{"as_of":"2026-08-18T18:43:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:822412b8aad3333a09c63da54b21569dfe6e17d239136add050ef59354fe68d8","coverage":[{"denominator":41,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":41,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-11T13:50:36.136332Z","state":"measured"},{"denominator":41,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":41,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-18T06:34:40.430872+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/2412.12851/citation-record","integrity":"/paper/2412.12851/integrity","json":"/paper/2412.12851/citation-record.json","paper":"/paper/2412.12851"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T13:50:36.929665Z","title":null,"venue":null,"work_id":"97c4da91-1706-4549-8a09-9dd7e97f6efb","year":1939},"citing_paper":{"arxiv_id":"2412.12851","last_updated":"2025-05-20T19:45:13Z","snapshot_observed_at":"2026-08-11T13:37:58.814786Z","submitted_at":"2024-12-17T12:25:39Z","title":"Uniqueness of solutions to the isotropic $L_{p}$ Gaussian Minkowski problem","version":2},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-11T13:50:35.920856Z"},"links":{"citing_paper":"/paper/2412.12851"},"observation_digest":"sha256:ca042974ec81abc16577c163d97e424aa0d8f506c5c32a928d26ebd6530dc9f8","observation_id":"d859f288-46b4-4458-981f-c0ae61ca1ce2","resolution":{"observed_at":"2026-08-11T13:50:36.934281Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-11T13:50:36.915095Z","title":null,"venue":null,"work_id":"b1ee2afc-8cfc-48c4-aa16-69485be6edbc","year":1938},"citing_paper":{"arxiv_id":"2412.12851","last_updated":"2025-05-20T19:45:13Z","snapshot_observed_at":"2026-08-11T13:37:58.814786Z","submitted_at":"2024-12-17T12:25:39Z","title":"Uniqueness of solutions to the isotropic $L_{p}$ Gaussian Minkowski problem","version":2},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-11T13:50:35.926401Z"},"links":{"citing_paper":"/paper/2412.12851"},"observation_digest":"sha256:b219d1e0be096420190401b2d7aaba90395191f5a5c03712dfe5f6424b865f0e","observation_id":"4979a561-4365-4272-bf3c-904a6a767e5d","resolution":{"observed_at":"2026-08-11T13:50:36.919977Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-11T13:50:36.899569Z","title":"Andrews, Monotone quantities and unique limits for ev olving convex hypersurfaces, Internat","venue":null,"work_id":"2268d241-78ac-48d0-a86b-f090ddcdeb94","year":1997},"citing_paper":{"arxiv_id":"2412.12851","last_updated":"2025-05-20T19:45:13Z","snapshot_observed_at":"2026-08-11T13:37:58.814786Z","submitted_at":"2024-12-17T12:25:39Z","title":"Uniqueness of solutions to the isotropic $L_{p}$ Gaussian Minkowski problem","version":2},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-11T13:50:35.931524Z"},"links":{"citing_paper":"/paper/2412.12851"},"observation_digest":"sha256:efbad71108b09c2c82d2b51a8142b72582d957a13ba4530d5b6fd9dac5c086ef","observation_id":"355cf559-e33c-4bb2-99fb-85948169f624","resolution":{"observed_at":"2026-08-11T13:50:36.904502Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-11T13:50:36.884667Z","title":"Andrews, Classiﬁcation of limiting shapes for isotro pic curve ﬂows, J","venue":null,"work_id":"9478b5f3-812b-4a7b-aa28-b1583311b172","year":2003},"citing_paper":{"arxiv_id":"2412.12851","last_updated":"2025-05-20T19:45:13Z","snapshot_observed_at":"2026-08-11T13:37:58.814786Z","submitted_at":"2024-12-17T12:25:39Z","title":"Uniqueness of solutions to the isotropic $L_{p}$ Gaussian Minkowski problem","version":2},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-11T13:50:35.936622Z"},"links":{"citing_paper":"/paper/2412.12851"},"observation_digest":"sha256:1eb6959525bbdefa5f6f14603d78a3009db6aeec162cb66c9587047a999f70c3","observation_id":"07822292-fa73-4bad-a26d-a6a5e85ee51c","resolution":{"observed_at":"2026-08-11T13:50:36.889552Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-11T13:50:36.869933Z","title":"Andrews, B","venue":null,"work_id":"0c70bd30-4c17-4af0-893a-e2800472a15e","year":2020},"citing_paper":{"arxiv_id":"2412.12851","last_updated":"2025-05-20T19:45:13Z","snapshot_observed_at":"2026-08-11T13:37:58.814786Z","submitted_at":"2024-12-17T12:25:39Z","title":"Uniqueness of solutions to the isotropic $L_{p}$ Gaussian Minkowski