{"as_of":"2026-08-12T18:17:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:be1277ab02fcc3b668264f68a326256b5a5c8ccfd5143b57a3e25deee1d232da","coverage":[{"denominator":20,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":20,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-06T20:21:17.760094Z","state":"measured"},{"denominator":20,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":20,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-12T06:34:41.77262+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/2507.03452/citation-record","integrity":"/paper/2507.03452/integrity","json":"/paper/2507.03452/citation-record.json","paper":"/paper/2507.03452"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T20:21:21.494740Z","title":"Bhardwaj, The space of multipliers between model spaces complete or incomplete, J","venue":null,"work_id":"356f9047-a4b8-4941-af59-d6bd23ba06da","year":2025},"citing_paper":{"arxiv_id":"2507.03452","last_updated":"2025-07-12T13:44:26Z","snapshot_observed_at":"2026-08-10T23:38:41.071260Z","submitted_at":"2025-07-04T10:11:11Z","title":"Multiplier Between Generalized Toeplitz Kernels","version":2},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-06T20:21:15.901485Z"},"links":{"citing_paper":"/paper/2507.03452"},"observation_digest":"sha256:74a1ea4014d8f055cabd1623ea76cf93142881fbf985d6e73c8a0f8667be1181","observation_id":"a564cb2d-5e16-4112-8b69-fcf32517d215","resolution":{"observed_at":"2026-08-06T20:21:21.545507Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-06T20:21:21.385745Z","title":"Cˆ amara, and J.R","venue":null,"work_id":"04779e63-963d-4dd0-889b-99c3aa908da6","year":2014},"citing_paper":{"arxiv_id":"2507.03452","last_updated":"2025-07-12T13:44:26Z","snapshot_observed_at":"2026-08-10T23:38:41.071260Z","submitted_at":"2025-07-04T10:11:11Z","title":"Multiplier Between Generalized Toeplitz Kernels","version":2},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-06T20:21:15.987299Z"},"links":{"citing_paper":"/paper/2507.03452"},"observation_digest":"sha256:c9ab84314ffae8be869c2db91bc37f3229a45e48cf1cbbf5931d215264579db4","observation_id":"c68e0980-e9d5-4078-a4a1-c90cc8c25bbb","resolution":{"observed_at":"2026-08-06T20:21:21.432772Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-06T20:21:21.174120Z","title":"Cˆ amara, J.R","venue":null,"work_id":"eba33d9c-cb3b-4d02-aa5a-f0a113c1dc37","year":2018},"citing_paper":{"arxiv_id":"2507.03452","last_updated":"2025-07-12T13:44:26Z","snapshot_observed_at":"2026-08-10T23:38:41.071260Z","submitted_at":"2025-07-04T10:11:11Z","title":"Multiplier Between Generalized Toeplitz Kernels","version":2},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-06T20:21:16.110476Z"},"links":{"citing_paper":"/paper/2507.03452"},"observation_digest":"sha256:a2d327649ead38e4f2e399e1c44939c3ff966ebfa8abb8c8b9ab19292bb81e36","observation_id":"b9dddbe1-71b7-4afd-b3f4-48735265cd07","resolution":{"observed_at":"2026-08-06T20:21:21.280582Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-06T20:21:20.918426Z","title":"Cohn, A maximum principle for star invariant subspaces, Houst","venue":null,"work_id":"19d1d548-ed2a-43a5-80d0-b835b338bd14","year":1988},"citing_paper":{"arxiv_id":"2507.03452","last_updated":"2025-07-12T13:44:26Z","snapshot_observed_at":"2026-08-10T23:38:41.071260Z","submitted_at":"2025-07-04T10:11:11Z","title":"Multiplier Between Generalized Toeplitz Kernels","version":2},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-06T20:21:16.191111Z"},"links":{"citing_paper":"/paper/2507.03452"},"observation_digest":"sha256:b80bbe33222528c22c61972de965e2b01c5210b9ec25f5e6adeb283ff64dbefe","observation_id":"1f8af98d-fdd9-4777-8b36-e03e617b2239","resolution":{"observed_at":"2026-08-06T20:21:21.034865Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-06T20:21:20.641606Z","title":"Crofoot, Multipliers between invariant subspaces of the backward shift, Pacific J.Math","venue":null,"work_id":"f17a241f-6460-479c-b9b8-8119833d70e5","year":1994},"citing_paper":{"arxiv_id":"2507.03452","last_updated":"2025-07-12T13:44:26Z","snapshot_observed_at":"2026-08-10T23:38:41.071260Z","submitted_at":"2025-07-04T10:11:11Z","title":"Multiplier