{"as_of":"2026-08-07T14:05:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:43e57a48d5fbe30f41b46211cde3060d24e62bbdb8713c37c33156078aa2033e","coverage":[{"denominator":45,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":45,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-06T21:33:59.051985Z","state":"measured"},{"denominator":45,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":45,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-07T06:34:17.273281+00:00","state":"measured"},{"denominator":0,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":0,"source":"paper_references, paper_reference_links","source_observed_at":null,"state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"cited_works","source_observed_at":null,"state":"measured"}],"external_citation_measurements":[],"inbound":[],"links":{"evidence":"/evidence","html":"/paper/2507.00342/citation-record","integrity":"/paper/2507.00342/integrity","json":"/paper/2507.00342/citation-record.json","paper":"/paper/2507.00342"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T21:34:06.672084Z","title":null,"venue":null,"work_id":"9880e6a3-0893-4143-88ef-159280addc28","year":1966},"citing_paper":{"arxiv_id":"2507.00342","last_updated":"2025-07-01T00:43:21Z","snapshot_observed_at":"2026-08-06T21:15:52.769122Z","submitted_at":"2025-07-01T00:43:21Z","title":"Complete two-sided $\\delta$-stable minimal hypersurfaces in $\\mathbf R^{n+1}$","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-06T21:33:53.908786Z"},"links":{"citing_paper":"/paper/2507.00342"},"observation_digest":"sha256:b35a80b7f33ec8deca4761bc9d65bd17581b571892552898c7908ee7c743a93a","observation_id":"9e3bb23b-5805-4765-a372-079897ef3fb7","resolution":{"observed_at":"2026-08-06T21:34:06.753885Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T21:34:06.484597Z","title":"Anderson, The compactﬁcation of a minimal submanifold by its Gauss map","venue":null,"work_id":"0747233d-168d-4535-8840-bac0714e9dc7","year":null},"citing_paper":{"arxiv_id":"2507.00342","last_updated":"2025-07-01T00:43:21Z","snapshot_observed_at":"2026-08-06T21:15:52.769122Z","submitted_at":"2025-07-01T00:43:21Z","title":"Complete two-sided $\\delta$-stable minimal hypersurfaces in $\\mathbf R^{n+1}$","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-06T21:33:55.268073Z"},"links":{"citing_paper":"/paper/2507.00342"},"observation_digest":"sha256:4165ba7d62aee0a7fa1954b9e39fc2340b65c166821b9e36f5f28c98fbe0a259","observation_id":"371cf9d0-14ee-44fb-b1d7-a8ecec642150","resolution":{"observed_at":"2026-08-06T21:34:06.594374Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2405.08918","last_updated":"2026-07-11T09:25:50Z","snapshot_observed_at":"2026-08-07T13:50:24.758187Z","submitted_at":"2024-05-14T19:15:17Z","title":"New spectral Bishop-Gromov and Bonnet-Myers theorems and applications to isoperimetry","version":4},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2405.08918","snapshot_observed_at":"2026-08-06T21:33:55.916062Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2507.00342","last_updated":"2025-07-01T00:43:21Z","snapshot_observed_at":"2026-08-06T21:15:52.769122Z","submitted_at":"2025-07-01T00:43:21Z","title":"Complete two-sided $\\delta$-stable minimal hypersurfaces in $\\mathbf R^{n+1}$","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-06T21:33:55.916062Z"},"links":{"cited_paper":"/paper/2405.08918","citing_paper":"/paper/2507.00342"},"observation_digest":"sha256:7c0e6659df54b6f2b25d2d5447c22ee6cf110fe59f531117538f7d46c6266eb8","observation_id":"748fb266-3d06-41f8-ae3f-5de0ddbed43d","resolution":{"observed_at":"2026-08-06T21:33:55.916062Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2310.01340","last_updated":"2025-09-12T14:26:06Z","snapshot_observed_at":"2026-07-06T16:26:38.284922Z","submitted_at":"2023-10-02T17:04:18Z","title":"Extensions of Schoen--Simon--Yau and Schoen--Simon theorems via iteration \\`{a} la De Giorgi","version":2},"cited_work":{"arxiv_id":"2310.01340","doi":null,"metadata_source":"pith","pith_arxiv_id":"2310.01340","snapshot_observed_at":"2026-08-06T21:33:59.470986Z","title":"Extensions