problem","version":2},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-11T13:50:35.941850Z"},"links":{"citing_paper":"/paper/2412.12851"},"observation_digest":"sha256:c6f7b7bd01fe0b6675b0b5448ba819f011984839545083f9451768a51cd90070","observation_id":"9e18a061-8963-4a35-b5c0-99f2a7fe4c51","resolution":{"observed_at":"2026-08-11T13:50:36.874683Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-11T13:50:36.854423Z","title":"Bianchi, K","venue":null,"work_id":"dce6b78f-a86f-49b4-acbf-588cb98022c7","year":2019},"citing_paper":{"arxiv_id":"2412.12851","last_updated":"2025-05-20T19:45:13Z","snapshot_observed_at":"2026-08-11T13:37:58.814786Z","submitted_at":"2024-12-17T12:25:39Z","title":"Uniqueness of solutions to the isotropic $L_{p}$ Gaussian Minkowski problem","version":2},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-11T13:50:35.946359Z"},"links":{"citing_paper":"/paper/2412.12851"},"observation_digest":"sha256:a9d898234a772bf2fc4f0d3d18a368b7c451fe4905733559b70da9d04b9b35a3","observation_id":"3ea9419d-8244-4e9b-b4fe-d55f517f58da","resolution":{"observed_at":"2026-08-11T13:50:36.859316Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-11T13:50:36.839397Z","title":"Bonnesen and W","venue":null,"work_id":"e71ac695-7247-4433-8890-2418bbf30296","year":1987},"citing_paper":{"arxiv_id":"2412.12851","last_updated":"2025-05-20T19:45:13Z","snapshot_observed_at":"2026-08-11T13:37:58.814786Z","submitted_at":"2024-12-17T12:25:39Z","title":"Uniqueness of solutions to the isotropic $L_{p}$ Gaussian Minkowski problem","version":2},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-11T13:50:35.951618Z"},"links":{"citing_paper":"/paper/2412.12851"},"observation_digest":"sha256:562535c10acad3063ac57dd0709554a5808c8b07347e8987762eea020b58d5af","observation_id":"8b2bec63-ecd6-40b4-829a-7a43273344f5","resolution":{"observed_at":"2026-08-11T13:50:36.843890Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-11T13:50:36.824378Z","title":"B¨ or¨ oczky, E","venue":null,"work_id":"3c0845d7-209e-452e-9d43-98c6450558f3","year":2013},"citing_paper":{"arxiv_id":"2412.12851","last_updated":"2025-05-20T19:45:13Z","snapshot_observed_at":"2026-08-11T13:37:58.814786Z","submitted_at":"2024-12-17T12:25:39Z","title":"Uniqueness of solutions to the isotropic $L_{p}$ Gaussian Minkowski problem","version":2},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-11T13:50:35.956262Z"},"links":{"citing_paper":"/paper/2412.12851"},"observation_digest":"sha256:35b6e9eb145bf4b6a3979332df7be7008ac5eb7a4c2381ecd5be8b3b5727167b","observation_id":"2955bf5f-95ab-405b-8019-0ebf5acfe825","resolution":{"observed_at":"2026-08-11T13:50:36.829278Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-11T13:50:36.809415Z","title":null,"venue":null,"work_id":"38765001-7446-4051-8c82-444891114f25","year":2017},"citing_paper":{"arxiv_id":"2412.12851","last_updated":"2025-05-20T19:45:13Z","snapshot_observed_at":"2026-08-11T13:37:58.814786Z","submitted_at":"2024-12-17T12:25:39Z","title":"Uniqueness of solutions to the isotropic $L_{p}$ Gaussian Minkowski problem","version":2},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-11T13:50:35.961049Z"},"links":{"citing_paper":"/paper/2412.12851"},"observation_digest":"sha256:465629813f134fa805cc3977ad9cfe5f503786a64ab0345e2793444570c6558a","observation_id":"e9df228a-d0b1-4519-88ab-59e7751ab89e","resolution":{"observed_at":"2026-08-11T13:50:36.814011Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-11T13:50:36.794762Z","title":null,"venue":null,"work_id":"7a17a574-5cdb-41d0-81b3-48b2e63408bf","year":2023},"citing_paper":{"arxiv_id":"2412.12851","last_updated":"2025-05-20T19:45:13Z","snapshot_observed_at":"2026-08-11T13:37:58.814786Z","submitted_at":"2024-12-17T12:25:39Z","title":"Uniqueness of solutions to the isotropic $L_{p}$ Gaussian Minkowski problem","version":2},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-11T13:50:35.965946Z"},"links":{"citing_paper":"/paper/2412.12851"},"observation_digest":"sha256:a33543d984c952d9e22fb3b6f20eb3e43ec8b2a99673a204e0af5ee4bcae6c1b","observation_id":"120ad136-3a12-48e5-9be1-3bde9521cf5b","resolution":{"observed_at":"2026-08-11T13:50:36.799336Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-11T13:50:36.779858Z","title":null,"venue":null,"work_id":"b92d000b-aeb9-4ba2-9b91-a2a07bf6ed8b","year":2017},"citing_paper":{"arxiv_id":"2412.12851","last_updated":"2025-05-20T19:45:13Z","snapshot_observed_at":"2026-08-11T13:37:58.814786Z","submitted_at":"2024-12-17T12:25:39Z","title":"Uniqueness of solutions