defocusing Ablowitz-Ladik equation with large background amplitude","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-10T23:10:24.018734Z"},"links":{"citing_paper":"/paper/2501.00121"},"observation_digest":"sha256:b8488a7e566f4d26386cbc73b967c1ae796af6f91ed0063bd787c433b38f486a","observation_id":"3d3b765a-d829-49a9-97c8-1b37e4953aa0","resolution":{"observed_at":"2026-08-10T23:10:24.515988Z","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":"2026-08-10T23:10:24.496548Z","title":"Rogue waves arising on the standing periodic waves in the Ablowitz- Ladik equation","venue":null,"work_id":"8ba3ad95-c5e4-4a4a-bd5f-e7bc23ddbec9","year":2024},"citing_paper":{"arxiv_id":"2501.00121","last_updated":"2024-12-30T19:41:20Z","snapshot_observed_at":"2026-08-13T18:21:12.428826Z","submitted_at":"2024-12-30T19:41:20Z","title":"On the discrete Kuznetsov-Ma solutions for the defocusing Ablowitz-Ladik equation with large background amplitude","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-10T23:10:24.023652Z"},"links":{"citing_paper":"/paper/2501.00121"},"observation_digest":"sha256:616053aa51b499a9e1af9d9d0d17c8a79158b71a370aa6ca5e7e7547039b8e08","observation_id":"99d119ac-cd88-4e46-8d47-0920bfb40d23","resolution":{"observed_at":"2026-08-10T23:10:24.501281Z","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":"2026-08-10T23:10:24.482506Z","title":"Some features of the repulsive discrete nonlinear Schr¨ odinger equation","venue":null,"work_id":"420271c1-bed2-48c2-b451-41241f4d92cc","year":1992},"citing_paper":{"arxiv_id":"2501.00121","last_updated":"2024-12-30T19:41:20Z","snapshot_observed_at":"2026-08-13T18:21:12.428826Z","submitted_at":"2024-12-30T19:41:20Z","title":"On the discrete Kuznetsov-Ma solutions for the defocusing Ablowitz-Ladik equation with large background amplitude","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-10T23:10:24.028112Z"},"links":{"citing_paper":"/paper/2501.00121"},"observation_digest":"sha256:8af8381d070cfaa5537d0368bcb0e549f43d14998776cfb7469aa99920ca481e","observation_id":"fa59cb7a-5562-4a34-9a7b-3baedfd0e290","resolution":{"observed_at":"2026-08-10T23:10:24.486785Z","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":"2026-08-10T23:10:24.469183Z","title":"Modulation instability, periodic anomalous wave recurrence, and blow up in the Ablowitz–Ladik lattices","venue":null,"work_id":"56cb53d3-b3d2-471f-9e0c-3680390a1402","year":2024},"citing_paper":{"arxiv_id":"2501.00121","last_updated":"2024-12-30T19:41:20Z","snapshot_observed_at":"2026-08-13T18:21:12.428826Z","submitted_at":"2024-12-30T19:41:20Z","title":"On the discrete Kuznetsov-Ma solutions for the defocusing Ablowitz-Ladik equation with large background amplitude","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-10T23:10:24.032080Z"},"links":{"citing_paper":"/paper/2501.00121"},"observation_digest":"sha256:0a46d581e866b45e4f41a327b2342a32a0b1945afe943396ba2b9bb62a87f5de","observation_id":"68c5d448-61dd-4692-906d-be4e8e6d215b","resolution":{"observed_at":"2026-08-10T23:10:24.473400Z","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":"2026-08-10T23:10:24.455185Z","title":"Floquet analysis of Kuznetsov-Ma breathers: A path towards spectral stability of rogue waves","venue":null,"work_id":"deffdd2e-2c83-47f3-a7c3-7abb10e0da21","year":2017},"citing_paper":{"arxiv_id":"2501.00121","last_updated":"2024-12-30T19:41:20Z","snapshot_observed_at":"2026-08-13T18:21:12.428826Z","submitted_at":"2024-12-30T19:41:20Z","title":"On the discrete Kuznetsov-Ma solutions for the defocusing Ablowitz-Ladik equation with large background