{"as_of":"2026-08-10T19:30:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:6381f0c2796b677caae9855034bf59adac812b304937b937c5173fd198ea6be2","coverage":[{"denominator":22,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":22,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-06T16:17:26.451006Z","state":"measured"},{"denominator":24,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":24,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-10T06:31:04.303077+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":"2026-07-14T10:18:32.879564Z","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":"2026-05-11T22:46:13.279723Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2507.14112","last_updated":"2025-07-18T17:44:01Z","snapshot_observed_at":"2026-08-06T15:58:28.806551Z","submitted_at":"2025-07-18T17:44:01Z","title":"Existence of a non-standard isoperimetric triple partition","version":1},"cited_work":{"arxiv_id":"2507.14112","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2507.14112","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Novaga, E","venue":null,"work_id":"f6e3da36-a6a7-443a-9fd4-69a832029caf","year":2025},"citing_paper":{"arxiv_id":"2604.23920","last_updated":"2026-04-27T00:33:42Z","snapshot_observed_at":"2026-07-06T23:10:02.659384Z","submitted_at":"2026-04-27T00:33:42Z","title":"Survey on topological methods for Allen--Cahn equations and systems","version":1},"reference_index":104,"source":"pdf_text","source_observed_at":"2026-05-08T02:26:01.978801Z"},"links":{"cited_paper":"/paper/2507.14112","citing_paper":"/paper/2604.23920"},"observation_digest":"sha256:c5748efd975b6415469cf1a1f5b6ee08418866a7b2f2dbd24bc63396007aff40","observation_id":"bf5200da-23e3-40a1-8e35-406e01eefd10","resolution":{"observed_at":"2026-05-11T22:46:13.282273Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2507.14112","last_updated":"2025-07-18T17:44:01Z","snapshot_observed_at":"2026-08-06T15:58:28.806551Z","submitted_at":"2025-07-18T17:44:01Z","title":"Existence of a non-standard isoperimetric triple partition","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2507.14112","snapshot_observed_at":"2026-07-14T10:18:32.879564Z","title":"Existence of a non-standard isoperimetric triple partition","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.10636","last_updated":"2026-07-12T08:09:11Z","snapshot_observed_at":"2026-08-03T04:59:16.548222Z","submitted_at":"2026-07-12T08:09:11Z","title":"Anisotropic isoperimetric double tilings of the plane","version":1},"reference_index":53,"source":"arxiv_source","source_observed_at":"2026-07-14T10:18:32.879564Z"},"links":{"cited_paper":"/paper/2507.14112","citing_paper":"/paper/2607.10636"},"observation_digest":"sha256:e350313b625a096f3348cfbc15fb61158fecc815034b595abc3750622cd8c9a2","observation_id":"84542002-c556-4c09-bdd6-31263598d62e","resolution":{"observed_at":"2026-07-14T10:18:32.879564Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"links":{"evidence":"/evidence","html":"/paper/2507.14112/citation-record","integrity":"/paper/2507.14112/integrity","json":"/paper/2507.14112/citation-record.json","paper":"/paper/2507.14112"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T16:17:31.237134Z","title":null,"venue":null,"work_id":"c26abf48-9861-431e-aa78-c63759aa3a03","year":2025},"citing_paper":{"arxiv_id":"2507.14112","last_updated":"2025-07-18T17:44:01Z","snapshot_observed_at":"2026-08-06T15:58:28.806551Z","submitted_at":"2025-07-18T17:44:01Z","title":"Existence of a