to the isotropic $L_{p}$ Gaussian Minkowski problem","version":2},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-11T13:50:35.970832Z"},"links":{"citing_paper":"/paper/2412.12851"},"observation_digest":"sha256:57c2f70d88d629b49ecc2da1dbe294fbce87ddd66ef40ba52736168d32095341","observation_id":"b5dfa2f7-8474-4fe7-afdd-5c1207c953bb","resolution":{"observed_at":"2026-08-11T13:50:36.784499Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-11T13:50:36.762830Z","title":null,"venue":null,"work_id":"93d928b8-3159-489d-94e7-eb146708656e","year":2019},"citing_paper":{"arxiv_id":"2412.12851","last_updated":"2025-05-20T19:45:13Z","snapshot_observed_at":"2026-08-11T13:37:58.814786Z","submitted_at":"2024-12-17T12:25:39Z","title":"Uniqueness of solutions to the isotropic $L_{p}$ Gaussian Minkowski problem","version":2},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-11T13:50:35.975564Z"},"links":{"citing_paper":"/paper/2412.12851"},"observation_digest":"sha256:2da6edb4f6ab7fb036c52f1c59f65087862adcf31dbfe7b038cc7ec5cc461f97","observation_id":"933c4fb4-4733-457a-a5cb-0d443a90498d","resolution":{"observed_at":"2026-08-11T13:50:36.768352Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-11T13:50:36.745955Z","title":null,"venue":null,"work_id":"802c9210-83a1-4758-8d86-ec89d5594704","year":1976},"citing_paper":{"arxiv_id":"2412.12851","last_updated":"2025-05-20T19:45:13Z","snapshot_observed_at":"2026-08-11T13:37:58.814786Z","submitted_at":"2024-12-17T12:25:39Z","title":"Uniqueness of solutions to the isotropic $L_{p}$ Gaussian Minkowski problem","version":2},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-11T13:50:35.980568Z"},"links":{"citing_paper":"/paper/2412.12851"},"observation_digest":"sha256:98909ffbb51d2c34a2b621a6070bd2f7bd96dcc5d669020148e4325fa7deacb1","observation_id":"fef60a86-fd94-4fbd-9477-bc838dcb75e3","resolution":{"observed_at":"2026-08-11T13:50:36.751040Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-11T13:50:36.730659Z","title":"Fenchel and B","venue":null,"work_id":"5429f5d4-431e-4703-b5dc-eb4a1f149e49","year":1938},"citing_paper":{"arxiv_id":"2412.12851","last_updated":"2025-05-20T19:45:13Z","snapshot_observed_at":"2026-08-11T13:37:58.814786Z","submitted_at":"2024-12-17T12:25:39Z","title":"Uniqueness of solutions to the isotropic $L_{p}$ Gaussian Minkowski problem","version":2},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-11T13:50:35.985453Z"},"links":{"citing_paper":"/paper/2412.12851"},"observation_digest":"sha256:984bf38d10a4c84d0b3bae0865ddf38c46ec376a1f4b51a848f023b901952a49","observation_id":"890d67ce-b4d7-4028-8421-48cf3de8f517","resolution":{"observed_at":"2026-08-11T13:50:36.735234Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-11T13:50:36.715787Z","title":null,"venue":null,"work_id":"1b3447e8-cf3c-409d-b496-65394a7067f1","year":2023},"citing_paper":{"arxiv_id":"2412.12851","last_updated":"2025-05-20T19:45:13Z","snapshot_observed_at":"2026-08-11T13:37:58.814786Z","submitted_at":"2024-12-17T12:25:39Z","title":"Uniqueness of solutions to the isotropic $L_{p}$ Gaussian Minkowski problem","version":2},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-11T13:50:35.990230Z"},"links":{"citing_paper":"/paper/2412.12851"},"observation_digest":"sha256:16883553742bbda68a81b3a1982a2a00f912ac1c41093563adb6a08e39638035","observation_id":"4fd39f77-c78c-4553-b94b-94892f0b89f1","resolution":{"observed_at":"2026-08-11T13:50:36.720667Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-11T13:50:36.700938Z","title":null,"venue":null,"work_id":"cf11fe68-cb81-4759-ac7a-1ea534019454","year":2006},"citing_paper":{"arxiv_id":"2412.12851","last_updated":"2025-05-20T19:45:13Z","snapshot_observed_at":"2026-08-11T13:37:58.814786Z","submitted_at":"2024-12-17T12:25:39Z","title":"Uniqueness of solutions to the isotropic $L_{p}$ Gaussian Minkowski problem","version":2},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-11T13:50:35.994991Z"},"links":{"citing_paper":"/paper/2412.12851"},"observation_digest":"sha256:a32087e3fcdc0474955ddd0ffe5325e02c6e7a671802030d27ffa5b9903cbcfe","observation_id":"2f3e41a6-6fb7-4cc1-97ea-79c3385f10c5","resolution":{"observed_at":"2026-08-11T13:50:36.705708Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-11T13:50:36.686686Z","title":"Haberl, E","venue":null,"work_id":"24846037-4829-4e95-92cd-81db472243d7","year":2010},"citing_paper":{"arxiv_id":"2412.12851","last_updated":"2025-05-20T19:45:13Z","snapshot_observed_at":"2026-08-11T13:37:58.814786Z","submitted_at":"2024-12-17T12:25:39Z","title":"Uniqueness