{"as_of":"2026-08-12T22:51:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:fc93c3bff42d57efccccbdf6d255a8bd8149a7d20420d94ab52ce2469b1e4098","coverage":[{"denominator":22,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":22,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-06T20:07:39.018998Z","state":"measured"},{"denominator":22,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":22,"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/2507.04242/citation-record","integrity":"/paper/2507.04242/integrity","json":"/paper/2507.04242/citation-record.json","paper":"/paper/2507.04242"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T20:07:39.493352Z","title":"Abramowitz and I.A","venue":null,"work_id":"61503be7-8ab5-496a-a128-eb1058ef58cf","year":1965},"citing_paper":{"arxiv_id":"2507.04242","last_updated":"2025-07-06T04:38:12Z","snapshot_observed_at":"2026-08-12T17:44:56.777685Z","submitted_at":"2025-07-06T04:38:12Z","title":"Generalized Rellich's lemmas, uniqueness theorem and inside-out duality for scattering poles","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-06T20:07:38.581606Z"},"links":{"citing_paper":"/paper/2507.04242"},"observation_digest":"sha256:5d5067e19dd18ac9f23b1970da7a45985667e109eee4e7ed0ffba8d660fee820","observation_id":"567e7bce-10d3-402e-9c54-b757ac28a052","resolution":{"observed_at":"2026-08-06T20:07:39.500281Z","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":"2026-08-06T20:07:39.474340Z","title":"Cakoni, M","venue":null,"work_id":"e616b430-0ce2-40d2-ba6e-07c65c4e329a","year":2008},"citing_paper":{"arxiv_id":"2507.04242","last_updated":"2025-07-06T04:38:12Z","snapshot_observed_at":"2026-08-12T17:44:56.777685Z","submitted_at":"2025-07-06T04:38:12Z","title":"Generalized Rellich's lemmas, uniqueness theorem and inside-out duality for scattering poles","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-06T20:07:38.637798Z"},"links":{"citing_paper":"/paper/2507.04242"},"observation_digest":"sha256:9150d8b2483329d9c850c4f8d7874d7065965de047b5cfbb7c7d587a10d48edc","observation_id":"52234eba-5e00-4c2d-a60d-01c130b66570","resolution":{"observed_at":"2026-08-06T20:07:39.479320Z","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":"2026-08-06T20:07:39.450383Z","title":"Cakoni, D","venue":null,"work_id":"8b645d82-ef1c-4787-97a7-a3c06915c024","year":2010},"citing_paper":{"arxiv_id":"2507.04242","last_updated":"2025-07-06T04:38:12Z","snapshot_observed_at":"2026-08-12T17:44:56.777685Z","submitted_at":"2025-07-06T04:38:12Z","title":"Generalized Rellich's lemmas, uniqueness theorem and inside-out duality for scattering poles","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-06T20:07:38.725063Z"},"links":{"citing_paper":"/paper/2507.04242"},"observation_digest":"sha256:5d306d8d8bc1d87d2754518c06bb2677deb9c639444fd03869bf715c65eb0291","observation_id":"1032609a-bbba-4920-b67c-21c07611ba74","resolution":{"observed_at":"2026-08-06T20:07:39.456550Z","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":"2026-08-06T20:07:39.417148Z","title":"Cakoni, D","venue":null,"work_id":"3b87f31f-283a-4e8a-a99a-0ad2b640fdde","year":2020},"citing_paper":{"arxiv_id":"2507.04242","last_updated":"2025-07-06T04:38:12Z","snapshot_observed_at":"2026-08-12T17:44:56.777685Z","submitted_at":"2025-07-06T04:38:12Z","title":"Generalized Rellich's lemmas, uniqueness theorem and inside-out duality for scattering poles","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-06T20:07:38.749279Z"},"links":{"citing_paper":"/paper/2507.04242"},"observation_digest":"sha256:8e42d0e6970bc1e84b105a24bccd92473d62f77fbe92bcd4a9f356afd5d7bff5","observation_id":"41eeda90-e2f4-435c-a157-15f9ed61e68c","resolution":{"observed_at":"2026-08-06T20:07:39.430267Z","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":"2026-08-06T20:07:39.379551Z","title":"Cakoni, H","venue":null,"work_id":"6d849a40-60c0-4b58-9fbc-a3d970990d55","year":2024},"citing_paper":{"arxiv_id":"2507.04242","last_updated":"2025-07-06T04:38:12Z","snapshot_observed_at":"2026-08-12T17:44:56.777685Z","submitted_at":"2025-07-06T04:38:12Z","title":"Generalized