of Schoen--Simon--Yau and Schoen--Simon theorems via iteration \\`{a} la De Giorgi","venue":"math.AP","work_id":"8993f699-a4a9-459b-93e4-17bc41c36b25","year":2023},"citing_paper":{"arxiv_id":"2507.00342","last_updated":"2025-07-01T00:43:21Z","snapshot_observed_at":"2026-08-06T21:15:52.769122Z","submitted_at":"2025-07-01T00:43:21Z","title":"Complete two-sided $\\delta$-stable minimal hypersurfaces in $\\mathbf R^{n+1}$","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-06T21:33:56.090628Z"},"links":{"cited_paper":"/paper/2310.01340","citing_paper":"/paper/2507.00342"},"observation_digest":"sha256:4d19b77417ba9e62a72bd52e224de71bac81cf62a85b37d7189eeb94438cd7e0","observation_id":"b9d6b32d-f8e5-4ad0-a89f-80d9d1c45d0c","resolution":{"observed_at":"2026-08-06T21:33:59.506673Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T21:34:06.329519Z","title":"Über ein geometrisches Theorem und sein e Anwendung auf die partiellen Diferential- gleichungen vom elliptischen Typus","venue":null,"work_id":"b7a91cf9-a2be-45a1-b582-81b34c7ea0b6","year":1927},"citing_paper":{"arxiv_id":"2507.00342","last_updated":"2025-07-01T00:43:21Z","snapshot_observed_at":"2026-08-06T21:15:52.769122Z","submitted_at":"2025-07-01T00:43:21Z","title":"Complete two-sided $\\delta$-stable minimal hypersurfaces in $\\mathbf R^{n+1}$","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-06T21:33:56.235499Z"},"links":{"citing_paper":"/paper/2507.00342"},"observation_digest":"sha256:cebc7efb2415b0a556bfdb1c534ea59d9c0fb94a7e25ed1fdb5c82bb6063c674","observation_id":"333f47ba-368a-4a1a-82ce-601f9bf8a646","resolution":{"observed_at":"2026-08-06T21:34:06.418507Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T21:34:06.121563Z","title":"Bombieri, E","venue":null,"work_id":"7b8acb8b-6929-4cf5-9ce1-e88d7196b3b6","year":1969},"citing_paper":{"arxiv_id":"2507.00342","last_updated":"2025-07-01T00:43:21Z","snapshot_observed_at":"2026-08-06T21:15:52.769122Z","submitted_at":"2025-07-01T00:43:21Z","title":"Complete two-sided $\\delta$-stable minimal hypersurfaces in $\\mathbf R^{n+1}$","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-06T21:33:56.320887Z"},"links":{"citing_paper":"/paper/2507.00342"},"observation_digest":"sha256:aabe6785f8d101644ef4d581355e5269cd4abf3c2f8d3e6a8286db0b747e8289","observation_id":"b44a8e7b-ce07-4fe3-8a52-36a082732d60","resolution":{"observed_at":"2026-08-06T21:34:06.210895Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T21:34:05.938656Z","title":null,"venue":null,"work_id":"0ded2c45-c86a-4ea6-9d80-b090af74ba2c","year":2021},"citing_paper":{"arxiv_id":"2507.00342","last_updated":"2025-07-01T00:43:21Z","snapshot_observed_at":"2026-08-06T21:15:52.769122Z","submitted_at":"2025-07-01T00:43:21Z","title":"Complete two-sided $\\delta$-stable minimal hypersurfaces in $\\mathbf R^{n+1}$","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-06T21:33:56.404771Z"},"links":{"citing_paper":"/paper/2507.00342"},"observation_digest":"sha256:5a540f81e66545f0a43e574f4e617411a0af5a82b1fb8f779a20c8ff340c6c95","observation_id":"86443c69-fe1b-45c6-8988-c428c7375c1c","resolution":{"observed_at":"2026-08-06T21:34:06.011964Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T21:34:05.717830Z","title":null,"venue":null,"work_id":"72ca294b-c2b2-43c9-907c-6f5f59412575","year":1997},"citing_paper":{"arxiv_id":"2507.00342","last_updated":"2025-07-01T00:43:21Z","snapshot_observed_at":"2026-08-06T21:15:52.769122Z","submitted_at":"2025-07-01T00:43:21Z","title":"Complete two-sided $\\delta$-stable minimal hypersurfaces in $\\mathbf R^{n+1}$","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-06T21:33:56.512235Z"},"links":{"citing_paper":"/paper/2507.00342"},"observation_digest":"sha256:81b5468ec170c8a7c109f86669ff238eb3edb4819c35619bc3044d1629461127","observation_id":"d955ddbe-8253-4290-bdc7-ceafc4322d46","resolution":{"observed_at":"2026-08-06T21:34:05.800729Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T21:34:05.528036Z","title":"Cheng, On