{"as_of":"2026-08-07T23:49:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:f0ccca70741d710935877be05edba4bb1aae28bc25fb791272762f91d2009962","coverage":[{"denominator":15,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":15,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-07T13:50:28.699767Z","state":"measured"},{"denominator":17,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":17,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-07T06:34:17.273281+00:00","state":"measured"},{"denominator":2,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":2,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-07T05:24:37.990288Z","state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"arxiv_reference","source_observed_at":"2026-06-29T17:53:47.606321Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2505.21078","last_updated":"2025-05-27T12:02:20Z","snapshot_observed_at":"2026-08-07T13:33:53.184605Z","submitted_at":"2025-05-27T12:02:20Z","title":"Geometric results for hyperbolic operators with spectral transition of the Hamilton map","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2505.21078","snapshot_observed_at":"2026-08-07T05:24:37.990288Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2506.08481","last_updated":"2025-06-11T05:16:36Z","snapshot_observed_at":"2026-08-07T06:58:58.077952Z","submitted_at":"2025-06-10T06:12:07Z","title":"Notes on tangent bicharacteristics and ill-posedness of the Cauchy problem","version":2},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-07T05:24:37.990288Z"},"links":{"cited_paper":"/paper/2505.21078","citing_paper":"/paper/2506.08481"},"observation_digest":"sha256:bcb1c26abc318bfdb6d0364d661d632115cc3970b6e0f36d2a8f0f019efdc99f","observation_id":"ea2e2f2c-61dd-4169-ab68-b7f659792824","resolution":{"observed_at":"2026-08-07T05:24:37.990288Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2505.21078","last_updated":"2025-05-27T12:02:20Z","snapshot_observed_at":"2026-08-07T13:33:53.184605Z","submitted_at":"2025-05-27T12:02:20Z","title":"Geometric results for hyperbolic operators with spectral transition of the Hamilton map","version":1},"cited_work":{"arxiv_id":"2505.21078","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2505.21078","snapshot_observed_at":"2026-06-29T17:53:47.606321Z","title":"Geometric results for hyperbolic operators with spectral transition of the hamilton map, 2025","venue":null,"work_id":"06c26cb1-2531-42f5-8847-f20d17ebd719","year":2025},"citing_paper":{"arxiv_id":"2605.27054","last_updated":"2026-05-26T14:08:08Z","snapshot_observed_at":"2026-08-03T17:17:27.625538Z","submitted_at":"2026-05-26T14:08:08Z","title":"Lack of Gevrey solvability for a model operator","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-06-29T17:44:55.504387Z"},"links":{"cited_paper":"/paper/2505.21078","citing_paper":"/paper/2605.27054"},"observation_digest":"sha256:a28bf5b956e87d635c82dd2edd7c35fe018077f6a168a074198d6a5f0278eb1f","observation_id":"07afd185-e398-4f71-aff1-3f0dedc1eb19","resolution":{"observed_at":"2026-06-29T17:53:47.607849Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}}],"links":{"evidence":"/evidence","html":"/paper/2505.21078/citation-record","integrity":"/paper/2505.21078/integrity","json":"/paper/2505.21078/citation-record.json","paper":"/paper/2505.21078"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T13:50:30.742464Z","title":"Geometric transition for a class of hyper- bolic operators with double characteristics","venue":null,"work_id":"de87efbd-47db-4034-aa44-10582fafc584","year":1997},"citing_paper":{"arxiv_id":"2505.21078","last_updated":"2025-05-27T12:02:20Z","snapshot_observed_at":"2026-08-07T13:33:53.184605Z","submitted_at":"2025-05-27T12:02:20Z","title":"Geometric results for hyperbolic operators with spectral transition of the Hamilton map","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-07T13:50:27.662214Z"},"links":{"citing_paper":"/paper/2505.21078"},"observation_digest":"sha256:b2248b2f7ef68f49831f91c299ce303d399555f0c4361d61a05bcf6ad36193b4","observation_id":"f2bbb6a3-3380-41a9-aef1-c541b823b1b5","resolution":{"observed_at":"2026-08-07T13:50:30.813634Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-07T13:50:30.538437Z","title":"On