of solutions to the isotropic $L_{p}$ Gaussian Minkowski problem","version":2},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-11T13:50:36.000884Z"},"links":{"citing_paper":"/paper/2412.12851"},"observation_digest":"sha256:7b56330225a9f19d0cefb9ac4c93163e368a756aac56a62484938012e9d7743c","observation_id":"ac82ea87-0852-487f-b44a-ce15aa4f4eb0","resolution":{"observed_at":"2026-08-11T13:50:36.691156Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-11T13:50:36.672040Z","title":"Hu, The generalized Gaussian log-Minkowski problem , Proc","venue":null,"work_id":"a48d06a8-d92a-43f5-bc3a-5e58e6e6dc03","year":2025},"citing_paper":{"arxiv_id":"2412.12851","last_updated":"2025-05-20T19:45:13Z","snapshot_observed_at":"2026-08-11T13:37:58.814786Z","submitted_at":"2024-12-17T12:25:39Z","title":"Uniqueness of solutions to the isotropic $L_{p}$ Gaussian Minkowski problem","version":2},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-11T13:50:36.005570Z"},"links":{"citing_paper":"/paper/2412.12851"},"observation_digest":"sha256:20bda6cbc13148f39d3662e3a26b1bba5576a66bceec19a01704ce04e5049c9b","observation_id":"3ec9b4fa-3476-404a-8eed-c207c310df92","resolution":{"observed_at":"2026-08-11T13:50:36.676749Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-11T13:50:36.656551Z","title":"Hu and M","venue":null,"work_id":"c8542f84-c1fb-4924-8183-fd46d59661cd","year":2024},"citing_paper":{"arxiv_id":"2412.12851","last_updated":"2025-05-20T19:45:13Z","snapshot_observed_at":"2026-08-11T13:37:58.814786Z","submitted_at":"2024-12-17T12:25:39Z","title":"Uniqueness of solutions to the isotropic $L_{p}$ Gaussian Minkowski problem","version":2},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-11T13:50:36.010470Z"},"links":{"citing_paper":"/paper/2412.12851"},"observation_digest":"sha256:691e6ced331096a52cd398c040f6af605d20455a8ee6619511cef2a1dd102ab4","observation_id":"33e36848-02ab-4baa-b163-15f486c22abd","resolution":{"observed_at":"2026-08-11T13:50:36.661829Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-11T13:50:36.642050Z","title":"Huang, E","venue":null,"work_id":"aae42a6b-a8b2-4432-8ce4-be23f159e35b","year":2016},"citing_paper":{"arxiv_id":"2412.12851","last_updated":"2025-05-20T19:45:13Z","snapshot_observed_at":"2026-08-11T13:37:58.814786Z","submitted_at":"2024-12-17T12:25:39Z","title":"Uniqueness of solutions to the isotropic $L_{p}$ Gaussian Minkowski problem","version":2},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-11T13:50:36.015291Z"},"links":{"citing_paper":"/paper/2412.12851"},"observation_digest":"sha256:ef8c52847e81189dc04e21df94101377d8bd18b5814f47b6ebf5ff75e5f41f4f","observation_id":"1ada5da4-e138-4a29-8270-01d25a0aa014","resolution":{"observed_at":"2026-08-11T13:50:36.646641Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-11T13:50:36.627112Z","title":"Huang, D","venue":null,"work_id":"208d089f-70c1-470e-8581-ac0a97bdb052","year":2021},"citing_paper":{"arxiv_id":"2412.12851","last_updated":"2025-05-20T19:45:13Z","snapshot_observed_at":"2026-08-11T13:37:58.814786Z","submitted_at":"2024-12-17T12:25:39Z","title":"Uniqueness of solutions to the isotropic $L_{p}$ Gaussian Minkowski problem","version":2},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-11T13:50:36.021014Z"},"links":{"citing_paper":"/paper/2412.12851"},"observation_digest":"sha256:8a189f7689458f75595cf1ea36226851a8ac935539e8813d2b8d67e422a2cb8d","observation_id":"f8c88f3a-110e-438e-8dd1-96d4f54fd215","resolution":{"observed_at":"2026-08-11T13:50:36.632024Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2307.06252","last_updated":"2023-07-14T14:20:08Z","snapshot_observed_at":"2026-08-16T15:16:46.166298Z","submitted_at":"2023-07-12T15:41:33Z","title":"Uniqueness of solutions to a class of non-homogeneous curvature problems","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2307.06252","snapshot_observed_at":"2026-08-11T13:50:36.026186Z","title":null,"venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2412.12851","last_updated":"2025-05-20T19:45:13Z","snapshot_observed_at":"2026-08-11T13:37:58.814786Z","submitted_at":"2024-12-17T12:25:39Z","title":"Uniqueness of solutions to the isotropic $L_{p}$ Gaussian Minkowski