Between Generalized Toeplitz Kernels","version":2},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-06T20:21:16.305724Z"},"links":{"citing_paper":"/paper/2507.03452"},"observation_digest":"sha256:2c981475dae810db62acb9c9124c60b2877fef8d6df86e736a0045ed083e2ea9","observation_id":"417048f3-af1c-4e3f-b53e-5b2d7fca0847","resolution":{"observed_at":"2026-08-06T20:21:20.785543Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-06T20:21:20.428147Z","title":null,"venue":null,"work_id":"ee98f8d1-7ce6-4d71-857f-f03a74da664d","year":2000},"citing_paper":{"arxiv_id":"2507.03452","last_updated":"2025-07-12T13:44:26Z","snapshot_observed_at":"2026-08-10T23:38:41.071260Z","submitted_at":"2025-07-04T10:11:11Z","title":"Multiplier Between Generalized Toeplitz Kernels","version":2},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-06T20:21:16.395556Z"},"links":{"citing_paper":"/paper/2507.03452"},"observation_digest":"sha256:2aabd567a5fb24203a3a4b88e3a887a93a045bf094caf4ac69f86e5eec7f8d36","observation_id":"6a7bdb48-6ce0-41df-acb5-11e7ba391f57","resolution":{"observed_at":"2026-08-06T20:21:20.521762Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-06T20:21:20.259772Z","title":"Devinatz and M","venue":null,"work_id":"fe59b1f1-fbce-4190-bb9a-3cfa9b7575b8","year":1969},"citing_paper":{"arxiv_id":"2507.03452","last_updated":"2025-07-12T13:44:26Z","snapshot_observed_at":"2026-08-10T23:38:41.071260Z","submitted_at":"2025-07-04T10:11:11Z","title":"Multiplier Between Generalized Toeplitz Kernels","version":2},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-06T20:21:16.478344Z"},"links":{"citing_paper":"/paper/2507.03452"},"observation_digest":"sha256:b1799a2d19f01c0ae2f203686d481e5a6ddc54f7b6bfd6bfe32d95c6464dc5dd","observation_id":"b078a5fd-9d2f-4dbd-bc59-644839b65be1","resolution":{"observed_at":"2026-08-06T20:21:20.337606Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-06T20:21:20.002089Z","title":"Fricain, A","venue":null,"work_id":"ce7c9cef-1ed2-4fe7-ac39-111c063e186e","year":2018},"citing_paper":{"arxiv_id":"2507.03452","last_updated":"2025-07-12T13:44:26Z","snapshot_observed_at":"2026-08-10T23:38:41.071260Z","submitted_at":"2025-07-04T10:11:11Z","title":"Multiplier Between Generalized Toeplitz Kernels","version":2},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-06T20:21:16.560258Z"},"links":{"citing_paper":"/paper/2507.03452"},"observation_digest":"sha256:10e3fdf344468660ddeda15b31bbcbfa2011cb4851bc7ee8e50614f4e80afa24","observation_id":"29319c4d-dae7-4eca-b473-61009aed0d18","resolution":{"observed_at":"2026-08-06T20:21:20.100374Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-06T20:21:19.785701Z","title":"Fricain, and R","venue":null,"work_id":"e60a2de6-ef63-4b77-b846-124cef1fb938","year":2018},"citing_paper":{"arxiv_id":"2507.03452","last_updated":"2025-07-12T13:44:26Z","snapshot_observed_at":"2026-08-10T23:38:41.071260Z","submitted_at":"2025-07-04T10:11:11Z","title":"Multiplier Between Generalized Toeplitz Kernels","version":2},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-06T20:21:16.653840Z"},"links":{"citing_paper":"/paper/2507.03452"},"observation_digest":"sha256:ac0e5153a524453a3632cc53d84702466592ebd89f074edc843d2c4f5a40b1ee","observation_id":"64848ab5-53b2-4a51-8098-a012e4294b0d","resolution":{"observed_at":"2026-08-06T20:21:19.887791Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-06T20:21:19.521969Z","title":"Garcia, J","venue":null,"work_id":"d9f03f0f-8591-4e66-9d5f-9f226296c2a7","year":2016},"citing_paper":{"arxiv_id":"2507.03452","last_updated":"2025-07-12T13:44:26Z","snapshot_observed_at":"2026-08-10T23:38:41.071260Z","submitted_at":"2025-07-04T10:11:11Z","title":"Multiplier Between Generalized Toeplitz Kernels","version":2},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-06T20:21:16.744316Z"},"links":{"citing_paper":"/paper/2507.03452"},"observation_digest":"sha256:85a6957b18ad01fc385fdb746316ad9f8a4d7c5057eb117ea84c31610bc63ab6","observation_id":"be193a34-46ce-424c-897f-7a8bf7973cb3","resolution":{"observed_at":"2026-08-06T20:21:19.675441Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-06T20:21:19.316977Z","title":"Hayashi, The