amplitude","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-10T23:10:24.036081Z"},"links":{"citing_paper":"/paper/2501.00121"},"observation_digest":"sha256:7a96842e49d64c2f7762e8557fd564518d116895028f89f9d0278456a5f9ef87","observation_id":"9cd6a9e6-7cbb-4d2b-b405-266be11e87de","resolution":{"observed_at":"2026-08-10T23:10:24.459695Z","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":"2026-08-10T23:10:24.440079Z","title":"Integrable dynamics of a discrete curve and the Ablowitz-Ladik hier- archy","venue":null,"work_id":"27d4129a-8700-43a5-9070-baf4790769bc","year":1995},"citing_paper":{"arxiv_id":"2501.00121","last_updated":"2024-12-30T19:41:20Z","snapshot_observed_at":"2026-08-13T18:21:12.428826Z","submitted_at":"2024-12-30T19:41:20Z","title":"On the discrete Kuznetsov-Ma solutions for the defocusing Ablowitz-Ladik equation with large background amplitude","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-10T23:10:24.040305Z"},"links":{"citing_paper":"/paper/2501.00121"},"observation_digest":"sha256:b0fa0c18648e730e2b7df92a2e05c2f9a89cd037775f7cd7f896c57ad9a74a56","observation_id":"78da121c-5814-4922-9059-00f2efcb7dca","resolution":{"observed_at":"2026-08-10T23:10:24.445036Z","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":"2026-08-10T23:10:24.419293Z","title":"Darboux transformation of the discrete Ablowitz-Ladik eigenvalue problem","venue":null,"work_id":"60f136df-816f-4930-a007-580552ee15d2","year":1989},"citing_paper":{"arxiv_id":"2501.00121","last_updated":"2024-12-30T19:41:20Z","snapshot_observed_at":"2026-08-13T18:21:12.428826Z","submitted_at":"2024-12-30T19:41:20Z","title":"On the discrete Kuznetsov-Ma solutions for the defocusing Ablowitz-Ladik equation with large background amplitude","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-10T23:10:24.044241Z"},"links":{"citing_paper":"/paper/2501.00121"},"observation_digest":"sha256:8d59f6d1414458e46ae24d36a76abc49270d7023b4b1eac8e4192328ab547e4a","observation_id":"e6ec3eec-1fc9-4a56-9eae-62a57800a30d","resolution":{"observed_at":"2026-08-10T23:10:24.424161Z","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":"2026-08-10T23:10:24.404805Z","title":"Solving Ordinary Differential Equations I: Nonstiff Prob- lems","venue":null,"work_id":"8b084a17-83d8-44b1-ac8c-37d96639045d","year":2008},"citing_paper":{"arxiv_id":"2501.00121","last_updated":"2024-12-30T19:41:20Z","snapshot_observed_at":"2026-08-13T18:21:12.428826Z","submitted_at":"2024-12-30T19:41:20Z","title":"On the discrete Kuznetsov-Ma solutions for the defocusing Ablowitz-Ladik equation with large background amplitude","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-10T23:10:24.048236Z"},"links":{"citing_paper":"/paper/2501.00121"},"observation_digest":"sha256:d9a0df9ac1c9d031a87dcfba6a0e1199c496aed8ce1c100d5aac2760389bf392","observation_id":"07f5385e-229e-463b-80cc-f8e6fc201622","resolution":{"observed_at":"2026-08-10T23:10:24.409617Z","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":"2026-08-10T23:10:24.390701Z","title":"An integrable classical spin chain","venue":null,"work_id":"d30bcfd8-2bd1-4b36-bd22-09e2c85717b3","year":1982},"citing_paper":{"arxiv_id":"2501.00121","last_updated":"2024-12-30T19:41:20Z","snapshot_observed_at":"2026-08-13T18:21:12.428826Z","submitted_at":"2024-12-30T19:41:20Z","title":"On the discrete Kuznetsov-Ma solutions for the defocusing Ablowitz-Ladik equation with large background amplitude","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-10T23:10:24.052507Z"},"links":{"citing_paper":"/paper/2501.00121"},"observation_digest":"sha256:1c1038307a44c47b9137b1486f9fedafc4177787459129eaf76b3acd06c3a013","observation_id":"29937ac9-c0fd-4d56-92ca-1274cbf9e372","resolution":{"observed_at":"2026-08-10T23:10:24.395426Z","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":"2026-08-10T23:10:24.376701Z","title":"Temperature