non-standard isoperimetric triple partition","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-06T16:17:24.366509Z"},"links":{"citing_paper":"/paper/2507.14112"},"observation_digest":"sha256:8f7dc8577bd6d9adcbc0315393c21945882cb1a8d7a85e3128916d92b94904a0","observation_id":"3af26961-b54b-452b-a748-4bce1b7d5fec","resolution":{"observed_at":"2026-08-06T16:17:31.379447Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-06T16:17:30.946939Z","title":"Allard, On the first variation of a varifold , Ann","venue":null,"work_id":"8a7d9997-ad54-4430-b45b-70c481bde208","year":1972},"citing_paper":{"arxiv_id":"2507.14112","last_updated":"2025-07-18T17:44:01Z","snapshot_observed_at":"2026-08-06T15:58:28.806551Z","submitted_at":"2025-07-18T17:44:01Z","title":"Existence of a non-standard isoperimetric triple partition","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-06T16:17:24.431684Z"},"links":{"citing_paper":"/paper/2507.14112"},"observation_digest":"sha256:c2782e33d14b4c258a8b7bcbe5ee0399938beae51f7e6b194dda621dc25ad01a","observation_id":"93701ee3-e6b1-455e-8067-da9ee606b6e8","resolution":{"observed_at":"2026-08-06T16:17:31.105638Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-06T16:17:30.704619Z","title":"Allard, On the first variation of a varifold: Boundary behavior , Annals of Math- ematics 101 (1975), no","venue":null,"work_id":"0ba113e8-24a4-4bc3-87ce-917e0770458d","year":1975},"citing_paper":{"arxiv_id":"2507.14112","last_updated":"2025-07-18T17:44:01Z","snapshot_observed_at":"2026-08-06T15:58:28.806551Z","submitted_at":"2025-07-18T17:44:01Z","title":"Existence of a non-standard isoperimetric triple partition","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-06T16:17:24.547930Z"},"links":{"citing_paper":"/paper/2507.14112"},"observation_digest":"sha256:d2902d3f9d2b67c3a713d4fc2d310335d579b4162543e2e926440782ae1441af","observation_id":"920daa9c-a1a6-4eea-9784-f7ca3faecefe","resolution":{"observed_at":"2026-08-06T16:17:30.775032Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-06T16:17:30.548501Z","title":"Bombieri, E","venue":null,"work_id":"182b0730-fa2b-4952-bd65-4b35a5febb86","year":1969},"citing_paper":{"arxiv_id":"2507.14112","last_updated":"2025-07-18T17:44:01Z","snapshot_observed_at":"2026-08-06T15:58:28.806551Z","submitted_at":"2025-07-18T17:44:01Z","title":"Existence of a non-standard isoperimetric triple partition","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-06T16:17:24.629987Z"},"links":{"citing_paper":"/paper/2507.14112"},"observation_digest":"sha256:e0a454730491593b24c4d34f49a6a9b7944cb8fb9a0208a73009c70cb8ed6837","observation_id":"24067448-ad6a-49a4-8459-9af632f939e7","resolution":{"observed_at":"2026-08-06T16:17:30.634250Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-06T16:17:30.349884Z","title":"Brakke, Minimal cones on hypercubes , J","venue":null,"work_id":"f9a23c64-20a5-4e94-b7bd-9cad97a30416","year":1991},"citing_paper":{"arxiv_id":"2507.14112","last_updated":"2025-07-18T17:44:01Z","snapshot_observed_at":"2026-08-06T15:58:28.806551Z","submitted_at":"2025-07-18T17:44:01Z","title":"Existence of a non-standard isoperimetric triple partition","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-06T16:17:24.731962Z"},"links":{"citing_paper":"/paper/2507.14112"},"observation_digest":"sha256:ba1a36274bad952d10792a4e78db9059d552c1588835ff69c1f9bfeebac4ca24","observation_id":"46f4a9fc-164b-4506-bef7-d534c6fe2e9b","resolution":{"observed_at":"2026-08-06T16:17:30.422272Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-06T16:17:30.173047Z","title":null,"venue":null,"work_id":"ee9243b6-07b6-4528-93b0-6e21c055f096","year":2025},"citing_paper":{"arxiv_id":"2507.14112","last_updated":"2025-07-18T17:44:01Z","snapshot_observed_at":"2026-08-06T15:58:28.806551Z","submitted_at":"2025-07-18T17:44:01Z","title":"Existence