problem","version":2},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-11T13:50:36.026186Z"},"links":{"cited_paper":"/paper/2307.06252","citing_paper":"/paper/2412.12851"},"observation_digest":"sha256:67e140a8c880f3bb29001eacc05f692714052119561b911b841ec3fac321598b","observation_id":"d0c0ebdd-7152-4983-bc7f-0ba37c9b4c37","resolution":{"observed_at":"2026-08-11T13:50:36.026186Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T13:50:36.611873Z","title":null,"venue":null,"work_id":"28145a60-dc98-4088-81b6-757d37692bb1","year":2023},"citing_paper":{"arxiv_id":"2412.12851","last_updated":"2025-05-20T19:45:13Z","snapshot_observed_at":"2026-08-11T13:37:58.814786Z","submitted_at":"2024-12-17T12:25:39Z","title":"Uniqueness of solutions to the isotropic $L_{p}$ Gaussian Minkowski problem","version":2},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-11T13:50:36.031408Z"},"links":{"citing_paper":"/paper/2412.12851"},"observation_digest":"sha256:54154719bb7795b9de120dba0b81e6e3b077ace9622381ae14a4fa46c87065be","observation_id":"91c39dff-26ef-46e3-acef-ff35080153a4","resolution":{"observed_at":"2026-08-11T13:50:36.616680Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-11T13:50:36.596986Z","title":"Jerison, Prescribing harmonic measure on convex dom ains, Invent","venue":null,"work_id":"575c1387-9b3a-48ea-b7d5-527b127e24bd","year":1991},"citing_paper":{"arxiv_id":"2412.12851","last_updated":"2025-05-20T19:45:13Z","snapshot_observed_at":"2026-08-11T13:37:58.814786Z","submitted_at":"2024-12-17T12:25:39Z","title":"Uniqueness of solutions to the isotropic $L_{p}$ Gaussian Minkowski problem","version":2},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-11T13:50:36.036260Z"},"links":{"citing_paper":"/paper/2412.12851"},"observation_digest":"sha256:bb1a55fe17a432e1e4bf4668a51097f161fb1c02bf385f9573dd7efcab9a62dc","observation_id":"7659b566-fb8a-4417-9cc6-921968636724","resolution":{"observed_at":"2026-08-11T13:50:36.601706Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-11T13:50:36.581605Z","title":null,"venue":null,"work_id":"e50b0749-e8fc-4ffa-be61-dc35263a95e7","year":2022},"citing_paper":{"arxiv_id":"2412.12851","last_updated":"2025-05-20T19:45:13Z","snapshot_observed_at":"2026-08-11T13:37:58.814786Z","submitted_at":"2024-12-17T12:25:39Z","title":"Uniqueness of solutions to the isotropic $L_{p}$ Gaussian Minkowski problem","version":2},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-11T13:50:36.042097Z"},"links":{"citing_paper":"/paper/2412.12851"},"observation_digest":"sha256:e8f88ce5575b0d0d4e6e6649c8b2ea30b3216953b3567598e9951086c25bbcf6","observation_id":"a846d48d-81a1-424d-88ac-e42b33e0218f","resolution":{"observed_at":"2026-08-11T13:50:36.586956Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1601.02925","last_updated":"2016-07-14T08:24:36Z","snapshot_observed_at":"2026-08-14T22:14:57.420616Z","submitted_at":"2016-01-12T15:49:25Z","title":"Sharp Poincar\\'e-type inequality for the Gaussian measure on the boundary of convex sets","version":2},"cited_work":{"arxiv_id":"1601.02925","doi":null,"metadata_source":"pith","pith_arxiv_id":"1601.02925","snapshot_observed_at":"2026-08-11T13:50:36.344922Z","title":"Sharp Poincar\\'e-type inequality for the Gaussian measure on the boundary of convex sets","venue":"math.FA","work_id":"20be6077-ca7f-4e14-ae27-3170cd89d4d9","year":2016},"citing_paper":{"arxiv_id":"2412.12851","last_updated":"2025-05-20T19:45:13Z","snapshot_observed_at":"2026-08-11T13:37:58.814786Z","submitted_at":"2024-12-17T12:25:39Z","title":"Uniqueness of solutions to the isotropic $L_{p}$ Gaussian Minkowski problem","version":2},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-11T13:50:36.048647Z"},"links":{"cited_paper":"/paper/1601.02925","citing_paper":"/paper/2412.12851"},"observation_digest":"sha256:d397c60b67ad3c0ba243f3f385cbdbb567bf44df709c80a6d2782ad931fded64","observation_id":"b21fad5d-8f7d-4e32-80ef-3bab5f0d429b","resolution":{"observed_at":"2026-08-11T13:50:36.350719Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-11T13:50:36.567306Z","title":"Kryvonos and D","venue":null,"work_id":"95d4a703-dcbc-4931-9998-a30fe55430c2","year":2023},"citing_paper":{"arxiv_id":"2412.12851","last_updated":"2025-05-20T19:45:13Z","snapshot_observed_at":"2026-08-11T13:37:58.814786Z","submitted_at":"2024-12-17T12:25:39Z","title":"Uniqueness of solutions to the isotropic $L_{p}$ Gaussian Minkowski