correlations of quantum spins","venue":null,"work_id":"1878a1aa-cb41-4bf1-9951-dbb0764e20ae","year":1991},"citing_paper":{"arxiv_id":"2501.00121","last_updated":"2024-12-30T19:41:20Z","snapshot_observed_at":"2026-08-13T18:21:12.428826Z","submitted_at":"2024-12-30T19:41:20Z","title":"On the discrete Kuznetsov-Ma solutions for the defocusing Ablowitz-Ladik equation with large background amplitude","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-10T23:10:24.057229Z"},"links":{"citing_paper":"/paper/2501.00121"},"observation_digest":"sha256:f310ab4e66f687724b5a89f06072cbd4211c92cf979e7c03a03138be0785912a","observation_id":"50a21135-a800-4faf-af3a-4b9e2ee69c75","resolution":{"observed_at":"2026-08-10T23:10:24.381421Z","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":"2026-08-10T23:10:24.362572Z","title":null,"venue":null,"work_id":"f7ce65b8-2b6d-42a7-b129-174ccc490e06","year":2009},"citing_paper":{"arxiv_id":"2501.00121","last_updated":"2024-12-30T19:41:20Z","snapshot_observed_at":"2026-08-13T18:21:12.428826Z","submitted_at":"2024-12-30T19:41:20Z","title":"On the discrete Kuznetsov-Ma solutions for the defocusing Ablowitz-Ladik equation with large background amplitude","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-10T23:10:24.061678Z"},"links":{"citing_paper":"/paper/2501.00121"},"observation_digest":"sha256:1546ec45b737e29cab25aaaf2a6a90e91b11af489f6fc43bf7baf78143c37a06","observation_id":"a12425a0-0927-4562-babd-0175104809f3","resolution":{"observed_at":"2026-08-10T23:10:24.366889Z","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":"2026-08-10T23:10:24.348082Z","title":"Solitons in a parametrically unstable plasma","venue":null,"work_id":"1d487149-49ad-4b94-894b-cef59439d8a2","year":1977},"citing_paper":{"arxiv_id":"2501.00121","last_updated":"2024-12-30T19:41:20Z","snapshot_observed_at":"2026-08-13T18:21:12.428826Z","submitted_at":"2024-12-30T19:41:20Z","title":"On the discrete Kuznetsov-Ma solutions for the defocusing Ablowitz-Ladik equation with large background amplitude","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-10T23:10:24.066190Z"},"links":{"citing_paper":"/paper/2501.00121"},"observation_digest":"sha256:2f96cd8fdd32dc398cfa7093303111336819029879cc6b02cfff515aed442e48","observation_id":"3105f5df-e5e1-4e78-bc6b-9462de84bdff","resolution":{"observed_at":"2026-08-10T23:10:24.352634Z","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":"2026-08-10T23:10:24.333386Z","title":"Two soluble models of an antiferromagnetic chain","venue":null,"work_id":"368ce061-57d6-4d76-9a6f-eacfdea9278e","year":1961},"citing_paper":{"arxiv_id":"2501.00121","last_updated":"2024-12-30T19:41:20Z","snapshot_observed_at":"2026-08-13T18:21:12.428826Z","submitted_at":"2024-12-30T19:41:20Z","title":"On the discrete Kuznetsov-Ma solutions for the defocusing Ablowitz-Ladik equation with large background amplitude","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-10T23:10:24.070608Z"},"links":{"citing_paper":"/paper/2501.00121"},"observation_digest":"sha256:570737edcdfc76118bb5be99a293241e4e0d6c54ae6b0582d05f5ca333e8750c","observation_id":"1bb33c6b-93ec-4dec-81f8-8513261541a7","resolution":{"observed_at":"2026-08-10T23:10:24.338278Z","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":"2026-08-10T23:10:24.318966Z","title":"On the Ablowitz–Ladik equations with self-consistent sources","venue":null,"work_id":"4171dbdc-5230-4e21-8890-68c5e6547f9d","year":2007},"citing_paper":{"arxiv_id":"2501.00121","last_updated":"2024-12-30T19:41:20Z","snapshot_observed_at":"2026-08-13T18:21:12.428826Z","submitted_at":"2024-12-30T19:41:20Z","title":"On