{"as_of":"2026-08-10T00:54:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:8ef5fefed1e6f0634cee158cf76c50b4538437bdda2973ffab0253572e940953","coverage":[{"denominator":21,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":21,"source":"paper_references, paper_reference_links","source_observed_at":"2026-07-10T19:48:39.761787Z","state":"measured"},{"denominator":21,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":21,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-09T06:31:02.800959+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/2607.07171/citation-record","integrity":"/paper/2607.07171/integrity","json":"/paper/2607.07171/citation-record.json","paper":"/paper/2607.07171"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-10T19:57:34.475771Z","title":"137, Springer, New York, 2001","venue":null,"work_id":"ae118438-a6f7-406e-9ff5-ff94fe744583","year":2001},"citing_paper":{"arxiv_id":"2607.07171","last_updated":"2026-07-09T11:54:26Z","snapshot_observed_at":"2026-08-10T00:34:28.319382Z","submitted_at":"2026-07-08T09:05:58Z","title":"$L^p$-Asymptotic Profiles for the Heat Equation with a Hardy Potential","version":2},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-07-10T19:48:39.761787Z"},"links":{"citing_paper":"/paper/2607.07171"},"observation_digest":"sha256:f3826dc48e624de4bdfbff718215924bc80d4a800cff45a1ff1bf00bfc43cb34","observation_id":"d72a4be6-0a34-4104-b797-726e4d66c859","resolution":{"observed_at":"2026-07-10T19:57:34.477690Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-07-10T19:57:34.478231Z","title":"A.,The heat equation with a singular potential, Transactions of the American Mathematical Society284(1984), no","venue":null,"work_id":"32e4eb7c-73d9-4bf3-b5f3-da4b23c26471","year":1984},"citing_paper":{"arxiv_id":"2607.07171","last_updated":"2026-07-09T11:54:26Z","snapshot_observed_at":"2026-08-10T00:34:28.319382Z","submitted_at":"2026-07-08T09:05:58Z","title":"$L^p$-Asymptotic Profiles for the Heat Equation with a Hardy Potential","version":2},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-07-10T19:48:39.761787Z"},"links":{"citing_paper":"/paper/2607.07171"},"observation_digest":"sha256:db147ba25ffc047c1cc445aee1d8a954411cfaf12800c0beb83a8d3c862a5774","observation_id":"e16a44fc-902f-4cd6-afe9-ee1ebb77efdd","resolution":{"observed_at":"2026-07-10T19:57:34.479442Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-07-10T19:57:34.479991Z","title":"Classe di Scienze25(1997), no","venue":null,"work_id":"66e246fc-d509-4e10-96ed-9eb8d25df898","year":1997},"citing_paper":{"arxiv_id":"2607.07171","last_updated":"2026-07-09T11:54:26Z","snapshot_observed_at":"2026-08-10T00:34:28.319382Z","submitted_at":"2026-07-08T09:05:58Z","title":"$L^p$-Asymptotic Profiles for the Heat Equation with a Hardy Potential","version":2},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-07-10T19:48:39.761787Z"},"links":{"citing_paper":"/paper/2607.07171"},"observation_digest":"sha256:f854a0c09fc7a89421612109a841e6c80b1dfa4ec33cfa559191770296a4c9e4","observation_id":"db4ddf05-4897-4e6c-927b-4f72e0456fe5","resolution":{"observed_at":"2026-07-10T19:57:34.481036Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-07-10T19:57:34.471046Z","title":null,"venue":null,"work_id":"c1f4e2ac-57fb-4ff5-9d69-72432f411106","year":2011},"citing_paper":{"arxiv_id":"2607.07171","last_updated":"2026-07-09T11:54:26Z","snapshot_observed_at":"2026-08-10T00:34:28.319382Z","submitted_at":"2026-07-08T09:05:58Z","title":"$L^p$-Asymptotic Profiles for the Heat Equation with a Hardy