constant mean curvature hypersurfaces with ﬁ nite index, Arch","venue":null,"work_id":"194c3d24-1425-47a0-b93b-7a89fe902128","year":2006},"citing_paper":{"arxiv_id":"2507.00342","last_updated":"2025-07-01T00:43:21Z","snapshot_observed_at":"2026-08-06T21:15:52.769122Z","submitted_at":"2025-07-01T00:43:21Z","title":"Complete two-sided $\\delta$-stable minimal hypersurfaces in $\\mathbf R^{n+1}$","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-06T21:33:56.580688Z"},"links":{"citing_paper":"/paper/2507.00342"},"observation_digest":"sha256:a800e94b308d25c604d8ab8668573c092cffd325f5eac94575b0a987f0de273e","observation_id":"27e7d234-2ef5-4214-a442-00ed127436f4","resolution":{"observed_at":"2026-08-06T21:34:05.647301Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T21:34:05.326213Z","title":null,"venue":null,"work_id":"4c38e133-d908-467e-86fd-10dc5083fce5","year":2009},"citing_paper":{"arxiv_id":"2507.00342","last_updated":"2025-07-01T00:43:21Z","snapshot_observed_at":"2026-08-06T21:15:52.769122Z","submitted_at":"2025-07-01T00:43:21Z","title":"Complete two-sided $\\delta$-stable minimal hypersurfaces in $\\mathbf R^{n+1}$","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-06T21:33:56.653789Z"},"links":{"citing_paper":"/paper/2507.00342"},"observation_digest":"sha256:4074e43f3b31b3cdee360bee19db40c9e7a31cf551d76b8c2427068acff6b9a3","observation_id":"cc6b32e4-a60f-40da-8770-8e7010b7766b","resolution":{"observed_at":"2026-08-06T21:34:05.439494Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2412.12631","last_updated":"2026-04-09T08:15:37Z","snapshot_observed_at":"2026-08-03T13:19:41.699706Z","submitted_at":"2024-12-17T07:46:11Z","title":"Criticality, splitting theorems under spectral Ricci bounds and the topology of stable minimal hypersurfaces","version":5},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2412.12631","snapshot_observed_at":"2026-08-06T21:33:56.709729Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2507.00342","last_updated":"2025-07-01T00:43:21Z","snapshot_observed_at":"2026-08-06T21:15:52.769122Z","submitted_at":"2025-07-01T00:43:21Z","title":"Complete two-sided $\\delta$-stable minimal hypersurfaces in $\\mathbf R^{n+1}$","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-06T21:33:56.709729Z"},"links":{"cited_paper":"/paper/2412.12631","citing_paper":"/paper/2507.00342"},"observation_digest":"sha256:ff5ef0b376dda48d8ef6292d8c4a02c933c78dc6a582ea0b31d71c7f24666a2c","observation_id":"58a81c3a-a5aa-4208-a526-e1a0e48ecae6","resolution":{"observed_at":"2026-08-06T21:33:56.709729Z","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":"2026-08-06T21:34:05.144357Z","title":null,"venue":null,"work_id":"3e055f35-2690-4647-8d18-77e08f9e13ca","year":2024},"citing_paper":{"arxiv_id":"2507.00342","last_updated":"2025-07-01T00:43:21Z","snapshot_observed_at":"2026-08-06T21:15:52.769122Z","submitted_at":"2025-07-01T00:43:21Z","title":"Complete two-sided $\\delta$-stable minimal hypersurfaces in $\\mathbf R^{n+1}$","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-06T21:33:56.764353Z"},"links":{"citing_paper":"/paper/2507.00342"},"observation_digest":"sha256:291708959d44c2f12d52fa0fafc74a85fc97c2b0bb3b1f3b29092cec0dcbf628","observation_id":"1d83c2c1-a416-44c0-a600-af69d18e6041","resolution":{"observed_at":"2026-08-06T21:34:05.247299Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T21:34:04.960160Z","title":"Generalized soap bubbles and th e topology of manifolds with positive scalar curvature, Ann","venue":null,"work_id":"5f4bacd0-041d-483d-bc20-8a3dba3ac97f","year":2024},"citing_paper":{"arxiv_id":"2507.00342","last_updated":"2025-07-01T00:43:21Z","snapshot_observed_at":"2026-08-06T21:15:52.769122Z","submitted_at":"2025-07-01T00:43:21Z","title":"Complete two-sided $\\delta$-stable minimal hypersurfaces in $\\mathbf