the discrete Kuznetsov-Ma solutions for the defocusing Ablowitz-Ladik equation with large background amplitude","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-10T23:10:24.075011Z"},"links":{"citing_paper":"/paper/2501.00121"},"observation_digest":"sha256:6939c250da83c19d29e43a548cb0282343f6901f758c7cfe802aae494f9dfea7","observation_id":"7e48fc88-6367-41a5-9436-2782271d9e3b","resolution":{"observed_at":"2026-08-10T23:10:24.323657Z","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":"2026-08-10T23:10:24.304176Z","title":"The perturbed plane-wave solutions of the cubic Schr¨ odinger equation","venue":null,"work_id":"71e10e03-baa4-4030-ac1c-45a6c29c3da8","year":1979},"citing_paper":{"arxiv_id":"2501.00121","last_updated":"2024-12-30T19:41:20Z","snapshot_observed_at":"2026-08-13T18:21:12.428826Z","submitted_at":"2024-12-30T19:41:20Z","title":"On the discrete Kuznetsov-Ma solutions for the defocusing Ablowitz-Ladik equation with large background amplitude","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-10T23:10:24.079286Z"},"links":{"citing_paper":"/paper/2501.00121"},"observation_digest":"sha256:20bbc9df1e10a4f0ce7b9621ef9ba82056743d9828a2761aefee4b47e73980e1","observation_id":"6b69f10e-d9da-458f-a364-5e41dc893bf3","resolution":{"observed_at":"2026-08-10T23:10:24.309130Z","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":"2026-08-10T23:10:24.288072Z","title":"Observation of nonlinear localized modes in an electrical lattice","venue":null,"work_id":"e8775289-3c4f-4d04-829a-3d541aad62fa","year":1995},"citing_paper":{"arxiv_id":"2501.00121","last_updated":"2024-12-30T19:41:20Z","snapshot_observed_at":"2026-08-13T18:21:12.428826Z","submitted_at":"2024-12-30T19:41:20Z","title":"On the discrete Kuznetsov-Ma solutions for the defocusing Ablowitz-Ladik equation with large background amplitude","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-10T23:10:24.083466Z"},"links":{"citing_paper":"/paper/2501.00121"},"observation_digest":"sha256:6cfff4560f6abed30dc4007e348500a68e7c36a2fb6f7188b316c43e2a114a8e","observation_id":"52748dab-26fc-488e-b7ea-541b726683f0","resolution":{"observed_at":"2026-08-10T23:10:24.293325Z","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":"2026-08-10T23:10:24.272863Z","title":"General rogues waves in the focusing and defocusing Ablowitz-Ladik equa- tions","venue":null,"work_id":"e6740989-688f-4fb1-b981-4847bb7751fc","year":2014},"citing_paper":{"arxiv_id":"2501.00121","last_updated":"2024-12-30T19:41:20Z","snapshot_observed_at":"2026-08-13T18:21:12.428826Z","submitted_at":"2024-12-30T19:41:20Z","title":"On the discrete Kuznetsov-Ma solutions for the defocusing Ablowitz-Ladik equation with large background amplitude","version":1},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-10T23:10:24.087345Z"},"links":{"citing_paper":"/paper/2501.00121"},"observation_digest":"sha256:2f07315f56dfd65cb4a145a3bd094ad385d81122f36de268ce86b16a8b622393","observation_id":"3589c78f-1aea-472c-98e5-fcae31b307fe","resolution":{"observed_at":"2026-08-10T23:10:24.277586Z","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":"2026-08-10T23:10:24.257040Z","title":"Inverse scattering transform for the defocusing Ablowitz-Ladik equation with arbitrarily large background","venue":null,"work_id":"1cf9134a-4a09-4986-b164-d2a12114eb4a","year":2019},"citing_paper":{"arxiv_id":"2501.00121","last_updated":"2024-12-30T19:41:20Z","snapshot_observed_at":"2026-08-13T18:21:12.428826Z","submitted_at":"2024-12-30T19:41:20Z","title":"On the discrete Kuznetsov-Ma solutions for the