Potential","version":2},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-07-10T19:48:39.761787Z"},"links":{"citing_paper":"/paper/2607.07171"},"observation_digest":"sha256:31da72a737e16db5e9076d8f7429ae11d3501db5f1d28900f61734820150682a","observation_id":"66af3d4c-0c88-483a-b871-2034b2bc934a","resolution":{"observed_at":"2026-07-10T19:57:34.472096Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-07-10T19:57:34.469400Z","title":null,"venue":null,"work_id":"7e2ba5d6-9fa9-4372-9774-576a13ba33d4","year":2023},"citing_paper":{"arxiv_id":"2607.07171","last_updated":"2026-07-09T11:54:26Z","snapshot_observed_at":"2026-08-10T00:34:28.319382Z","submitted_at":"2026-07-08T09:05:58Z","title":"$L^p$-Asymptotic Profiles for the Heat Equation with a Hardy Potential","version":2},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-07-10T19:48:39.761787Z"},"links":{"citing_paper":"/paper/2607.07171"},"observation_digest":"sha256:81b8568366e879febf16007241c9fcb7b2da0c63206914351c7616a7a4be182e","observation_id":"ee46ac4d-e5b8-4b21-bf7e-ead1576dc831","resolution":{"observed_at":"2026-07-10T19:57:34.470481Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-07-10T19:57:34.472608Z","title":"W.; Rodriguez-Bernal, A.,Self-similarity in homogeneous stationary and evolution prob- lems, Journal of Evolution Equations23(2023), Paper No","venue":null,"work_id":"01df3521-d784-4970-b475-83334155d0f5","year":2023},"citing_paper":{"arxiv_id":"2607.07171","last_updated":"2026-07-09T11:54:26Z","snapshot_observed_at":"2026-08-10T00:34:28.319382Z","submitted_at":"2026-07-08T09:05:58Z","title":"$L^p$-Asymptotic Profiles for the Heat Equation with a Hardy Potential","version":2},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-07-10T19:48:39.761787Z"},"links":{"citing_paper":"/paper/2607.07171"},"observation_digest":"sha256:94e7e0e80e2b392a892c2cdb501693c794f6ba387cc2695ea18266194aedf8ee","observation_id":"19bd31fe-2897-4fec-b761-7040bccc932d","resolution":{"observed_at":"2026-07-10T19:57:34.473851Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-07-10T19:57:34.481541Z","title":null,"venue":null,"work_id":"9ce16e30-aac5-491f-ba95-20408625cb83","year":2017},"citing_paper":{"arxiv_id":"2607.07171","last_updated":"2026-07-09T11:54:26Z","snapshot_observed_at":"2026-08-10T00:34:28.319382Z","submitted_at":"2026-07-08T09:05:58Z","title":"$L^p$-Asymptotic Profiles for the Heat Equation with a Hardy Potential","version":2},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-07-10T19:48:39.761787Z"},"links":{"citing_paper":"/paper/2607.07171"},"observation_digest":"sha256:95056d93121746bbbf2c15d8f833cf5bc21fd21a46cec08bdb7e8d9c21bd92a6","observation_id":"5d405ec6-ae33-4d96-8b41-1e312fc29c22","resolution":{"observed_at":"2026-07-10T19:57:34.482583Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-07-10T19:57:34.483093Z","title":"N.; Kalf, H.,The Bessel differential equation and the Hankel transform, Journal of Computational and Applied Mathematics208(2007), 3–19","venue":null,"work_id":"68a8d7ec-d40d-4be3-9995-c221c36742ea","year":2007},"citing_paper":{"arxiv_id":"2607.07171","last_updated":"2026-07-09T11:54:26Z","snapshot_observed_at":"2026-08-10T00:34:28.319382Z","submitted_at":"2026-07-08T09:05:58Z","title":"$L^p$-Asymptotic Profiles for the Heat Equation with a Hardy Potential","version":2},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-07-10T19:48:39.761787Z"},"links":{"citing_paper":"/paper/2607.07171"},"observation_digest":"sha256:51d991467a2830ff7a705bb4bf9ca993676346088e3999cf201530e018c5ace5","observation_id":"a7cd3293-92cb-4e46-9656-abcc7de1be60","resolution":{"observed_at":"2026-07-10T19:57:34.484282Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-07-10T19:57:34.467910Z","title":"1, 237–281","venue":null,"work_id":"4981dd7e-4df4-4cbd-899c-604d69c22829","year":2007},"citing_paper":{"arxiv_id":"2607.07171","last_updated":"2026-07-09T11:54:26Z","snapshot_observed_at":"2026-08-10T00:34:28.319382Z","submitted_at":"2026-07-08T09:05:58Z","title":"$L^p$-Asymptotic