R^{n+1}$","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-06T21:33:56.846542Z"},"links":{"citing_paper":"/paper/2507.00342"},"observation_digest":"sha256:8d81b1ff99d9915030cf1abb4ac85a04ac662181d69d063aeb825c43b3aef71e","observation_id":"3fea8aff-80f3-46b5-b4a1-62ece90be623","resolution":{"observed_at":"2026-08-06T21:34:05.068054Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T21:34:04.756228Z","title":"Chodosh, C","venue":null,"work_id":"4b996a90-4077-40a0-b9f1-cc3a95add54c","year":2024},"citing_paper":{"arxiv_id":"2507.00342","last_updated":"2025-07-01T00:43:21Z","snapshot_observed_at":"2026-08-06T21:15:52.769122Z","submitted_at":"2025-07-01T00:43:21Z","title":"Complete two-sided $\\delta$-stable minimal hypersurfaces in $\\mathbf R^{n+1}$","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-06T21:33:56.891521Z"},"links":{"citing_paper":"/paper/2507.00342"},"observation_digest":"sha256:98df541faba4449b6b33882264ac35fae6bfeab83112eb48563893af64890422","observation_id":"25ac15e9-2a29-4124-8910-61baa92f3273","resolution":{"observed_at":"2026-08-06T21:34:04.847298Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T21:34:04.577346Z","title":"Stable anisotropic minimal hyp ersurfaces in R4, Forum Math","venue":null,"work_id":"f562cc74-9a98-47fa-9e75-b8ded9fa66e7","year":2023},"citing_paper":{"arxiv_id":"2507.00342","last_updated":"2025-07-01T00:43:21Z","snapshot_observed_at":"2026-08-06T21:15:52.769122Z","submitted_at":"2025-07-01T00:43:21Z","title":"Complete two-sided $\\delta$-stable minimal hypersurfaces in $\\mathbf R^{n+1}$","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-06T21:33:56.955064Z"},"links":{"citing_paper":"/paper/2507.00342"},"observation_digest":"sha256:ed71a0cc3687f58234a8c1d3b7297ab17210ef2ce4861cc520e5431a4b42711d","observation_id":"c2be292b-9cb4-4346-bc07-e2f636ef6a51","resolution":{"observed_at":"2026-08-06T21:34:04.648158Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T21:34:04.488721Z","title":"Complete sta ble minimal hypersurfaces in positively curved 4-manifolds, to appear in J","venue":null,"work_id":"ec7041db-7516-4d48-8335-8c0c38f53333","year":null},"citing_paper":{"arxiv_id":"2507.00342","last_updated":"2025-07-01T00:43:21Z","snapshot_observed_at":"2026-08-06T21:15:52.769122Z","submitted_at":"2025-07-01T00:43:21Z","title":"Complete two-sided $\\delta$-stable minimal hypersurfaces in $\\mathbf R^{n+1}$","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-06T21:33:57.008613Z"},"links":{"citing_paper":"/paper/2507.00342"},"observation_digest":"sha256:ad265bd972f53a7f1c6b8e676bae0ea1016b804139e1161a9406871e06e0a38a","observation_id":"bfd63fe1-5af4-4eaf-8614-0278b27e8cbe","resolution":{"observed_at":"2026-08-06T21:34:04.570993Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2401.01492","last_updated":"2025-11-05T18:37:28Z","snapshot_observed_at":"2026-08-07T13:32:55.955263Z","submitted_at":"2024-01-03T01:37:54Z","title":"Stable minimal hypersurfaces in $\\mathbf{R}^5$","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2401.01492","snapshot_observed_at":"2026-08-06T21:33:57.066447Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2507.00342","last_updated":"2025-07-01T00:43:21Z","snapshot_observed_at":"2026-08-06T21:15:52.769122Z","submitted_at":"2025-07-01T00:43:21Z","title":"Complete two-sided $\\delta$-stable minimal hypersurfaces in $\\mathbf R^{n+1}$","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-06T21:33:57.066447Z"},"links":{"cited_paper":"/paper/2401.01492","citing_paper":"/paper/2507.00342"},"observation_digest":"sha256:d7af0d10cf6a9a96574b9e0c57dd16fe4c029ab8f20bc75f8985e516728e6357","observation_id":"840c06c9-c2d6-4256-99ba-b7cad22d8271","resolution":{"observed_at":"2026-08-06T21:33:57.066447Z","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":"2026-08-06T21:34:04.319626Z","title":"Colding and William P","venue":null,"work_id":"c73bcc90-4351-4ecf-8e10-7b9d114427a4","year":2004},"citing_paper":{"arxiv_id":"2507.00342","last_updated":"2025-07-01T00:43:21Z","snapshot_observed_at":"2026-08-06T21:15:52.769122Z","submitted_at":"2025-07-01T00:43:21Z","title":"Complete two-sided $\\delta$-stable minimal hypersurfaces in $\\mathbf