defocusing Ablowitz-Ladik equation with large background amplitude","version":1},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-10T23:10:24.091441Z"},"links":{"citing_paper":"/paper/2501.00121"},"observation_digest":"sha256:124c3e1b1e21fff1cdad82a8356272ef37b605374c92ca1c0b32e250a95f375b","observation_id":"a6fbf6be-f10d-4c4d-a393-0317fd4bc8c3","resolution":{"observed_at":"2026-08-10T23:10:24.262526Z","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":"2026-08-10T23:10:24.242778Z","title":"Water waves, nonlinear Schr¨ odinger equations and their solutions","venue":null,"work_id":"2814e928-3fdd-40c6-9286-595b72b4f4a8","year":1983},"citing_paper":{"arxiv_id":"2501.00121","last_updated":"2024-12-30T19:41:20Z","snapshot_observed_at":"2026-08-13T18:21:12.428826Z","submitted_at":"2024-12-30T19:41:20Z","title":"On the discrete Kuznetsov-Ma solutions for the defocusing Ablowitz-Ladik equation with large background amplitude","version":1},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-10T23:10:24.095313Z"},"links":{"citing_paper":"/paper/2501.00121"},"observation_digest":"sha256:51c51f6e9927f273c95b659202940e11f09bf68199adbb4be10b7caa96aaaa7a","observation_id":"2a082166-c13b-4469-991d-9a8b8cee10ba","resolution":{"observed_at":"2026-08-10T23:10:24.247411Z","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":"2026-08-10T23:10:24.227123Z","title":"Discrete solitons of the Ablowitz-Ladik equation with nonzero boundary conditions via inverse scattering","venue":null,"work_id":"c44bcf15-5699-4933-9255-cd05adbeec03","year":2016},"citing_paper":{"arxiv_id":"2501.00121","last_updated":"2024-12-30T19:41:20Z","snapshot_observed_at":"2026-08-13T18:21:12.428826Z","submitted_at":"2024-12-30T19:41:20Z","title":"On the discrete Kuznetsov-Ma solutions for the defocusing Ablowitz-Ladik equation with large background amplitude","version":1},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-10T23:10:24.099116Z"},"links":{"citing_paper":"/paper/2501.00121"},"observation_digest":"sha256:c4d08b8b4c31266d0ee3ee5be538190e79cd2cf56609fec4c95fa12acbac9f54","observation_id":"3f8a2b30-3271-45b9-a90f-f4d52058156f","resolution":{"observed_at":"2026-08-10T23:10:24.232109Z","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":"2026-08-10T23:10:24.212501Z","title":"Inverse scattering transform for the focusing Ablowitz-Ladik system with nonzero boundary conditions","venue":null,"work_id":"a5b178d5-60c9-41e6-a0f4-9ee590a29af5","year":2016},"citing_paper":{"arxiv_id":"2501.00121","last_updated":"2024-12-30T19:41:20Z","snapshot_observed_at":"2026-08-13T18:21:12.428826Z","submitted_at":"2024-12-30T19:41:20Z","title":"On the discrete Kuznetsov-Ma solutions for the defocusing Ablowitz-Ladik equation with large background amplitude","version":1},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-10T23:10:24.103580Z"},"links":{"citing_paper":"/paper/2501.00121"},"observation_digest":"sha256:996953989e02b49d5845206d3057fc71515248a9d327ddf080122c9ec773cc65","observation_id":"c6ebcc95-1b07-4e56-adf6-a1a9769170a4","resolution":{"observed_at":"2026-08-10T23:10:24.216731Z","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":"2026-08-10T23:10:24.196812Z","title":"Kuznetsov–Ma breather-like solutions in the Salerno model","venue":null,"work_id":"00ec11ea-fe7e-43e8-b2ff-bb358b4ed6a5","year":2020},"citing_paper":{"arxiv_id":"2501.00121","last_updated":"2024-12-30T19:41:20Z","snapshot_observed_at":"2026-08-13T18:21:12.428826Z","submitted_at":"2024-12-30T19:41:20Z","title":"On the discrete Kuznetsov-Ma solutions for the defocusing Ablowitz-Ladik equation with large background