of a non-standard isoperimetric triple partition","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-06T16:17:24.844234Z"},"links":{"citing_paper":"/paper/2507.14112"},"observation_digest":"sha256:470fc01ccb6da3bcd933be7ee62d380a997e28adbcf1ea656ba755d3d55d7530","observation_id":"65efb03b-e507-49ec-abe6-75ed324ba9fd","resolution":{"observed_at":"2026-08-06T16:17:30.265768Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2401.08063","last_updated":"2025-05-30T10:00:42Z","snapshot_observed_at":"2026-07-06T17:15:55.907520Z","submitted_at":"2024-01-16T02:46:40Z","title":"An Infinite Double Bubble Theorem","version":2},"cited_work":{"arxiv_id":"2401.08063","doi":null,"metadata_source":"pith","pith_arxiv_id":"2401.08063","snapshot_observed_at":"2026-08-06T16:17:26.599808Z","title":"An Infinite Double Bubble Theorem","venue":"math.AP","work_id":"cc651543-e3c7-45af-9164-8a259316befa","year":2024},"citing_paper":{"arxiv_id":"2507.14112","last_updated":"2025-07-18T17:44:01Z","snapshot_observed_at":"2026-08-06T15:58:28.806551Z","submitted_at":"2025-07-18T17:44:01Z","title":"Existence of a non-standard isoperimetric triple partition","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-06T16:17:24.907362Z"},"links":{"cited_paper":"/paper/2401.08063","citing_paper":"/paper/2507.14112"},"observation_digest":"sha256:6ac76494d17fe5067a70a1ba1ee97ed4599b583cba32ccd4ba248074ec66a1fc","observation_id":"abcb1d88-5b10-409b-bb16-950e00f31456","resolution":{"observed_at":"2026-08-06T16:17:26.686463Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-06T16:17:29.942096Z","title":null,"venue":null,"work_id":"6ff24ccc-152f-4eeb-8261-e1d7f809f25b","year":2009},"citing_paper":{"arxiv_id":"2507.14112","last_updated":"2025-07-18T17:44:01Z","snapshot_observed_at":"2026-08-06T15:58:28.806551Z","submitted_at":"2025-07-18T17:44:01Z","title":"Existence of a non-standard isoperimetric triple partition","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-06T16:17:24.952359Z"},"links":{"citing_paper":"/paper/2507.14112"},"observation_digest":"sha256:694e19c77573764e6d849aad5e4ecc509458493c22e13a0d0cba9f123b56c9f3","observation_id":"94875368-d295-40a2-a5f6-5670bf8d28d4","resolution":{"observed_at":"2026-08-06T16:17:30.065976Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-06T16:17:29.791822Z","title":null,"venue":null,"work_id":"e5b27b94-d433-4a40-9424-9da8b0f0c0c6","year":1993},"citing_paper":{"arxiv_id":"2507.14112","last_updated":"2025-07-18T17:44:01Z","snapshot_observed_at":"2026-08-06T15:58:28.806551Z","submitted_at":"2025-07-18T17:44:01Z","title":"Existence of a non-standard isoperimetric triple partition","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-06T16:17:25.014865Z"},"links":{"citing_paper":"/paper/2507.14112"},"observation_digest":"sha256:197e51bb653958931aa2675925ada5d2164ddc037e2b60afe715a73d8174a2a4","observation_id":"671b583a-9f78-4188-8cae-d23fb41f440d","resolution":{"observed_at":"2026-08-06T16:17:29.871673Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-06T16:17:29.564264Z","title":"3, 439–486","venue":null,"work_id":"d633c566-d03a-41f8-a191-5c16d0ced60f","year":1979},"citing_paper":{"arxiv_id":"2507.14112","last_updated":"2025-07-18T17:44:01Z","snapshot_observed_at":"2026-08-06T15:58:28.806551Z","submitted_at":"2025-07-18T17:44:01Z","title":"Existence