R^{n+1}$","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-06T21:33:57.128778Z"},"links":{"citing_paper":"/paper/2507.00342"},"observation_digest":"sha256:2e94a492219153711962c0c557193967e4a014aeb9c09fac6135bedc787f8e4f","observation_id":"8450fb20-de54-463a-9272-b83ef5f366ea","resolution":{"observed_at":"2026-08-06T21:34:04.420268Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T21:34:04.183625Z","title":"Scuola Norm","venue":null,"work_id":"b3352a11-a14a-4068-81fb-5aa2e64dc683","year":1965},"citing_paper":{"arxiv_id":"2507.00342","last_updated":"2025-07-01T00:43:21Z","snapshot_observed_at":"2026-08-06T21:15:52.769122Z","submitted_at":"2025-07-01T00:43:21Z","title":"Complete two-sided $\\delta$-stable minimal hypersurfaces in $\\mathbf R^{n+1}$","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-06T21:33:57.231025Z"},"links":{"citing_paper":"/paper/2507.00342"},"observation_digest":"sha256:05a2b17626522c516a0e04cd692cb53724f0ccc8750d99a5776e846e15bd97bc","observation_id":"8ef0cf76-ac2e-47d3-8304-83c06c7bc65c","resolution":{"observed_at":"2026-08-06T21:34:04.257413Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T21:34:04.029886Z","title":"do Carmo and C","venue":null,"work_id":"061bf3db-5f4d-4362-bc6e-36198d30dff9","year":1979},"citing_paper":{"arxiv_id":"2507.00342","last_updated":"2025-07-01T00:43:21Z","snapshot_observed_at":"2026-08-06T21:15:52.769122Z","submitted_at":"2025-07-01T00:43:21Z","title":"Complete two-sided $\\delta$-stable minimal hypersurfaces in $\\mathbf R^{n+1}$","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-06T21:33:57.320394Z"},"links":{"citing_paper":"/paper/2507.00342"},"observation_digest":"sha256:77ecf85123b755961a917cfc220d5b3afc065381f28e4255e654ceed3563b538","observation_id":"11866da4-ea89-4573-9cf6-158da54ef612","resolution":{"observed_at":"2026-08-06T21:34:04.119463Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T21:34:03.825776Z","title":"Math., 82(1985), 121-132","venue":null,"work_id":"7f4cd11d-e6b6-4d85-bebf-d48ca0e02c09","year":1985},"citing_paper":{"arxiv_id":"2507.00342","last_updated":"2025-07-01T00:43:21Z","snapshot_observed_at":"2026-08-06T21:15:52.769122Z","submitted_at":"2025-07-01T00:43:21Z","title":"Complete two-sided $\\delta$-stable minimal hypersurfaces in $\\mathbf R^{n+1}$","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-06T21:33:57.381592Z"},"links":{"citing_paper":"/paper/2507.00342"},"observation_digest":"sha256:58f6d4adcea0a0105a5759499f2cbca2a6058225628e20178a0acee292bd6229","observation_id":"f4badc14-a38a-4faa-ac66-673c89ea7778","resolution":{"observed_at":"2026-08-06T21:34:03.904651Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T21:34:03.663872Z","title":"Pure Appl","venue":null,"work_id":"0c62aaf9-133f-4f8a-b155-c970586666e0","year":1980},"citing_paper":{"arxiv_id":"2507.00342","last_updated":"2025-07-01T00:43:21Z","snapshot_observed_at":"2026-08-06T21:15:52.769122Z","submitted_at":"2025-07-01T00:43:21Z","title":"Complete two-sided $\\delta$-stable minimal hypersurfaces in $\\mathbf R^{n+1}$","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-06T21:33:57.447429Z"},"links":{"citing_paper":"/paper/2507.00342"},"observation_digest":"sha256:36dd0f841cbb3a665bbd579a9f4ae3ec762bab09be7ec0b04d44dc44fa6aacd7","observation_id":"b84f5661-38cf-40d6-9288-a03ba963a075","resolution":{"observed_at":"2026-08-06T21:34:03.743258Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T21:34:03.534055Z","title":"Fleming, On the oriented Plateau problem, Ren d","venue":null,"work_id":"fa9580bc-25af-45bf-8bfb-f19812c79112","year":1962},"citing_paper":{"arxiv_id":"2507.00342","last_updated":"2025-07-01T00:43:21Z","snapshot_observed_at":"2026-08-06T21:15:52.769122Z","submitted_at":"2025-07-01T00:43:21Z","title":"Complete two-sided $\\delta$-stable minimal hypersurfaces in $\\mathbf R^{n+1}$","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-06T21:33:57.515361Z"},"links":{"citing_paper":"/paper/2507.00342"},"observation_digest":"sha256:dff60eee1485b636978c9f0d37f8b8691cb68618f7627c940b55f9016cc228e4","observation_id":"5892aabe-85e9-4607-82e4-f9127468cc71","resolution":{"observed_at":"2026-08-06T21:34:03.602757Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T21:34:03.382595Z","title":"Fu