problem","version":2},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-11T13:50:36.054519Z"},"links":{"citing_paper":"/paper/2412.12851"},"observation_digest":"sha256:17021085cdea7670c63aa8dd3b8f8b767d0c17c3129bd2151db99d3b15175ea3","observation_id":"fece8926-e2e8-4842-9c3c-6ae4f35bf57b","resolution":{"observed_at":"2026-08-11T13:50:36.571874Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-11T13:50:36.552538Z","title":null,"venue":null,"work_id":"45b0d53c-6e4c-4d2d-80f6-9a9ca2af3230","year":1989},"citing_paper":{"arxiv_id":"2412.12851","last_updated":"2025-05-20T19:45:13Z","snapshot_observed_at":"2026-08-11T13:37:58.814786Z","submitted_at":"2024-12-17T12:25:39Z","title":"Uniqueness of solutions to the isotropic $L_{p}$ Gaussian Minkowski problem","version":2},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-11T13:50:36.059616Z"},"links":{"citing_paper":"/paper/2412.12851"},"observation_digest":"sha256:d98ac143ed373a98a0c037e8f1e3049c2cd3f1c5aa6b68d066c624e1697746d6","observation_id":"bf21a165-fe64-4606-8b49-f4e6c6fdfbf9","resolution":{"observed_at":"2026-08-11T13:50:36.557415Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-11T13:50:36.537790Z","title":"Liu, The Lp-Gaussian Minkowski problem, Calc","venue":null,"work_id":"e1017990-81b1-4742-b507-ea84e8fa5610","year":2022},"citing_paper":{"arxiv_id":"2412.12851","last_updated":"2025-05-20T19:45:13Z","snapshot_observed_at":"2026-08-11T13:37:58.814786Z","submitted_at":"2024-12-17T12:25:39Z","title":"Uniqueness of solutions to the isotropic $L_{p}$ Gaussian Minkowski problem","version":2},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-11T13:50:36.077050Z"},"links":{"citing_paper":"/paper/2412.12851"},"observation_digest":"sha256:be6f8839debb2ba78e3c12098e5ecde88c2fda99d8537a4f5c7164b05447944c","observation_id":"55fa6cc6-2da6-4a5d-b2c4-8c06b6f38f04","resolution":{"observed_at":"2026-08-11T13:50:36.542382Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":"2405.13725","doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T13:50:36.318246Z","title":"Liu, On the planar Lp Gaussian Minkowski problem, arxiv: 2405.13725","venue":null,"work_id":"72ac25e8-78f6-453a-a9e6-21293125c790","year":null},"citing_paper":{"arxiv_id":"2412.12851","last_updated":"2025-05-20T19:45:13Z","snapshot_observed_at":"2026-08-11T13:37:58.814786Z","submitted_at":"2024-12-17T12:25:39Z","title":"Uniqueness of solutions to the isotropic $L_{p}$ Gaussian Minkowski problem","version":2},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-11T13:50:36.082100Z"},"links":{"citing_paper":"/paper/2412.12851"},"observation_digest":"sha256:33f3745c99dc6ba8c740bbfed92869f11d282225d1586878119be78da01938d3","observation_id":"6999dc9b-0ea4-4834-9e51-1a490a03ed6d","resolution":{"observed_at":"2026-08-11T13:50:36.327053Z","resolver_source":"raw_fallback","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-11T13:50:36.522918Z","title":"Lutwak, The Brunn-Minkowski-Fir ey theory","venue":null,"work_id":"73076d05-b5c4-4d74-a8e8-2c39a6d18a86","year":1993},"citing_paper":{"arxiv_id":"2412.12851","last_updated":"2025-05-20T19:45:13Z","snapshot_observed_at":"2026-08-11T13:37:58.814786Z","submitted_at":"2024-12-17T12:25:39Z","title":"Uniqueness of solutions to the isotropic $L_{p}$ Gaussian Minkowski problem","version":2},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-11T13:50:36.086929Z"},"links":{"citing_paper":"/paper/2412.12851"},"observation_digest":"sha256:bf1224a5ea081620b5ccba5714f51b91f746e0d90bd3612d31a99fefcf527ac8","observation_id":"f1f1b69c-e0e4-4c8f-837c-af4cfad97eed","resolution":{"observed_at":"2026-08-11T13:50:36.527691Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-11T13:50:36.507552Z","title":"Lutwak, D","venue":null,"work_id":"e3e1dd18-1836-4cb0-99c5-bfcbe8148555","year":2004},"citing_paper":{"arxiv_id":"2412.12851","last_updated":"2025-05-20T19:45:13Z","snapshot_observed_at":"2026-08-11T13:37:58.814786Z","submitted_at":"2024-12-17T12:25:39Z","title":"Uniqueness of solutions to the isotropic $L_{p}$ Gaussian Minkowski problem","version":2},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-11T13:50:36.091965Z"},"links":{"citing_paper":"/paper/2412.12851"},"observation_digest":"sha256:4fbec9dabb73b0f3fff8a87c64a74477fa294e5c747d5f4e437a4dc157111265","observation_id":"5cd1b072-17b3-42a2-adaf-148cfcfd8470","resolution":{"observed_at":"2026-08-11T13:50:36.512584Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2104.12408","last_updated":"2023-03-01T11:30:42Z","snapshot_observed_at":"2026-08-16T18:29:08.091302Z","submitted_at":"2021-04-26T09:06:40Z","title":"Centro-Affine