kernel of a Toeplitz operator, Integral Equ","venue":null,"work_id":"5b5de6c4-bd32-4909-9619-8e3555f09e7d","year":1986},"citing_paper":{"arxiv_id":"2507.03452","last_updated":"2025-07-12T13:44:26Z","snapshot_observed_at":"2026-08-10T23:38:41.071260Z","submitted_at":"2025-07-04T10:11:11Z","title":"Multiplier Between Generalized Toeplitz Kernels","version":2},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-06T20:21:16.841674Z"},"links":{"citing_paper":"/paper/2507.03452"},"observation_digest":"sha256:d03054afd1a21c8c08e96f03a9b03ac28ccc79c3d9b8a9c00c29d804729044d1","observation_id":"ff40a116-cd7b-4bc7-9559-d581ca2d9134","resolution":{"observed_at":"2026-08-06T20:21:19.388325Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-06T20:21:19.173909Z","title":"Mashreghi, Representation theorems in Hardy spaces","venue":null,"work_id":"639d8f19-1948-451b-938e-b9718dabdbdd","year":2009},"citing_paper":{"arxiv_id":"2507.03452","last_updated":"2025-07-12T13:44:26Z","snapshot_observed_at":"2026-08-10T23:38:41.071260Z","submitted_at":"2025-07-04T10:11:11Z","title":"Multiplier Between Generalized Toeplitz Kernels","version":2},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-06T20:21:16.938361Z"},"links":{"citing_paper":"/paper/2507.03452"},"observation_digest":"sha256:9870d45ae7ffa33ffe5ac529fe056952cf6c7c79f93b800351ada3f4d961094b","observation_id":"0aab633a-624a-4c28-a1ee-fea722e74fce","resolution":{"observed_at":"2026-08-06T20:21:19.239919Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-06T20:21:19.019430Z","title":"Makarov, and A","venue":null,"work_id":"281b6db6-9807-4331-9670-94ce54c908bb","year":2005},"citing_paper":{"arxiv_id":"2507.03452","last_updated":"2025-07-12T13:44:26Z","snapshot_observed_at":"2026-08-10T23:38:41.071260Z","submitted_at":"2025-07-04T10:11:11Z","title":"Multiplier Between Generalized Toeplitz Kernels","version":2},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-06T20:21:17.038348Z"},"links":{"citing_paper":"/paper/2507.03452"},"observation_digest":"sha256:78c7bfed97211612e95cde5b9f20ec37c7610637ad6dd7aaa0df17be4ad2068d","observation_id":"4d73b64c-6327-4502-bb1a-1e592b7d744d","resolution":{"observed_at":"2026-08-06T20:21:19.117345Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-06T20:21:18.858026Z","title":"Makarov, and A","venue":null,"work_id":"22e6621f-2d8a-419d-8f0e-02d41014be4c","year":2010},"citing_paper":{"arxiv_id":"2507.03452","last_updated":"2025-07-12T13:44:26Z","snapshot_observed_at":"2026-08-10T23:38:41.071260Z","submitted_at":"2025-07-04T10:11:11Z","title":"Multiplier Between Generalized Toeplitz Kernels","version":2},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-06T20:21:17.119456Z"},"links":{"citing_paper":"/paper/2507.03452"},"observation_digest":"sha256:a0a0217e2842807cebec3f3ad542aeb70c58b360959c065be00b02f9098003d5","observation_id":"3901be14-d9ec-4168-b4ca-0e5a419b2865","resolution":{"observed_at":"2026-08-06T20:21:18.919720Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-06T20:21:18.690799Z","title":"Mitkovski, Spaces of Analytic Functions and Their Applications","venue":null,"work_id":"a5a7f9e5-b961-4033-a5f9-20b5436a28ca","year":2011},"citing_paper":{"arxiv_id":"2507.03452","last_updated":"2025-07-12T13:44:26Z","snapshot_observed_at":"2026-08-10T23:38:41.071260Z","submitted_at":"2025-07-04T10:11:11Z","title":"Multiplier Between Generalized Toeplitz Kernels","version":2},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-06T20:21:17.191702Z"},"links":{"citing_paper":"/paper/2507.03452"},"observation_digest":"sha256:be23420c86eac7d88fa7bf66be35ca217ad43148f69f7cbcd250dd136d9ec20f","observation_id":"f36b0aae-e0b2-4bcc-95e5-02c3e80bcbd7","resolution":{"observed_at":"2026-08-06T20:21:18.766700Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-06T20:21:18.537197Z","title":"Mitkovski, and A","venue":null,"work_id":"ed5cf72f-1df8-4282-ac13-1f774946aa0f","year":2010},"citing_paper":{"arxiv_id":"2507.03452","last_updated":"2025-07-12T13:44:26Z","snapshot_observed_at":"2026-08-10T23:38:41.071260Z","submitted_at":"2025-07-04T10:11:11Z","title":"Multiplier Between