Rellich's lemmas, uniqueness theorem and inside-out duality for scattering poles","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-06T20:07:38.786171Z"},"links":{"citing_paper":"/paper/2507.04242"},"observation_digest":"sha256:46fb829e4b94176612aa5c17c02dc5a0b8d738e04272035444ae13ee255f9e9b","observation_id":"51d69fb8-6f1a-46d4-9a90-947cc97e9c0e","resolution":{"observed_at":"2026-08-06T20:07:39.386207Z","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":"2026-08-06T20:07:39.364005Z","title":"Colton and R","venue":null,"work_id":"d904c830-b57f-4197-ba07-d647db5aab69","year":1983},"citing_paper":{"arxiv_id":"2507.04242","last_updated":"2025-07-06T04:38:12Z","snapshot_observed_at":"2026-08-12T17:44:56.777685Z","submitted_at":"2025-07-06T04:38:12Z","title":"Generalized Rellich's lemmas, uniqueness theorem and inside-out duality for scattering poles","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-06T20:07:38.856225Z"},"links":{"citing_paper":"/paper/2507.04242"},"observation_digest":"sha256:4180aa3bd466c1473f0564517df42c7dcd07c118ba838a915b1bcd1905379a16","observation_id":"3e427cb5-9191-4120-88c0-9bd727da2baf","resolution":{"observed_at":"2026-08-06T20:07:39.368875Z","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":"2026-08-06T20:07:39.346603Z","title":null,"venue":null,"work_id":"abf4ea39-948f-4e03-85a4-50374bbe1f64","year":1970},"citing_paper":{"arxiv_id":"2507.04242","last_updated":"2025-07-06T04:38:12Z","snapshot_observed_at":"2026-08-12T17:44:56.777685Z","submitted_at":"2025-07-06T04:38:12Z","title":"Generalized Rellich's lemmas, uniqueness theorem and inside-out duality for scattering poles","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-06T20:07:38.905849Z"},"links":{"citing_paper":"/paper/2507.04242"},"observation_digest":"sha256:8eb11a0440bbe1db0f27238ef9bc5665e258c32a5ecf558ff685b0458af5278c","observation_id":"c4f95a51-4bab-4fa7-ba4f-40a9ce59cfb3","resolution":{"observed_at":"2026-08-06T20:07:39.351659Z","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":"2026-08-06T20:07:39.326910Z","title":"Colton and R","venue":null,"work_id":"c695a2b6-78e1-40b9-b747-f7c14fdc4971","year":2019},"citing_paper":{"arxiv_id":"2507.04242","last_updated":"2025-07-06T04:38:12Z","snapshot_observed_at":"2026-08-12T17:44:56.777685Z","submitted_at":"2025-07-06T04:38:12Z","title":"Generalized Rellich's lemmas, uniqueness theorem and inside-out duality for scattering poles","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-06T20:07:38.954957Z"},"links":{"citing_paper":"/paper/2507.04242"},"observation_digest":"sha256:0f99c5c0aa55519e41274464bf3db8911e5ad6da209e725befd7d7b035c56204","observation_id":"4aa9325a-35ac-4344-ac4c-75de4043b994","resolution":{"observed_at":"2026-08-06T20:07:39.334074Z","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":"2026-08-06T20:07:39.305006Z","title":"Dyatlov and M","venue":null,"work_id":"149c3f44-f98d-4068-b693-20f0288d4ffe","year":2019},"citing_paper":{"arxiv_id":"2507.04242","last_updated":"2025-07-06T04:38:12Z","snapshot_observed_at":"2026-08-12T17:44:56.777685Z","submitted_at":"2025-07-06T04:38:12Z","title":"Generalized Rellich's lemmas, uniqueness theorem and inside-out duality for scattering