amplitude","version":1},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-10T23:10:24.107603Z"},"links":{"citing_paper":"/paper/2501.00121"},"observation_digest":"sha256:6bbd27512508c3393938bdf822db0f3191a74af695e8484a9cca065ef49fa338","observation_id":"b8aac137-837e-4649-8cb6-29415440d5b0","resolution":{"observed_at":"2026-08-10T23:10:24.202532Z","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":"2026-08-10T23:10:24.181359Z","title":"Breather solutions to the focusing nonlinear Schr¨ odinger equation","venue":null,"work_id":"efde012d-10b4-4236-9bb7-b294f4e471be","year":1998},"citing_paper":{"arxiv_id":"2501.00121","last_updated":"2024-12-30T19:41:20Z","snapshot_observed_at":"2026-08-13T18:21:12.428826Z","submitted_at":"2024-12-30T19:41:20Z","title":"On the discrete Kuznetsov-Ma solutions for the defocusing Ablowitz-Ladik equation with large background amplitude","version":1},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-10T23:10:24.111459Z"},"links":{"citing_paper":"/paper/2501.00121"},"observation_digest":"sha256:f0e8bd98cda73c02fc9e9e2c4c81846b9a196beab9effddf3849177543f22369","observation_id":"5f663540-25b6-4620-bb65-e3f26fb587a4","resolution":{"observed_at":"2026-08-10T23:10:24.186255Z","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":"2026-08-10T23:10:24.166165Z","title":"A propagating self-localized mode in a one-dimensional lattice with quartic anharmonicity","venue":null,"work_id":"1ca18a5c-b2a3-4ef1-a38f-9f552d9cee21","year":1990},"citing_paper":{"arxiv_id":"2501.00121","last_updated":"2024-12-30T19:41:20Z","snapshot_observed_at":"2026-08-13T18:21:12.428826Z","submitted_at":"2024-12-30T19:41:20Z","title":"On the discrete Kuznetsov-Ma solutions for the defocusing Ablowitz-Ladik equation with large background amplitude","version":1},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-08-10T23:10:24.115396Z"},"links":{"citing_paper":"/paper/2501.00121"},"observation_digest":"sha256:8e9784b9d37fbe503bc79fa05822140ed95749ac6938d5e56dd78d4f7a4c6459","observation_id":"3fe156e6-63a0-4ab4-b02b-3171e903a409","resolution":{"observed_at":"2026-08-10T23:10:24.170936Z","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":"2026-08-10T23:10:24.149786Z","title":"Discrete nonlinear Schr¨ odinger equation under non-vanishing boundary conditions","venue":null,"work_id":"5c557aee-ffca-49f4-bd7b-4394fd99cdb6","year":1992},"citing_paper":{"arxiv_id":"2501.00121","last_updated":"2024-12-30T19:41:20Z","snapshot_observed_at":"2026-08-13T18:21:12.428826Z","submitted_at":"2024-12-30T19:41:20Z","title":"On the discrete Kuznetsov-Ma solutions for the defocusing Ablowitz-Ladik equation with large background amplitude","version":1},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-08-10T23:10:24.119619Z"},"links":{"citing_paper":"/paper/2501.00121"},"observation_digest":"sha256:a4bde123e6c50255f06aff6ddcad501b3f06e4cc0f7360d485b312e216de8112","observation_id":"5856d75d-f7dc-4b32-8a3b-0878a9e40b78","resolution":{"observed_at":"2026-08-10T23:10:24.155866Z","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":"2501.00121","last_updated":"2024-12-30T19:41:20Z","latest_version":1,"primary_category":"nlin.SI","snapshot_observed_at":"2026-08-13T18:21:12.428826Z","submitted_at":"2024-12-30T19:41:20Z","title":"On the discrete Kuznetsov-Ma solutions for the defocusing Ablowitz-Ladik equation with large background amplitude"},"reference_resolution":{"displayed":36,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":3,"verified_exact":0,"verified_fuzzy":33},"total_outbound_references":36},"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 36 of 36 outbound references and 0 inbound Pith citation observations for arXiv:2501.00121."}