Differential Geometry and the Log-Minkowski Problem","version":4},"cited_work":{"arxiv_id":"2104.12408","doi":null,"metadata_source":"pith","pith_arxiv_id":"2104.12408","snapshot_observed_at":"2026-08-11T13:50:36.192929Z","title":"Centro-Affine Differential Geometry and the Log-Minkowski Problem","venue":"math.FA","work_id":"52c6946b-c116-4d29-b145-7e077325b977","year":2021},"citing_paper":{"arxiv_id":"2412.12851","last_updated":"2025-05-20T19:45:13Z","snapshot_observed_at":"2026-08-11T13:37:58.814786Z","submitted_at":"2024-12-17T12:25:39Z","title":"Uniqueness of solutions to the isotropic $L_{p}$ Gaussian Minkowski problem","version":2},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-11T13:50:36.096788Z"},"links":{"cited_paper":"/paper/2104.12408","citing_paper":"/paper/2412.12851"},"observation_digest":"sha256:72dc10b490f74c375095181c251ecae07a56ab1dc9a45a2078bff81d3b554408","observation_id":"56f58a59-0b15-4781-beb7-6a1029f8dfb5","resolution":{"observed_at":"2026-08-11T13:50:36.200248Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-11T13:50:36.491491Z","title":"Minkowski, Allgemeine Lehrs¨ atze ¨ uber die convexen Polyeder, Nachr","venue":null,"work_id":"13c49835-331a-4de4-8457-15010875cf26","year":null},"citing_paper":{"arxiv_id":"2412.12851","last_updated":"2025-05-20T19:45:13Z","snapshot_observed_at":"2026-08-11T13:37:58.814786Z","submitted_at":"2024-12-17T12:25:39Z","title":"Uniqueness of solutions to the isotropic $L_{p}$ Gaussian Minkowski problem","version":2},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-11T13:50:36.102403Z"},"links":{"citing_paper":"/paper/2412.12851"},"observation_digest":"sha256:535011379f2cfb4009579048fde3b3d0ff7b02af14ba075407f4c19c3a8a4b3d","observation_id":"446e5eee-d7a6-43f1-afb1-c0e913826f71","resolution":{"observed_at":"2026-08-11T13:50:36.496468Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-11T13:50:36.475383Z","title":"Minkowski, Volumen und Oberﬂ¨ ache, Math","venue":null,"work_id":"c7e2c24f-ac57-41c7-91a4-0e6e6da1e025","year":1903},"citing_paper":{"arxiv_id":"2412.12851","last_updated":"2025-05-20T19:45:13Z","snapshot_observed_at":"2026-08-11T13:37:58.814786Z","submitted_at":"2024-12-17T12:25:39Z","title":"Uniqueness of solutions to the isotropic $L_{p}$ Gaussian Minkowski problem","version":2},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-08-11T13:50:36.107247Z"},"links":{"citing_paper":"/paper/2412.12851"},"observation_digest":"sha256:bd90dfe93568cc30406adf1a93b20afb0fd3ae29bed34cf400bfe9a13dee71aa","observation_id":"c416bc09-cbe3-4776-905f-8a52206501b3","resolution":{"observed_at":"2026-08-11T13:50:36.480541Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-11T13:50:36.458924Z","title":"Schneider, Convex bodies: the Brunn-Minkowski theory , second expanded edition, Encyclopedia of Mathematics and its Applications, 151, Cambridge Universi ty Press, Cambridge, 2014","venue":null,"work_id":"ee7fa75f-2aa5-4223-8f23-aa9a1ddf4a67","year":2014},"citing_paper":{"arxiv_id":"2412.12851","last_updated":"2025-05-20T19:45:13Z","snapshot_observed_at":"2026-08-11T13:37:58.814786Z","submitted_at":"2024-12-17T12:25:39Z","title":"Uniqueness of solutions to the isotropic $L_{p}$ Gaussian Minkowski problem","version":2},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-08-11T13:50:36.111852Z"},"links":{"citing_paper":"/paper/2412.12851"},"observation_digest":"sha256:e613482919571a1f298ca82b3f9a9058c98af50343560c4abfc65dd52fabc4a5","observation_id":"e61db73c-f997-4141-bd4f-501f30e30ede","resolution":{"observed_at":"2026-08-11T13:50:36.464453Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-11T13:50:36.443427Z","title":"Shenfeld and R","venue":null,"work_id":"54c902d2-6823-4f3e-8d1b-11e2e18adb22","year":2018},"citing_paper":{"arxiv_id":"2412.12851","last_updated":"2025-05-20T19:45:13Z","snapshot_observed_at":"2026-08-11T13:37:58.814786Z","submitted_at":"2024-12-17T12:25:39Z","title":"Uniqueness of solutions to the isotropic $L_{p}$ Gaussian Minkowski