the Cauchy problem for non- effectively hyperbolic operators, the Gevrey 5 well-posedness","venue":null,"work_id":"4d88aa34-b8a2-4f26-b1c7-b18481788b72","year":2008},"citing_paper":{"arxiv_id":"2505.21078","last_updated":"2025-05-27T12:02:20Z","snapshot_observed_at":"2026-08-07T13:33:53.184605Z","submitted_at":"2025-05-27T12:02:20Z","title":"Geometric results for hyperbolic operators with spectral transition of the Hamilton map","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-07T13:50:27.724810Z"},"links":{"citing_paper":"/paper/2505.21078"},"observation_digest":"sha256:da2bea0a8ff6a31462e72a54540bf4f9fbdd377469c357496314e1f1a5a5639f","observation_id":"37f543cf-22b9-4dfd-9762-8152d3a76e74","resolution":{"observed_at":"2026-08-07T13:50:30.636032Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-07T13:50:30.417365Z","title":"The Cauchy prob- lem for hyperbolic operators with double characteristics in presence of tran- sition","venue":null,"work_id":"c94eeef1-31a5-43b3-8d76-93a4a93373c3","year":2012},"citing_paper":{"arxiv_id":"2505.21078","last_updated":"2025-05-27T12:02:20Z","snapshot_observed_at":"2026-08-07T13:33:53.184605Z","submitted_at":"2025-05-27T12:02:20Z","title":"Geometric results for hyperbolic operators with spectral transition of the Hamilton map","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-07T13:50:27.803527Z"},"links":{"citing_paper":"/paper/2505.21078"},"observation_digest":"sha256:bdea02fb2b40d595c8460bf64ba557ca774a6dfd0795c6d5e4cf38adde3eef04","observation_id":"03f4e05e-db35-4081-b529-74e94e2d4cba","resolution":{"observed_at":"2026-08-07T13:50:30.452810Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-07T13:50:30.339031Z","title":"On the well posedness of the Cauchy problem for a class of hyperbolic operators with double characteristics","venue":null,"work_id":"d6708a8b-8158-4178-8fc3-3756e3cf9e2c","year":2000},"citing_paper":{"arxiv_id":"2505.21078","last_updated":"2025-05-27T12:02:20Z","snapshot_observed_at":"2026-08-07T13:33:53.184605Z","submitted_at":"2025-05-27T12:02:20Z","title":"Geometric results for hyperbolic operators with spectral transition of the Hamilton map","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-07T13:50:27.890057Z"},"links":{"citing_paper":"/paper/2505.21078"},"observation_digest":"sha256:d96e3b4dfae86dced8fe5e37dea159002d9177fb58f55cc37779ff2a94c9b3a2","observation_id":"4f14ae66-6abd-46d9-9535-86cc296b55e0","resolution":{"observed_at":"2026-08-07T13:50:30.368963Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-07T13:50:30.230805Z","title":"The Cauchy problem for differential equations with double characteristics","venue":null,"work_id":"9d7842e3-70c1-42cb-a421-5d1b008b1c68","year":1977},"citing_paper":{"arxiv_id":"2505.21078","last_updated":"2025-05-27T12:02:20Z","snapshot_observed_at":"2026-08-07T13:33:53.184605Z","submitted_at":"2025-05-27T12:02:20Z","title":"Geometric results for hyperbolic operators with spectral transition of the Hamilton map","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-07T13:50:27.972175Z"},"links":{"citing_paper":"/paper/2505.21078"},"observation_digest":"sha256:235d68ae4e62f00fd8cc0d00cfe38fc931cc213a7d47bd41a04d6eb90ab8ffa3","observation_id":"80b0a9dc-ef18-4f01-87d0-e8351b145a18","resolution":{"observed_at":"2026-08-07T13:50:30.279390Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-07T13:50:30.080954Z","title":"III , vol- ume 274 of Grundlehren der mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences]","venue":null,"work_id":"e9152e17-0eb0-4dd4-a6a6-96bb6534950e","year":1985},"citing_paper":{"arxiv_id":"2505.21078","last_updated":"2025-05-27T12:02:20Z","snapshot_observed_at":"2026-08-07T13:33:53.184605Z","submitted_at":"2025-05-27T12:02:20Z","title":"Geometric results for hyperbolic operators with spectral transition of the Hamilton