poles","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-06T20:07:38.959504Z"},"links":{"citing_paper":"/paper/2507.04242"},"observation_digest":"sha256:6003a33b23260eb412fc48ea06ed4baba7ab242c5ac34e4e13657351b120d346","observation_id":"db2ec1ae-14fd-473f-8d0e-29cb1d72f569","resolution":{"observed_at":"2026-08-06T20:07:39.313797Z","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":"2026-08-06T20:07:39.282648Z","title":"Keller, S.I","venue":null,"work_id":"f2d8d2d8-8f0b-4e97-b259-7d68990ea225","year":1963},"citing_paper":{"arxiv_id":"2507.04242","last_updated":"2025-07-06T04:38:12Z","snapshot_observed_at":"2026-08-12T17:44:56.777685Z","submitted_at":"2025-07-06T04:38:12Z","title":"Generalized Rellich's lemmas, uniqueness theorem and inside-out duality for scattering poles","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-06T20:07:38.963865Z"},"links":{"citing_paper":"/paper/2507.04242"},"observation_digest":"sha256:298070758395f39b3c4ba3ff15478aaf26bb6b50f491a2309bc3a22766a050fc","observation_id":"51b87d93-29b6-481b-ac20-6f74cec680cb","resolution":{"observed_at":"2026-08-06T20:07:39.288231Z","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":"2026-08-06T20:07:39.263302Z","title":"Kirsch and A","venue":null,"work_id":"a2323996-59b4-4e28-87c7-941cd80747c8","year":2013},"citing_paper":{"arxiv_id":"2507.04242","last_updated":"2025-07-06T04:38:12Z","snapshot_observed_at":"2026-08-12T17:44:56.777685Z","submitted_at":"2025-07-06T04:38:12Z","title":"Generalized Rellich's lemmas, uniqueness theorem and inside-out duality for scattering poles","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-06T20:07:38.968376Z"},"links":{"citing_paper":"/paper/2507.04242"},"observation_digest":"sha256:e9292c7034522054bd129f084141080d9175e9c455d14246af03d1a769ccd1e7","observation_id":"b47c4795-292e-45e0-b12f-afbdf5705fc4","resolution":{"observed_at":"2026-08-06T20:07:39.268515Z","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":"2026-08-06T20:07:39.246344Z","title":"Labreuche, Uniqueness and stability of the recovery of a sound soft obst acle from a knowl- dege of its scattering resonances","venue":null,"work_id":"06a3e24d-8e71-4ce9-9095-7de7d011dd83","year":1998},"citing_paper":{"arxiv_id":"2507.04242","last_updated":"2025-07-06T04:38:12Z","snapshot_observed_at":"2026-08-12T17:44:56.777685Z","submitted_at":"2025-07-06T04:38:12Z","title":"Generalized Rellich's lemmas, uniqueness theorem and inside-out duality for scattering poles","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-06T20:07:38.973117Z"},"links":{"citing_paper":"/paper/2507.04242"},"observation_digest":"sha256:aa0298c01c2c683f4841a6b32559572bcd0e6a6f5d6c38dd9da4c5fec1fc5fc5","observation_id":"5438869e-d7a3-4902-8ac4-165fce254beb","resolution":{"observed_at":"2026-08-06T20:07:39.252222Z","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":"2026-08-06T20:07:39.225589Z","title":"Lax and R.S","venue":null,"work_id":"230bcb15-c312-4660-9cd9-a404c1840e80","year":1989},"citing_paper":{"arxiv_id":"2507.04242","last_updated":"2025-07-06T04:38:12Z","snapshot_observed_at":"2026-08-12T17:44:56.777685Z","submitted_at":"2025-07-06T04:38:12Z","title":"Generalized Rellich's lemmas, uniqueness theorem and inside-out duality for scattering poles","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-06T20:07:38.977437Z"},"links":{"citing_paper":"/paper/2507.04242"},"observation_digest":"sha256:34a36aa567fb014304c1faa2fd5aeb9819805326cdc3602c6a262d415f0017db","observation_id":"35412002-f0ad-409e-961b-a6649d8d24ed","resolution":{"observed_at":"2026-08-06T20:07:39.231169Z","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":"2026-08-06T20:07:39.208882Z","title":"Liu and J","venue":null,"work_id":"8b1b373a-5d70-4770-b799-9302b7bf2ba5","year":2014},"citing_paper":{"arxiv_id":"2507.04242","last_updated":"2025-07-06T04:38:12Z","snapshot_observed_at":"2026-08-12T17:44:56.777685Z","submitted_at":"2025-07-06T04:38:12Z","title":"Generalized Rellich's lemmas, uniqueness theorem and inside-out duality for scattering