and Z","venue":null,"work_id":"832a12cf-1243-4b33-9b46-ec91ff189cf9","year":2010},"citing_paper":{"arxiv_id":"2507.00342","last_updated":"2025-07-01T00:43:21Z","snapshot_observed_at":"2026-08-06T21:15:52.769122Z","submitted_at":"2025-07-01T00:43:21Z","title":"Complete two-sided $\\delta$-stable minimal hypersurfaces in $\\mathbf R^{n+1}$","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-06T21:33:57.581313Z"},"links":{"citing_paper":"/paper/2507.00342"},"observation_digest":"sha256:07f52b1539916be5bce03b2772f7f9f1f95606dfbd7d96b9a6b73c653a739f1c","observation_id":"af295c89-74d0-4fc7-b041-3a82660ef94f","resolution":{"observed_at":"2026-08-06T21:34:03.464411Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T21:34:03.257877Z","title":null,"venue":null,"work_id":"af6b88b7-feba-4044-a15d-c4321c4d9a5d","year":1984},"citing_paper":{"arxiv_id":"2507.00342","last_updated":"2025-07-01T00:43:21Z","snapshot_observed_at":"2026-08-06T21:15:52.769122Z","submitted_at":"2025-07-01T00:43:21Z","title":"Complete two-sided $\\delta$-stable minimal hypersurfaces in $\\mathbf R^{n+1}$","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-06T21:33:57.652090Z"},"links":{"citing_paper":"/paper/2507.00342"},"observation_digest":"sha256:1888339dd742375b529833f4a0e133fd7d5cd5d1db065959a275d36950f2958d","observation_id":"61acc9c1-ef48-45e5-b382-30af9d0fed93","resolution":{"observed_at":"2026-08-06T21:34:03.297185Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T21:34:03.131560Z","title":null,"venue":null,"work_id":"7d082c78-a6b6-411a-87a0-e4db8d61ef34","year":1953},"citing_paper":{"arxiv_id":"2507.00342","last_updated":"2025-07-01T00:43:21Z","snapshot_observed_at":"2026-08-06T21:15:52.769122Z","submitted_at":"2025-07-01T00:43:21Z","title":"Complete two-sided $\\delta$-stable minimal hypersurfaces in $\\mathbf R^{n+1}$","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-06T21:33:57.732174Z"},"links":{"citing_paper":"/paper/2507.00342"},"observation_digest":"sha256:1ac47b2a387936844297cd06ef2e1ddf683c4329380473d22a9c4f5865b1ccf7","observation_id":"827a6020-ec17-419f-a9c2-dce5b2bdde46","resolution":{"observed_at":"2026-08-06T21:34:03.191449Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2407.03222","last_updated":"2024-07-03T15:49:34Z","snapshot_observed_at":"2026-07-06T18:41:01.720889Z","submitted_at":"2024-07-03T15:49:34Z","title":"On $\\delta$-Stable Minimal Hypersurfaces in $\\mathbb{R}^{n+1}$","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2407.03222","snapshot_observed_at":"2026-08-06T21:33:57.785441Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2507.00342","last_updated":"2025-07-01T00:43:21Z","snapshot_observed_at":"2026-08-06T21:15:52.769122Z","submitted_at":"2025-07-01T00:43:21Z","title":"Complete two-sided $\\delta$-stable minimal hypersurfaces in $\\mathbf R^{n+1}$","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-06T21:33:57.785441Z"},"links":{"cited_paper":"/paper/2407.03222","citing_paper":"/paper/2507.00342"},"observation_digest":"sha256:622240696cc88da1eae6f83846ab98a2a9b92477751b3961b70a5d489300012a","observation_id":"13721fbe-c745-4749-a519-da1916216674","resolution":{"observed_at":"2026-08-06T21:33:57.785441Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2405.06867","last_updated":"2025-06-19T08:45:17Z","snapshot_observed_at":"2026-07-06T18:12:55.888082Z","submitted_at":"2024-05-11T01:48:09Z","title":"Rigidity of CMC hypersurfaces in 5-and 6-manifolds","version":3},"cited_work":{"arxiv_id":"2405.06867","doi":null,"metadata_source":"pith","pith_arxiv_id":"2405.06867","snapshot_observed_at":"2026-08-06T21:33:59.305280Z","title":"Rigidity of CMC hypersurfaces in 5-and 6-manifolds","venue":"math.DG","work_id":"2546c8a4-9b2b-45a6-a615-7ce1dfd2d905","year":2024},"citing_paper":{"arxiv_id":"2507.00342","last_updated":"2025-07-01T00:43:21Z","snapshot_observed_at":"2026-08-06T21:15:52.769122Z","submitted_at":"2025-07-01T00:43:21Z","title":"Complete two-sided $\\delta$-stable