of a non-standard isoperimetric triple partition","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-06T16:17:25.088109Z"},"links":{"citing_paper":"/paper/2507.14112"},"observation_digest":"sha256:b2612d60cc966ce5b6f22c5ed49172aab4ebeeb15e62848735407b208682bc95","observation_id":"cf428c62-6c3a-4395-90e2-16c20302e979","resolution":{"observed_at":"2026-08-06T16:17:29.688123Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-06T16:17:29.327677Z","title":null,"venue":null,"work_id":"c26dccdb-443b-446a-a33b-92951682dd9f","year":2002},"citing_paper":{"arxiv_id":"2507.14112","last_updated":"2025-07-18T17:44:01Z","snapshot_observed_at":"2026-08-06T15:58:28.806551Z","submitted_at":"2025-07-18T17:44:01Z","title":"Existence of a non-standard isoperimetric triple partition","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-06T16:17:25.168070Z"},"links":{"citing_paper":"/paper/2507.14112"},"observation_digest":"sha256:de6ad91369547d242c9764f80ec9ccc44db096cb9be520fa29a58abe8d94be38","observation_id":"f83a481d-c3bc-43ea-8c84-62dced60d314","resolution":{"observed_at":"2026-08-06T16:17:29.440538Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-06T16:17:29.106379Z","title":null,"venue":null,"work_id":"ba1c400b-d674-4874-b019-117fb4fa4d86","year":2022},"citing_paper":{"arxiv_id":"2507.14112","last_updated":"2025-07-18T17:44:01Z","snapshot_observed_at":"2026-08-06T15:58:28.806551Z","submitted_at":"2025-07-18T17:44:01Z","title":"Existence of a non-standard isoperimetric triple partition","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-06T16:17:25.320566Z"},"links":{"citing_paper":"/paper/2507.14112"},"observation_digest":"sha256:8e2824f3ebb5d9b81ff2dfb3643f58b4e8aac7a6e1581ac77ff3597dff8a4b46","observation_id":"460c43a7-1cbe-4c63-8bd4-500ca8c87796","resolution":{"observed_at":"2026-08-06T16:17:29.178899Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2307.08164","last_updated":"2024-12-28T13:25:32Z","snapshot_observed_at":"2026-07-06T15:54:35.654279Z","submitted_at":"2023-07-16T22:20:26Z","title":"Plateau Bubbles and the Quintuple Bubble Theorem on $\\mathbb{S}^n$","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2307.08164","snapshot_observed_at":"2026-08-06T16:17:25.442409Z","title":null,"venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2507.14112","last_updated":"2025-07-18T17:44:01Z","snapshot_observed_at":"2026-08-06T15:58:28.806551Z","submitted_at":"2025-07-18T17:44:01Z","title":"Existence of a non-standard isoperimetric triple partition","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-06T16:17:25.442409Z"},"links":{"cited_paper":"/paper/2307.08164","citing_paper":"/paper/2507.14112"},"observation_digest":"sha256:1632f3d9ec5c9ab21139c2ab2e9a70ea0a3604537a6b80b81edca278dd36ad09","observation_id":"017940d6-59ca-4b9f-be88-bac300373ba7","resolution":{"observed_at":"2026-08-06T16:17:25.442409Z","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":"2026-08-06T16:17:28.932267Z","title":null,"venue":null,"work_id":"29ff7824-d8e5-4653-a509-8d61d35e5f73","year":2025},"citing_paper":{"arxiv_id":"2507.14112","last_updated":"2025-07-18T17:44:01Z","snapshot_observed_at":"2026-08-06T15:58:28.806551Z","submitted_at":"2025-07-18T17:44:01Z","title":"Existence of a non-standard isoperimetric triple