map","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-07T13:50:28.073887Z"},"links":{"citing_paper":"/paper/2505.21078"},"observation_digest":"sha256:239794b5b79b576cde383e281fc6eced2b659378b3a092ed90fab63552a30a2c","observation_id":"3248d9b3-e789-4006-9640-087a488e287d","resolution":{"observed_at":"2026-08-07T13:50:30.185319Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-07T13:50:29.775930Z","title":null,"venue":null,"work_id":"368d2467-925b-430a-a8fc-3cb72aa39432","year":1978},"citing_paper":{"arxiv_id":"2505.21078","last_updated":"2025-05-27T12:02:20Z","snapshot_observed_at":"2026-08-07T13:33:53.184605Z","submitted_at":"2025-05-27T12:02:20Z","title":"Geometric results for hyperbolic operators with spectral transition of the Hamilton map","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-07T13:50:28.151897Z"},"links":{"citing_paper":"/paper/2505.21078"},"observation_digest":"sha256:505e521cb87769686ed2ac9d27c3c1f78d51b9b5320c580a376157217ce3243a","observation_id":"54a8b5a2-6b6d-4d45-a6b8-ebaba2f3ae8d","resolution":{"observed_at":"2026-08-07T13:50:29.900171Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-07T13:50:29.591529Z","title":null,"venue":null,"work_id":"92bab29d-c1dc-49b1-bdbd-74a8001be7e1","year":1974},"citing_paper":{"arxiv_id":"2505.21078","last_updated":"2025-05-27T12:02:20Z","snapshot_observed_at":"2026-08-07T13:33:53.184605Z","submitted_at":"2025-05-27T12:02:20Z","title":"Geometric results for hyperbolic operators with spectral transition of the Hamilton map","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-07T13:50:28.232599Z"},"links":{"citing_paper":"/paper/2505.21078"},"observation_digest":"sha256:9df1d25da7e37ee8c3bd38d2caf5d5d60b3738d4bf892725a63a6e435369f21e","observation_id":"7a4b9f5b-a236-4447-9558-a5b917e7a2c2","resolution":{"observed_at":"2026-08-07T13:50:29.681646Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-07T13:50:29.487969Z","title":"The hyperbolic Cauchy problem , volume 1505 of Lecture Notes in Mathematics","venue":null,"work_id":"774959cb-cced-4575-b6e3-f49549d7e900","year":1991},"citing_paper":{"arxiv_id":"2505.21078","last_updated":"2025-05-27T12:02:20Z","snapshot_observed_at":"2026-08-07T13:33:53.184605Z","submitted_at":"2025-05-27T12:02:20Z","title":"Geometric results for hyperbolic operators with spectral transition of the Hamilton map","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-07T13:50:28.317488Z"},"links":{"citing_paper":"/paper/2505.21078"},"observation_digest":"sha256:31e75cccce9866e160648b43231333dad7499ef3b0584a6089917622dddb6a68","observation_id":"0f943b45-e99e-439f-9ea0-bf3ec2d05bc7","resolution":{"observed_at":"2026-08-07T13:50:29.526252Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-07T13:50:29.395837Z","title":"On the Cauchy problem for noneffectively hyperbolic oper- ators, a transition case","venue":null,"work_id":"15fb6cf8-0102-4016-a70c-f8a1ee6dc36a","year":2013},"citing_paper":{"arxiv_id":"2505.21078","last_updated":"2025-05-27T12:02:20Z","snapshot_observed_at":"2026-08-07T13:33:53.184605Z","submitted_at":"2025-05-27T12:02:20Z","title":"Geometric results for hyperbolic operators with spectral transition of the Hamilton map","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-07T13:50:28.384007Z"},"links":{"citing_paper":"/paper/2505.21078"},"observation_digest":"sha256:7e5cab279967745fdfc6ad6398a10e139bd7fc7fc7940a4d0a0d04fa807b729e","observation_id":"7e210d3b-ffd4-4f59-bc52-db1da955dc30","resolution":{"observed_at":"2026-08-07T13:50:29.424221Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-07T13:50:29.292382Z","title":"On the Cauchy problem for hyperbolic operators with dou- ble characteristics, a transition case","venue":null,"work_id":"9310c8d1-3184-4a5b-9b1a-d92f5424de36","year":2014},"citing_paper":{"arxiv_id":"2505.21078","last_updated":"2025-05-27T12:02:20Z","snapshot_observed_at":"2026-08-07T13:33:53.184605Z","submitted_at":"2025-05-27T12:02:20Z","title":"Geometric results for hyperbolic operators with spectral transition of the Hamilton map","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-07T13:50:28.450252Z"},"links":{"citing_paper":"/paper/2505.21078"},"observation_digest":"sha256:282cf3c423ae32b74f45041c400302ebfeba6fbab6303d6d2428701d1ff8a659","observation_id":"f5f1f00a-c65d-4ddf-a071-91e6c105c2ff","resolution":{"observed_at":"2026-08-07T13:50:29.340398Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-07T13:50:29.168499Z","title":"Cauchy