Profiles for the Heat Equation with a Hardy Potential","version":2},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-07-10T19:48:39.761787Z"},"links":{"citing_paper":"/paper/2607.07171"},"observation_digest":"sha256:a4e566d0f58938415804ec8e26c7352bf29d62944839143e59fb0beda03c76b5","observation_id":"4c5d623a-d61f-433c-877c-c05eca80d368","resolution":{"observed_at":"2026-07-10T19:57:34.468899Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-07-10T19:57:34.484844Z","title":"S.; Ryzhik, I","venue":null,"work_id":"b47b9adc-df7e-402b-be8a-bd2c2dabc190","year":2007},"citing_paper":{"arxiv_id":"2607.07171","last_updated":"2026-07-09T11:54:26Z","snapshot_observed_at":"2026-08-10T00:34:28.319382Z","submitted_at":"2026-07-08T09:05:58Z","title":"$L^p$-Asymptotic Profiles for the Heat Equation with a Hardy Potential","version":2},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-07-10T19:48:39.761787Z"},"links":{"citing_paper":"/paper/2607.07171"},"observation_digest":"sha256:c645bc6bcf3e8089a323feaf1c94ce05a8be503637335e9dcf631003033c36a8","observation_id":"9e56e6f7-a5d2-4570-b7d0-9d5946f6f0b3","resolution":{"observed_at":"2026-07-10T19:57:34.485885Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-07-10T19:57:34.463179Z","title":"M.,The heat kernel of a Schroedinger operator with inverse square potential, Proceedings of the London Mathematical Society115(2017), 381–410","venue":null,"work_id":"d9d072ca-e52b-4660-a4ea-45e5b6757126","year":2017},"citing_paper":{"arxiv_id":"2607.07171","last_updated":"2026-07-09T11:54:26Z","snapshot_observed_at":"2026-08-10T00:34:28.319382Z","submitted_at":"2026-07-08T09:05:58Z","title":"$L^p$-Asymptotic Profiles for the Heat Equation with a Hardy Potential","version":2},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-07-10T19:48:39.761787Z"},"links":{"citing_paper":"/paper/2607.07171"},"observation_digest":"sha256:2f9474f1fbedc60a56312b7c5cbcd22d9345577fea20dbbb6c1f0c660602eb3c","observation_id":"1678814b-6238-47e7-9282-6a90b73a8115","resolution":{"observed_at":"2026-07-10T19:57:34.464369Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-07-10T19:57:34.461627Z","title":null,"venue":null,"work_id":"35ec9730-786c-4c12-9972-93d1ecbf07c2","year":2003},"citing_paper":{"arxiv_id":"2607.07171","last_updated":"2026-07-09T11:54:26Z","snapshot_observed_at":"2026-08-10T00:34:28.319382Z","submitted_at":"2026-07-08T09:05:58Z","title":"$L^p$-Asymptotic Profiles for the Heat Equation with a Hardy Potential","version":2},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-07-10T19:48:39.761787Z"},"links":{"citing_paper":"/paper/2607.07171"},"observation_digest":"sha256:08cb5e7671d346641872f076f65678f66bfcebf634f5d7d7e27fc1357c0f7ffd","observation_id":"2324de27-3488-4dbf-b202-5b651053755c","resolution":{"observed_at":"2026-07-10T19:57:34.462645Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-07-10T19:57:34.464890Z","title":null,"venue":null,"work_id":"e05b3daa-ebf9-477b-b27d-ce92dd0e0112","year":2018},"citing_paper":{"arxiv_id":"2607.07171","last_updated":"2026-07-09T11:54:26Z","snapshot_observed_at":"2026-08-10T00:34:28.319382Z","submitted_at":"2026-07-08T09:05:58Z","title":"$L^p$-Asymptotic Profiles for the Heat Equation with a Hardy Potential","version":2},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-07-10T19:48:39.761787Z"},"links":{"citing_paper":"/paper/2607.07171"},"observation_digest":"sha256:0c995480f6d91b92e5689b332a6445215c8aba17c51312099376aa7cfba2b6dc","observation_id":"d339c09e-e7ea-491e-aa1a-428568de16e2","resolution":{"observed_at":"2026-07-10T19:57:34.465853Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-07-10T19:57:34.466365Z","title":"D.; Semenov, Yu","venue":null,"work_id":"721161ff-ab34-472e-869b-ce47d72e3b2c","year":2003},"citing_paper":{"arxiv_id":"2607.07171","last_updated":"2026-07-09T11:54:26Z","snapshot_observed_at":"2026-08-10T00:34:28.319382Z","submitted_at":"2026-07-08T09:05:58Z","title":"$L^p$-Asymptotic