poles","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-06T20:07:38.981914Z"},"links":{"citing_paper":"/paper/2507.04242"},"observation_digest":"sha256:74ab4b59bc8f5280493ce8f3b5dc974cb56f7c89f5b0096cf6a3f8ee8f7ab3b3","observation_id":"ac926f80-b28f-4e71-afc7-c9e9c94c6658","resolution":{"observed_at":"2026-08-06T20:07:39.213568Z","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":"2026-08-06T20:07:39.192630Z","title":"Ma and J","venue":null,"work_id":"a19b1ddc-6656-4afb-86b2-15071bd5c470","year":2023},"citing_paper":{"arxiv_id":"2507.04242","last_updated":"2025-07-06T04:38:12Z","snapshot_observed_at":"2026-08-12T17:44:56.777685Z","submitted_at":"2025-07-06T04:38:12Z","title":"Generalized Rellich's lemmas, uniqueness theorem and inside-out duality for scattering poles","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-06T20:07:38.986170Z"},"links":{"citing_paper":"/paper/2507.04242"},"observation_digest":"sha256:7c0dc85f5de196e01abb61c3e086753850ace55d15b05e52c857364a1cfcf2c1","observation_id":"561c1cb9-95c7-4e83-8f16-acddb975c90f","resolution":{"observed_at":"2026-08-06T20:07:39.197228Z","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":"2026-08-06T20:07:39.173503Z","title":"Melrose, Geometric Scattering Theory","venue":null,"work_id":"3b529243-74d7-410a-b181-400894d2cd8f","year":1995},"citing_paper":{"arxiv_id":"2507.04242","last_updated":"2025-07-06T04:38:12Z","snapshot_observed_at":"2026-08-12T17:44:56.777685Z","submitted_at":"2025-07-06T04:38:12Z","title":"Generalized Rellich's lemmas, uniqueness theorem and inside-out duality for scattering poles","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-06T20:07:38.990803Z"},"links":{"citing_paper":"/paper/2507.04242"},"observation_digest":"sha256:7c35dc55e3257c09f0e88693ad0f2fe55436f326b8d982205279ba9f0d4adf6d","observation_id":"0caf567e-0b4e-42d3-a4ac-83f3bf366d92","resolution":{"observed_at":"2026-08-06T20:07:39.179096Z","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":"2026-08-06T20:07:39.152379Z","title":"Sjöstr and M","venue":null,"work_id":"494a4d6d-9e83-4c46-957b-b78dd317d891","year":1991},"citing_paper":{"arxiv_id":"2507.04242","last_updated":"2025-07-06T04:38:12Z","snapshot_observed_at":"2026-08-12T17:44:56.777685Z","submitted_at":"2025-07-06T04:38:12Z","title":"Generalized Rellich's lemmas, uniqueness theorem and inside-out duality for scattering poles","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-06T20:07:38.995465Z"},"links":{"citing_paper":"/paper/2507.04242"},"observation_digest":"sha256:3473552ddcb1957e0df5bf22854d5a9ba845162d6d961d676bc3991ff8366c6c","observation_id":"e815d3e7-93e7-40f3-8367-150c9cb47076","resolution":{"observed_at":"2026-08-06T20:07:39.158508Z","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":"2026-08-06T20:07:39.134660Z","title":"Steinbach & G","venue":null,"work_id":"54136eaa-808a-4087-a1e3-5525a37f802f","year":2012},"citing_paper":{"arxiv_id":"2507.04242","last_updated":"2025-07-06T04:38:12Z","snapshot_observed_at":"2026-08-12T17:44:56.777685Z","submitted_at":"2025-07-06T04:38:12Z","title":"Generalized Rellich's lemmas, uniqueness theorem and inside-out duality for scattering poles","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-06T20:07:39.000026Z"},"links":{"citing_paper":"/paper/2507.04242"},"observation_digest":"sha256:1f6de9d0837eb2f2a25f23b7014141dbc10b0725df0babf11ac07b617a6b1c8f","observation_id":"1a0522bc-8642-4f50-bccc-6955e2f430d3","resolution":{"observed_at":"2026-08-06T20:07:39.140079Z","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":"2026-08-06T20:07:39.116385Z","title":"Sun, Estimation of transmission eigenvalues and the index of ref raction from Cauchy data","venue":null,"work_id":"03fd8bd4-a77c-46b0-83f3-c80c452a7ff6","year":2011},"citing_paper":{"arxiv_id":"2507.04242","last_updated":"2025-07-06T04:38:12Z","snapshot_observed_at":"2026-08-12T17:44:56.777685Z","submitted_at":"2025-07-06T04:38:12Z","title":"Generalized