minimal hypersurfaces in $\\mathbf R^{n+1}$","version":1},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-06T21:33:57.830239Z"},"links":{"cited_paper":"/paper/2405.06867","citing_paper":"/paper/2507.00342"},"observation_digest":"sha256:5214c27bd3c56cf823d5a26666de5948a2db6655826310e19ef671bab58b8e4f","observation_id":"6215065c-dd38-471e-acb5-25c8260348fc","resolution":{"observed_at":"2026-08-06T21:33:59.368918Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T21:34:02.998666Z","title":"Operator ∆ − aK on surfaces","venue":null,"work_id":"f78d590f-7b01-4941-b874-9748afc43f2b","year":1988},"citing_paper":{"arxiv_id":"2507.00342","last_updated":"2025-07-01T00:43:21Z","snapshot_observed_at":"2026-08-06T21:15:52.769122Z","submitted_at":"2025-07-01T00:43:21Z","title":"Complete two-sided $\\delta$-stable minimal hypersurfaces in $\\mathbf R^{n+1}$","version":1},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-06T21:33:57.913384Z"},"links":{"citing_paper":"/paper/2507.00342"},"observation_digest":"sha256:f81cd66c386aeeceb8e4d5339b79f0237fb82276e84628710dc6828560a0606c","observation_id":"ebabb693-3fab-4eeb-a9fc-34ceb194ccba","resolution":{"observed_at":"2026-08-06T21:34:03.063998Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2405.14676","last_updated":"2024-05-23T15:11:53Z","snapshot_observed_at":"2026-07-06T18:18:43.328203Z","submitted_at":"2024-05-23T15:11:53Z","title":"Stable minimal hypersurfaces in $\\mathbb R^6$","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2405.14676","snapshot_observed_at":"2026-08-06T21:33:57.975521Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2507.00342","last_updated":"2025-07-01T00:43:21Z","snapshot_observed_at":"2026-08-06T21:15:52.769122Z","submitted_at":"2025-07-01T00:43:21Z","title":"Complete two-sided $\\delta$-stable minimal hypersurfaces in $\\mathbf R^{n+1}$","version":1},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-06T21:33:57.975521Z"},"links":{"cited_paper":"/paper/2405.14676","citing_paper":"/paper/2507.00342"},"observation_digest":"sha256:d78029548be71ff46409897e0639e53c73ac63e390bd7e7a47bdb4dfb3c36308","observation_id":"2fd8e427-69b5-4d66-ad94-2ef6592cd87f","resolution":{"observed_at":"2026-08-06T21:33:57.975521Z","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":"2026-08-06T21:34:02.861558Z","title":"Meeks, J","venue":null,"work_id":"1c53f056-e12e-4695-95ce-5a882d4657d1","year":2006},"citing_paper":{"arxiv_id":"2507.00342","last_updated":"2025-07-01T00:43:21Z","snapshot_observed_at":"2026-08-06T21:15:52.769122Z","submitted_at":"2025-07-01T00:43:21Z","title":"Complete two-sided $\\delta$-stable minimal hypersurfaces in $\\mathbf R^{n+1}$","version":1},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-06T21:33:58.030838Z"},"links":{"citing_paper":"/paper/2507.00342"},"observation_digest":"sha256:da666c786c226f3e24a33f6b3eecb229805fb726a5b9279617c9220a272dff6d","observation_id":"fc7111a4-f2dc-4d65-9f11-f220b9764a24","resolution":{"observed_at":"2026-08-06T21:34:02.943471Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T21:34:02.695072Z","title":null,"venue":null,"work_id":"44dd23dd-dda1-4359-b99e-4712b074790c","year":1973},"citing_paper":{"arxiv_id":"2507.00342","last_updated":"2025-07-01T00:43:21Z","snapshot_observed_at":"2026-08-06T21:15:52.769122Z","submitted_at":"2025-07-01T00:43:21Z","title":"Complete two-sided $\\delta$-stable minimal hypersurfaces in $\\mathbf R^{n+1}$","version":1},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-06T21:33:58.102338Z"},"links":{"citing_paper":"/paper/2507.00342"},"observation_digest":"sha256:de775c96d48d19b5c3ae5e00e0b3c239c6e3fdfaae5656c8c88985cbea14d8e4","observation_id":"5d1a3427-3e0b-4f57-b5e4-ec4dfe64dd8f","resolution":{"observed_at":"2026-08-06T21:34:02.770362Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T21:34:02.554658Z","title":"Amer Math","venue":null,"work_id":"cc6cad22-f985-40b2-bf0a-a856d0928405","year":2003},"citing_paper":{"arxiv_id":"2507.00342","last_updated":"2025-07-01T00:43:21Z","snapshot_observed_at":"2026-08-06T21:15:52.769122Z","submitted_at":"2025-07-01T00:43:21Z","title":"Complete