partition","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-06T16:17:25.528457Z"},"links":{"citing_paper":"/paper/2507.14112"},"observation_digest":"sha256:70f7ec56ba0af3688db44db4a5b47b7b3d5e57fa29ae877cb8f4e1085ceaa30e","observation_id":"d3e42760-7a6e-42a3-9589-14271112211d","resolution":{"observed_at":"2026-08-06T16:17:29.020537Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-06T16:17:28.682053Z","title":null,"venue":null,"work_id":"dd87eb69-91c4-4263-805f-10c68a530358","year":2025},"citing_paper":{"arxiv_id":"2507.14112","last_updated":"2025-07-18T17:44:01Z","snapshot_observed_at":"2026-08-06T15:58:28.806551Z","submitted_at":"2025-07-18T17:44:01Z","title":"Existence of a non-standard isoperimetric triple partition","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-06T16:17:25.643843Z"},"links":{"citing_paper":"/paper/2507.14112"},"observation_digest":"sha256:75b452d86bca4113172f0c41faa30a4a958b56e8d88b44d34ddd0e6a0b1a8588","observation_id":"3eee6899-c239-4485-ad21-ed258a70c55d","resolution":{"observed_at":"2026-08-06T16:17:28.834115Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-06T16:17:28.345613Z","title":null,"venue":null,"work_id":"0e11fcdc-7cf8-4f17-b0e9-f945d1e2866e","year":2022},"citing_paper":{"arxiv_id":"2507.14112","last_updated":"2025-07-18T17:44:01Z","snapshot_observed_at":"2026-08-06T15:58:28.806551Z","submitted_at":"2025-07-18T17:44:01Z","title":"Existence of a non-standard isoperimetric triple partition","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-06T16:17:25.770392Z"},"links":{"citing_paper":"/paper/2507.14112"},"observation_digest":"sha256:d7850f7f1a76e7a5d1e8bdadaaa86d1150e4065a89229b07b79e3c4d812cfa29","observation_id":"ce3dafbd-9db1-4d56-b0c1-f0c6815688cd","resolution":{"observed_at":"2026-08-06T16:17:28.537445Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-06T16:17:28.005792Z","title":null,"venue":null,"work_id":"bd041e7b-1379-4b05-a2b6-6659ac5db3c6","year":2025},"citing_paper":{"arxiv_id":"2507.14112","last_updated":"2025-07-18T17:44:01Z","snapshot_observed_at":"2026-08-06T15:58:28.806551Z","submitted_at":"2025-07-18T17:44:01Z","title":"Existence of a non-standard isoperimetric triple partition","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-06T16:17:25.882014Z"},"links":{"citing_paper":"/paper/2507.14112"},"observation_digest":"sha256:f4b268bd50cb83ea1800d556dd297e88784c73dffdaf1ab9c4bc213a90d22ac4","observation_id":"d3f72be9-87b0-4b77-91f2-5f3da7483458","resolution":{"observed_at":"2026-08-06T16:17:28.177613Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-06T16:17:27.645144Z","title":"Paolini and V","venue":null,"work_id":"77c94b5f-fe92-4619-adb4-81d6f978670b","year":2020},"citing_paper":{"arxiv_id":"2507.14112","last_updated":"2025-07-18T17:44:01Z","snapshot_observed_at":"2026-08-06T15:58:28.806551Z","submitted_at":"2025-07-18T17:44:01Z","title":"Existence of a non-standard isoperimetric triple partition","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-06T16:17:25.988978Z"},"links":{"citing_paper":"/paper/2507.14112"},"observation_digest":"sha256:538ae8cd7167d405c37044ffa01d694cb474296cb6c079fd6dcd023c060ad8f0","observation_id":"f3bdd258-a55a-4e7a-811e-28f941942ebe","resolution":{"observed_at":"2026-08-06T16:17:27.800713Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-06T16:17:27.405743Z","title":"3, 1303–1331, cvgmt preprint","venue":null,"work_id":"1f41f2fa-a4bf-4918-a1ac-d09a69b48fa4","year":2018},"citing_paper":{"arxiv_id":"2507.14112","last_updated":"2025-07-18T17:44:01Z","snapshot_observed_at":"2026-08-06T15:58:28.806551Z","submitted_at":"2025-07-18T17:44:01Z","title":"Existence