Generalized Toeplitz Kernels","version":2},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-06T20:21:17.293809Z"},"links":{"citing_paper":"/paper/2507.03452"},"observation_digest":"sha256:fb16f389cbf4cda76cf96ff222b0c32a7927d876d86006fa9854269508ef4c87","observation_id":"fb2e20e9-c0f0-4a0c-92a2-af6b270570f4","resolution":{"observed_at":"2026-08-06T20:21:18.607391Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-06T20:21:18.370118Z","title":"Natalia, and A","venue":null,"work_id":"357fe314-ab68-4592-aa95-38b87ff04c66","year":2016},"citing_paper":{"arxiv_id":"2507.03452","last_updated":"2025-07-12T13:44:26Z","snapshot_observed_at":"2026-08-10T23:38:41.071260Z","submitted_at":"2025-07-04T10:11:11Z","title":"Multiplier Between Generalized Toeplitz Kernels","version":2},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-06T20:21:17.383955Z"},"links":{"citing_paper":"/paper/2507.03452"},"observation_digest":"sha256:3d3cbb801e76735d56c14bd7414d969916f036ba4ce77eb9223f9fdf23e789ef","observation_id":"77fdc115-5f39-454f-8702-2ffe19d61ca4","resolution":{"observed_at":"2026-08-06T20:21:18.450775Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-06T20:21:18.175796Z","title":"Nikolskii, Operators, functions, and systems: an easy reading, Vol","venue":null,"work_id":"e372c0e6-cef9-4f00-b7d4-7fdd33133e96","year":2002},"citing_paper":{"arxiv_id":"2507.03452","last_updated":"2025-07-12T13:44:26Z","snapshot_observed_at":"2026-08-10T23:38:41.071260Z","submitted_at":"2025-07-04T10:11:11Z","title":"Multiplier Between Generalized Toeplitz Kernels","version":2},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-06T20:21:17.508698Z"},"links":{"citing_paper":"/paper/2507.03452"},"observation_digest":"sha256:92cdc77c875dc6c2095331b347e81763a6b68018521ce7d201e014ba58063a45","observation_id":"b7a3cec2-0f88-49f8-aa17-1ee3b4b05c80","resolution":{"observed_at":"2026-08-06T20:21:18.273393Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-06T20:21:18.021430Z","title":null,"venue":null,"work_id":"9eb9c10c-ccea-43f5-919f-e493cda17ef9","year":2002},"citing_paper":{"arxiv_id":"2507.03452","last_updated":"2025-07-12T13:44:26Z","snapshot_observed_at":"2026-08-10T23:38:41.071260Z","submitted_at":"2025-07-04T10:11:11Z","title":"Multiplier Between Generalized Toeplitz Kernels","version":2},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-06T20:21:17.633037Z"},"links":{"citing_paper":"/paper/2507.03452"},"observation_digest":"sha256:4548532c7fa52d8902783f61575b4d47e1690d4cc77b8012bbc9315da5fd3a83","observation_id":"72c992a1-4f7d-4794-a26e-00bfa26f1a12","resolution":{"observed_at":"2026-08-06T20:21:18.080741Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-06T20:21:17.889757Z","title":"Speck General Wiener-Hopf factorization methods, Res","venue":null,"work_id":"31ef8c48-e1bc-4da2-834c-ac6f63ccf9b1","year":1985},"citing_paper":{"arxiv_id":"2507.03452","last_updated":"2025-07-12T13:44:26Z","snapshot_observed_at":"2026-08-10T23:38:41.071260Z","submitted_at":"2025-07-04T10:11:11Z","title":"Multiplier Between Generalized Toeplitz Kernels","version":2},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-06T20:21:17.760094Z"},"links":{"citing_paper":"/paper/2507.03452"},"observation_digest":"sha256:c3ddda6f419188bc9d06daa198b26fd6bf70786303ff1fe3dc7a97ff6fb487de","observation_id":"30dbd913-a515-4780-a23c-ed11c872aca2","resolution":{"observed_at":"2026-08-06T20:21:17.936396Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2507.03452","last_updated":"2025-07-12T13:44:26Z","latest_version":2,"primary_category":"math.FA","snapshot_observed_at":"2026-08-10T23:38:41.071260Z","submitted_at":"2025-07-04T10:11:11Z","title":"Multiplier Between Generalized Toeplitz Kernels"},"reference_resolution":{"displayed":20,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":2,"verified_exact":0,"verified_fuzzy":18},"total_outbound_references":20},"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":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"thesis":"As of 12 August 2026, this Paper Citation Record lists 20 of 20 outbound references and 0 inbound Pith citation observations for arXiv:2507.03452."}