problem","version":2},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-08-11T13:50:36.116626Z"},"links":{"citing_paper":"/paper/2412.12851"},"observation_digest":"sha256:cfa11279598cf34d22174c89991ce0a3ddef03d269fa4474bfd1fdd045dadf3e","observation_id":"40464494-d437-4969-80c1-e047028129c6","resolution":{"observed_at":"2026-08-11T13:50:36.448354Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2212.01822","last_updated":"2022-12-04T13:55:56Z","snapshot_observed_at":"2026-08-18T16:42:59.813166Z","submitted_at":"2022-12-04T13:55:56Z","title":"Flow by Gauss curvature to the $L_p$-Gaussian Minkowski problem","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2212.01822","snapshot_observed_at":"2026-08-11T13:50:36.121329Z","title":"Sheng and K","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2412.12851","last_updated":"2025-05-20T19:45:13Z","snapshot_observed_at":"2026-08-11T13:37:58.814786Z","submitted_at":"2024-12-17T12:25:39Z","title":"Uniqueness of solutions to the isotropic $L_{p}$ Gaussian Minkowski problem","version":2},"reference_index":38,"source":"pdf_text","source_observed_at":"2026-08-11T13:50:36.121329Z"},"links":{"cited_paper":"/paper/2212.01822","citing_paper":"/paper/2412.12851"},"observation_digest":"sha256:365771788d21071ec96fc0073ee371f5efa0ab3735b739818d3ac150bff4d104","observation_id":"c06930e9-6e4d-44e6-83ea-7125482d83d9","resolution":{"observed_at":"2026-08-11T13:50:36.121329Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T13:50:36.425730Z","title":"Zhu, The logarithmic Minkowski problem for polytope s, Adv","venue":null,"work_id":"c463710d-1780-4c28-88a2-e9171db7d4ff","year":2014},"citing_paper":{"arxiv_id":"2412.12851","last_updated":"2025-05-20T19:45:13Z","snapshot_observed_at":"2026-08-11T13:37:58.814786Z","submitted_at":"2024-12-17T12:25:39Z","title":"Uniqueness of solutions to the isotropic $L_{p}$ Gaussian Minkowski problem","version":2},"reference_index":39,"source":"pdf_text","source_observed_at":"2026-08-11T13:50:36.126257Z"},"links":{"citing_paper":"/paper/2412.12851"},"observation_digest":"sha256:e5cb0672e3c6236be21d2f9b49e6c2034e480893257c9c027dc9fd2e32143c69","observation_id":"cef7eaab-dcac-4c62-a89a-4c0406a3c454","resolution":{"observed_at":"2026-08-11T13:50:36.431139Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-11T13:50:36.404208Z","title":"Zhu, The Lp Minkowski problem for polytopes for 0 < p < 1, J","venue":null,"work_id":"dab5537f-7d86-4fe7-a971-3f1c4c265c4e","year":2015},"citing_paper":{"arxiv_id":"2412.12851","last_updated":"2025-05-20T19:45:13Z","snapshot_observed_at":"2026-08-11T13:37:58.814786Z","submitted_at":"2024-12-17T12:25:39Z","title":"Uniqueness of solutions to the isotropic $L_{p}$ Gaussian Minkowski problem","version":2},"reference_index":40,"source":"pdf_text","source_observed_at":"2026-08-11T13:50:36.131348Z"},"links":{"citing_paper":"/paper/2412.12851"},"observation_digest":"sha256:dd0607dc2f0d236f4006bbe91ce7cbc9a818968885e6145e0c041da88c572bf7","observation_id":"32f3ddb1-2d46-4e4d-9f32-fd1885687a42","resolution":{"observed_at":"2026-08-11T13:50:36.410151Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-11T13:50:36.384513Z","title":"Zhu, The centro-aﬃne Minkowski problem for polytope s, J","venue":null,"work_id":"e93c831a-b587-4ce0-869c-0007a919d51e","year":2015},"citing_paper":{"arxiv_id":"2412.12851","last_updated":"2025-05-20T19:45:13Z","snapshot_observed_at":"2026-08-11T13:37:58.814786Z","submitted_at":"2024-12-17T12:25:39Z","title":"Uniqueness of solutions to the isotropic $L_{p}$ Gaussian Minkowski problem","version":2},"reference_index":41,"source":"pdf_text","source_observed_at":"2026-08-11T13:50:36.136332Z"},"links":{"citing_paper":"/paper/2412.12851"},"observation_digest":"sha256:65b2d5a81ee135ab31ac6ad9e0405223b3bf0e300f8a13d6041f75f59d83d1fb","observation_id":"2587b972-d1b6-437f-a9ba-95476f282fc8","resolution":{"observed_at":"2026-08-11T13:50:36.390536Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2412.12851","last_updated":"2025-05-20T19:45:13Z","latest_version":2,"primary_category":"math.AP","snapshot_observed_at":"2026-08-11T13:37:58.814786Z","submitted_at":"2024-12-17T12:25:39Z","title":"Uniqueness of solutions to the isotropic $L_{p}$ Gaussian Minkowski problem"},"reference_resolution":{"displayed":41,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":14,"verified_exact":3,"verified_fuzzy":24},"total_outbound_references":41},"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":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"thesis":"As of 18 August 2026, this Paper Citation Record lists 41 of 41 outbound references and 0 inbound Pith citation observations for arXiv:2412.12851."}