problem for differential operators with double char- acteristics, volume 2202 of Lecture Notes in Mathematics","venue":null,"work_id":"7fa25646-3705-4bcd-9c8f-19bb8f504e21","year":null},"citing_paper":{"arxiv_id":"2505.21078","last_updated":"2025-05-27T12:02:20Z","snapshot_observed_at":"2026-08-07T13:33:53.184605Z","submitted_at":"2025-05-27T12:02:20Z","title":"Geometric results for hyperbolic operators with spectral transition of the Hamilton map","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-07T13:50:28.505492Z"},"links":{"citing_paper":"/paper/2505.21078"},"observation_digest":"sha256:74eb932730b620897246bf3b9d4238f401eb0553fdae194e44fa5f8a1543577a","observation_id":"05aec62a-da10-4d73-882a-15363b4706ef","resolution":{"observed_at":"2026-08-07T13:50:29.215824Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-07T13:50:28.933103Z","title":"On the Cauchy problem for differential operators with dou- ble characteristics, a transition from non-effective to effective characteristics","venue":null,"work_id":"8f66659e-8a0a-49db-aae5-b02b9fe4ce84","year":2018},"citing_paper":{"arxiv_id":"2505.21078","last_updated":"2025-05-27T12:02:20Z","snapshot_observed_at":"2026-08-07T13:33:53.184605Z","submitted_at":"2025-05-27T12:02:20Z","title":"Geometric results for hyperbolic operators with spectral transition of the Hamilton map","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-07T13:50:28.638422Z"},"links":{"citing_paper":"/paper/2505.21078"},"observation_digest":"sha256:3fe87092cea618ac9a1755c2eddf27ae44750aa7fa8ec827ce41136684cce284","observation_id":"f1c31b39-5f0f-4dcb-ae26-f58d35f4f120","resolution":{"observed_at":"2026-08-07T13:50:28.974119Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-07T13:50:28.824513Z","title":"A more direct way to the Cauchy problem for effectively hyperbolic operators","venue":null,"work_id":"3e1a4c1c-90e3-4e21-8033-9e09f82faa29","year":2024},"citing_paper":{"arxiv_id":"2505.21078","last_updated":"2025-05-27T12:02:20Z","snapshot_observed_at":"2026-08-07T13:33:53.184605Z","submitted_at":"2025-05-27T12:02:20Z","title":"Geometric results for hyperbolic operators with spectral transition of the Hamilton map","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-07T13:50:28.699767Z"},"links":{"citing_paper":"/paper/2505.21078"},"observation_digest":"sha256:7b812da0395ef427b3b6fffa80be730c56587da6347c78dd4f0c135cd4723fed","observation_id":"d6d010ed-e8fd-4a40-a201-30a6098a9ea2","resolution":{"observed_at":"2026-08-07T13:50:28.870695Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-07T13:50:29.042549Z","title":null,"venue":null,"work_id":"dfd1c129-aa26-498b-84dc-5a56a5f8dea2","year":null},"citing_paper":{"arxiv_id":"2505.21078","last_updated":"2025-05-27T12:02:20Z","snapshot_observed_at":"2026-08-07T13:33:53.184605Z","submitted_at":"2025-05-27T12:02:20Z","title":"Geometric results for hyperbolic operators with spectral transition of the Hamilton map","version":1},"reference_index":2017,"source":"pdf_text","source_observed_at":"2026-08-07T13:50:28.575803Z"},"links":{"citing_paper":"/paper/2505.21078"},"observation_digest":"sha256:e229ef6ae3bb35a0910e6b32d36bf77dc273e49f65a47649e1e94de7b2898236","observation_id":"cafb92a9-5884-41e2-8f4a-23fbd104eb5d","resolution":{"observed_at":"2026-08-07T13:50:29.111553Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2505.21078","last_updated":"2025-05-27T12:02:20Z","latest_version":1,"primary_category":"math.AP","snapshot_observed_at":"2026-08-07T13:33:53.184605Z","submitted_at":"2025-05-27T12:02:20Z","title":"Geometric results for hyperbolic operators with spectral transition of the Hamilton map"},"reference_resolution":{"displayed":15,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":3,"verified_exact":0,"verified_fuzzy":12},"total_outbound_references":15},"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":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"thesis":"As of 7 August 2026, this Paper Citation Record lists 15 of 15 outbound references and 2 inbound Pith citation observations for arXiv:2505.21078."}