Profiles for the Heat Equation with a Hardy Potential","version":2},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-07-10T19:48:39.761787Z"},"links":{"citing_paper":"/paper/2607.07171"},"observation_digest":"sha256:1736a10adb6f885f215a4d1e58934849a8cee7e66a7291fe34b6611cd5aa7256","observation_id":"9da72527-1f29-4eae-a309-dda1733a0aeb","resolution":{"observed_at":"2026-07-10T19:57:34.467409Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-07-10T19:57:34.459993Z","title":"D.; Semenov, Yu","venue":null,"work_id":"e62f1efa-8908-4139-b52e-f0b82d5362c6","year":2004},"citing_paper":{"arxiv_id":"2607.07171","last_updated":"2026-07-09T11:54:26Z","snapshot_observed_at":"2026-08-10T00:34:28.319382Z","submitted_at":"2026-07-08T09:05:58Z","title":"$L^p$-Asymptotic Profiles for the Heat Equation with a Hardy Potential","version":2},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-07-10T19:48:39.761787Z"},"links":{"citing_paper":"/paper/2607.07171"},"observation_digest":"sha256:599e1e013ec8b9a8e916b46f11eaa1a923957fa9f188fd2ccb87a0198d2554d1","observation_id":"95b35e91-df7c-4598-a322-f482b88ce290","resolution":{"observed_at":"2026-07-10T19:57:34.461059Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-07-10T19:57:34.486442Z","title":"Matematica e Applicazioni16(2005), no","venue":null,"work_id":"c5e63d07-5b28-4d3f-b75a-5e1f039ba933","year":2005},"citing_paper":{"arxiv_id":"2607.07171","last_updated":"2026-07-09T11:54:26Z","snapshot_observed_at":"2026-08-10T00:34:28.319382Z","submitted_at":"2026-07-08T09:05:58Z","title":"$L^p$-Asymptotic Profiles for the Heat Equation with a Hardy Potential","version":2},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-07-10T19:48:39.761787Z"},"links":{"citing_paper":"/paper/2607.07171"},"observation_digest":"sha256:b7e8ba1f4447d775d702612bc7e50a8a6ec2d5bfd19d2066d9e0a109b9463696","observation_id":"3836572c-90c7-4620-bd83-bba962aeb802","resolution":{"observed_at":"2026-07-10T19:57:34.487561Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-07-10T19:57:34.488336Z","title":null,"venue":null,"work_id":"6f048521-1ff9-447d-87c1-cb871c7aec8f","year":2013},"citing_paper":{"arxiv_id":"2607.07171","last_updated":"2026-07-09T11:54:26Z","snapshot_observed_at":"2026-08-10T00:34:28.319382Z","submitted_at":"2026-07-08T09:05:58Z","title":"$L^p$-Asymptotic Profiles for the Heat Equation with a Hardy Potential","version":2},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-07-10T19:48:39.761787Z"},"links":{"citing_paper":"/paper/2607.07171"},"observation_digest":"sha256:4bc1cf72485b3d781dba47dcb0c5fe7fe2921dc8b98eceda77f1bd7c9b97ab0c","observation_id":"89aea503-d408-4f76-a009-42623a16638a","resolution":{"observed_at":"2026-07-10T19:57:34.489349Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-07-10T19:57:34.456169Z","title":"N.,The Use of Integral Transforms, McGraw-Hill, New York, 1972","venue":null,"work_id":"11ebf664-ddb6-45c6-a1af-7920bcc2057e","year":1972},"citing_paper":{"arxiv_id":"2607.07171","last_updated":"2026-07-09T11:54:26Z","snapshot_observed_at":"2026-08-10T00:34:28.319382Z","submitted_at":"2026-07-08T09:05:58Z","title":"$L^p$-Asymptotic Profiles for the Heat Equation with a Hardy Potential","version":2},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-07-10T19:48:39.761787Z"},"links":{"citing_paper":"/paper/2607.07171"},"observation_digest":"sha256:e5187b98a522f236c2639a871ee3006dc31f05a4b3844423857eef4214e2c95e","observation_id":"3aff17c5-db1f-48c6-8695-267a1875539b","resolution":{"observed_at":"2026-07-10T19:57:34.457441Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-07-10T19:57:34.458004Z","title":"L.; Zuazua, E.,The