Rellich's lemmas, uniqueness theorem and inside-out duality for scattering poles","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-06T20:07:39.004604Z"},"links":{"citing_paper":"/paper/2507.04242"},"observation_digest":"sha256:efaac125f573afbd213aa3742a712ed8040688d1f178a957c5781f2eda0e9497","observation_id":"3e4398e3-fa66-4b20-a47a-55e7e409ff0a","resolution":{"observed_at":"2026-08-06T20:07:39.122265Z","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":"2026-08-06T20:07:39.097494Z","title":"Sun and A","venue":null,"work_id":"03013ced-8af5-4905-99c9-0969b035e392","year":2017},"citing_paper":{"arxiv_id":"2507.04242","last_updated":"2025-07-06T04:38:12Z","snapshot_observed_at":"2026-08-12T17:44:56.777685Z","submitted_at":"2025-07-06T04:38:12Z","title":"Generalized Rellich's lemmas, uniqueness theorem and inside-out duality for scattering poles","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-06T20:07:39.009311Z"},"links":{"citing_paper":"/paper/2507.04242"},"observation_digest":"sha256:ad904157c71e0bde2adcb3344224af9b494af5b8aab6fa4d323a57e84d6d39f8","observation_id":"7870f02a-6ce2-47c9-b212-669f33a20f55","resolution":{"observed_at":"2026-08-06T20:07:39.104579Z","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":"2026-08-06T20:07:39.078427Z","title":"Taylor, Partial Differential Equations","venue":null,"work_id":"20f6541a-b735-44b9-940b-7accd0408103","year":1996},"citing_paper":{"arxiv_id":"2507.04242","last_updated":"2025-07-06T04:38:12Z","snapshot_observed_at":"2026-08-12T17:44:56.777685Z","submitted_at":"2025-07-06T04:38:12Z","title":"Generalized Rellich's lemmas, uniqueness theorem and inside-out duality for scattering poles","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-06T20:07:39.014468Z"},"links":{"citing_paper":"/paper/2507.04242"},"observation_digest":"sha256:7b327d34f1d7b285e7e3119f1203eee52a9e24161586a9af972f7347348d9578","observation_id":"00ed3b93-d4ba-4ad0-89bf-3c857f7b5c6a","resolution":{"observed_at":"2026-08-06T20:07:39.085046Z","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":{"arxiv_id":"2404.09300","last_updated":"2024-04-14T16:48:01Z","snapshot_observed_at":"2026-07-06T17:59:58.611072Z","submitted_at":"2024-04-14T16:48:01Z","title":"Analysis of a finite element DtN method for scattering resonances of sound hard obstacles","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2404.09300","snapshot_observed_at":"2026-08-06T20:07:39.018998Z","title":null,"venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2507.04242","last_updated":"2025-07-06T04:38:12Z","snapshot_observed_at":"2026-08-12T17:44:56.777685Z","submitted_at":"2025-07-06T04:38:12Z","title":"Generalized Rellich's lemmas, uniqueness theorem and inside-out duality for scattering poles","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-06T20:07:39.018998Z"},"links":{"cited_paper":"/paper/2404.09300","citing_paper":"/paper/2507.04242"},"observation_digest":"sha256:deae4e6602d959b47e1806250a0581e1bb1f074750c6166564923db42cdb1e41","observation_id":"e035c365-f5a4-4332-b371-deac53425437","resolution":{"observed_at":"2026-08-06T20:07:39.018998Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2507.04242","last_updated":"2025-07-06T04:38:12Z","latest_version":1,"primary_category":"math.NA","snapshot_observed_at":"2026-08-12T17:44:56.777685Z","submitted_at":"2025-07-06T04:38:12Z","title":"Generalized Rellich's lemmas, uniqueness theorem and inside-out duality for scattering poles"},"reference_resolution":{"displayed":22,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":2,"verified_exact":0,"verified_fuzzy":20},"total_outbound_references":22},"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 22 of 22 outbound references and 0 inbound Pith citation observations for arXiv:2507.04242."}