of a non-standard isoperimetric triple partition","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-06T16:17:26.132048Z"},"links":{"citing_paper":"/paper/2507.14112"},"observation_digest":"sha256:40c88d3baa90dcffa3cf5213086fe9673651ce76e79cc6588ece630c85f05a5b","observation_id":"2fbc364c-8e93-42ac-94d5-a8a90c941693","resolution":{"observed_at":"2026-08-06T16:17:27.538959Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-06T16:17:27.207155Z","title":"Reichardt, Proof of the double bubble conjecture in Rn, J","venue":null,"work_id":"2b948402-23fe-4eae-95a4-500a7d938617","year":2008},"citing_paper":{"arxiv_id":"2507.14112","last_updated":"2025-07-18T17:44:01Z","snapshot_observed_at":"2026-08-06T15:58:28.806551Z","submitted_at":"2025-07-18T17:44:01Z","title":"Existence of a non-standard isoperimetric triple partition","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-06T16:17:26.265810Z"},"links":{"citing_paper":"/paper/2507.14112"},"observation_digest":"sha256:687da6ffff03476f69f87af5be46fc9ce1d49d7f212e275134d718a8236aed9f","observation_id":"13d337bc-ab8e-410f-8186-7b69153d1f25","resolution":{"observed_at":"2026-08-06T16:17:27.299238Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-06T16:17:27.035542Z","title":null,"venue":null,"work_id":"95f3208b-c6b5-4809-b992-cf5427df42b2","year":1987},"citing_paper":{"arxiv_id":"2507.14112","last_updated":"2025-07-18T17:44:01Z","snapshot_observed_at":"2026-08-06T15:58:28.806551Z","submitted_at":"2025-07-18T17:44:01Z","title":"Existence of a non-standard isoperimetric triple partition","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-06T16:17:26.357543Z"},"links":{"citing_paper":"/paper/2507.14112"},"observation_digest":"sha256:5dc344d7c96472edff06d1ce0c1f706f7836ad292ec7cec20aee63698135f61f","observation_id":"8d469d29-82ea-4263-85ae-39c172463629","resolution":{"observed_at":"2026-08-06T16:17:27.103351Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-06T16:17:26.836882Z","title":"Reine Angew","venue":null,"work_id":"966ca085-6bbc-4962-8b5d-9c820a90f5eb","year":2004},"citing_paper":{"arxiv_id":"2507.14112","last_updated":"2025-07-18T17:44:01Z","snapshot_observed_at":"2026-08-06T15:58:28.806551Z","submitted_at":"2025-07-18T17:44:01Z","title":"Existence of a non-standard isoperimetric triple partition","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-06T16:17:26.451006Z"},"links":{"citing_paper":"/paper/2507.14112"},"observation_digest":"sha256:5d6d579051eb848222f077504237c93e14bcafd46b6a860a58ab5f3e27cc70db","observation_id":"40306dcb-1b22-4396-8d80-20fcc4efc1f6","resolution":{"observed_at":"2026-08-06T16:17:26.927941Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2507.14112","last_updated":"2025-07-18T17:44:01Z","latest_version":1,"primary_category":"math.AP","snapshot_observed_at":"2026-08-06T15:58:28.806551Z","submitted_at":"2025-07-18T17:44:01Z","title":"Existence of a non-standard isoperimetric triple partition"},"reference_resolution":{"displayed":22,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":12,"verified_exact":1,"verified_fuzzy":9},"total_outbound_references":22},"refusal":"A citation records a reference. It does not transfer a finding from one paper to another.","schema":"pith.paper-citation-record.v1","standing_sources":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"thesis":"As of 10 August 2026, this Paper Citation Record lists 22 of 22 outbound references and 2 inbound Pith citation observations for arXiv:2507.14112."}