Hardy inequality and the asymptotic behaviour of the heat equation with an inverse-square potential, Journal of Functional Analysis173(2000), 103–153","venue":null,"work_id":"fe6dafad-e945-4321-bad2-244271060600","year":2000},"citing_paper":{"arxiv_id":"2607.07171","last_updated":"2026-07-09T11:54:26Z","snapshot_observed_at":"2026-08-10T00:34:28.319382Z","submitted_at":"2026-07-08T09:05:58Z","title":"$L^p$-Asymptotic Profiles for the Heat Equation with a Hardy Potential","version":2},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-07-10T19:48:39.761787Z"},"links":{"citing_paper":"/paper/2607.07171"},"observation_digest":"sha256:a289a5f8d47d0ec1b1aca13879b4d58912dc3513ff79c29ff5affff60609ab67","observation_id":"933081ac-f7e8-41c0-8e79-37fa4a2de7ad","resolution":{"observed_at":"2026-07-10T19:57:34.459429Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-07-10T19:57:34.453846Z","title":"N.,A Treatise on the Theory of Bessel Functions, 2nd ed., Cambridge University Press, 1944","venue":null,"work_id":"5868215a-92e5-45d7-a51c-8b78e5182946","year":1944},"citing_paper":{"arxiv_id":"2607.07171","last_updated":"2026-07-09T11:54:26Z","snapshot_observed_at":"2026-08-10T00:34:28.319382Z","submitted_at":"2026-07-08T09:05:58Z","title":"$L^p$-Asymptotic Profiles for the Heat Equation with a Hardy Potential","version":2},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-07-10T19:48:39.761787Z"},"links":{"citing_paper":"/paper/2607.07171"},"observation_digest":"sha256:d55f2e10492c28b6e181ac086d816d035d755fda767756e06378695283b6262e","observation_id":"ee7d418a-d615-4f07-b7d2-ebaaf8493a78","resolution":{"observed_at":"2026-07-10T19:57:34.454956Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2003.11834","last_updated":"2020-03-26T11:05:26Z","snapshot_observed_at":"2026-08-09T14:08:01.727863Z","submitted_at":"2020-03-26T11:05:26Z","title":"Asymptotic behavior of scalar convection-diffusion equations","version":1},"cited_work":{"arxiv_id":"2003.11834","doi":null,"metadata_source":"pith","pith_arxiv_id":"2003.11834","snapshot_observed_at":"2026-07-10T19:57:34.110960Z","title":"Asymptotic behavior of scalar convection-diffusion equations","venue":"math.AP","work_id":"30c17852-f9f5-41a0-8c4e-641a150f759e","year":2020},"citing_paper":{"arxiv_id":"2607.07171","last_updated":"2026-07-09T11:54:26Z","snapshot_observed_at":"2026-08-10T00:34:28.319382Z","submitted_at":"2026-07-08T09:05:58Z","title":"$L^p$-Asymptotic Profiles for the Heat Equation with a Hardy Potential","version":2},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-07-10T19:48:39.761787Z"},"links":{"cited_paper":"/paper/2003.11834","citing_paper":"/paper/2607.07171"},"observation_digest":"sha256:0a39c05b69626c49e87fd52ae9df0272a05f68e07b0412c913f16497e3862fb9","observation_id":"b41329e4-4335-4ddf-a4c3-e7da6815afee","resolution":{"observed_at":"2026-07-10T19:57:34.112135Z","resolver_source":"local_arxiv","status":"metadata_mismatch"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2607.07171","last_updated":"2026-07-09T11:54:26Z","latest_version":2,"primary_category":"math.AP","snapshot_observed_at":"2026-08-10T00:34:28.319382Z","submitted_at":"2026-07-08T09:05:58Z","title":"$L^p$-Asymptotic Profiles for the Heat Equation with a Hardy Potential"},"reference_resolution":{"displayed":21,"state_counts":{"malformed_identifier":0,"metadata_mismatch":1,"parse_uncertain":0,"unresolved":6,"verified_exact":0,"verified_fuzzy":14},"total_outbound_references":21},"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":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"thesis":"As of 10 August 2026, this Paper Citation Record lists 21 of 21 outbound references and 0 inbound Pith citation observations for arXiv:2607.07171."}