two-sided $\\delta$-stable minimal hypersurfaces in $\\mathbf R^{n+1}$","version":1},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-06T21:33:58.165112Z"},"links":{"citing_paper":"/paper/2507.00342"},"observation_digest":"sha256:7c0d465f59fe06e3a33235e75f47efb712365c8856150235583bb3cc294b94d0","observation_id":"8cd0c3b7-6b28-47fd-9c93-15b99a005894","resolution":{"observed_at":"2026-08-06T21:34:02.609486Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T21:34:02.376010Z","title":null,"venue":null,"work_id":"d7a30b55-db08-495a-b514-545ce5d47931","year":1981},"citing_paper":{"arxiv_id":"2507.00342","last_updated":"2025-07-01T00:43:21Z","snapshot_observed_at":"2026-08-06T21:15:52.769122Z","submitted_at":"2025-07-01T00:43:21Z","title":"Complete two-sided $\\delta$-stable minimal hypersurfaces in $\\mathbf R^{n+1}$","version":1},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-06T21:33:58.267327Z"},"links":{"citing_paper":"/paper/2507.00342"},"observation_digest":"sha256:c03ca10a0159285213cf99967343b3d2b3c9cab2fee319a100e93759e3e790ad","observation_id":"dc776390-71eb-4bcb-af27-0424defa3d9b","resolution":{"observed_at":"2026-08-06T21:34:02.475832Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T21:34:02.208254Z","title":"Schoen, L","venue":null,"work_id":"08c47fc8-2dc2-47e8-86db-ab14402d0cb5","year":1975},"citing_paper":{"arxiv_id":"2507.00342","last_updated":"2025-07-01T00:43:21Z","snapshot_observed_at":"2026-08-06T21:15:52.769122Z","submitted_at":"2025-07-01T00:43:21Z","title":"Complete two-sided $\\delta$-stable minimal hypersurfaces in $\\mathbf R^{n+1}$","version":1},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-08-06T21:33:58.345745Z"},"links":{"citing_paper":"/paper/2507.00342"},"observation_digest":"sha256:f2a191f1b3e76725d05bb34d0d859290560d6796010a66e9149cdc0fd6f8d7be","observation_id":"17f84313-7e1d-40b7-a20d-ea910ea883f3","resolution":{"observed_at":"2026-08-06T21:34:02.283426Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T21:34:02.076347Z","title":null,"venue":null,"work_id":"38de92a4-593f-4e1a-b516-11ec9ddaf953","year":1981},"citing_paper":{"arxiv_id":"2507.00342","last_updated":"2025-07-01T00:43:21Z","snapshot_observed_at":"2026-08-06T21:15:52.769122Z","submitted_at":"2025-07-01T00:43:21Z","title":"Complete two-sided $\\delta$-stable minimal hypersurfaces in $\\mathbf R^{n+1}$","version":1},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-08-06T21:33:58.406475Z"},"links":{"citing_paper":"/paper/2507.00342"},"observation_digest":"sha256:2501566e21754b3d4d4526a55ee5e059af9be265fcf30e77a94328965b629e5f","observation_id":"a4bf7fae-74bf-4a7d-8711-031dc168eb28","resolution":{"observed_at":"2026-08-06T21:34:02.142758Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T21:34:01.916612Z","title":null,"venue":null,"work_id":"1445542a-f852-4c18-9e72-03dc13381caa","year":null},"citing_paper":{"arxiv_id":"2507.00342","last_updated":"2025-07-01T00:43:21Z","snapshot_observed_at":"2026-08-06T21:15:52.769122Z","submitted_at":"2025-07-01T00:43:21Z","title":"Complete two-sided $\\delta$-stable minimal hypersurfaces in $\\mathbf R^{n+1}$","version":1},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-08-06T21:33:58.496378Z"},"links":{"citing_paper":"/paper/2507.00342"},"observation_digest":"sha256:db9529b960e5793cdbc434aee9c9c114ffb1349c96c694773e16f52e16f973b2","observation_id":"798f3b9e-9b1b-4dea-9755-e1fc122d41d1","resolution":{"observed_at":"2026-08-06T21:34:02.009116Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T21:34:01.780166Z","title":null,"venue":null,"work_id":"59c75381-7e06-4743-a17e-6524214a1a92","year":1997},"citing_paper":{"arxiv_id":"2507.00342","last_updated":"2025-07-01T00:43:21Z","snapshot_observed_at":"2026-08-06T21:15:52.769122Z","submitted_at":"2025-07-01T00:43:21Z","title":"Complete two-sided $\\delta$-stable minimal hypersurfaces in $\\mathbf R^{n+1}$","version":1},"reference_index":38,"source":"pdf_text","source_observed_at":"2026-08-06T21:33:58.560480Z"},"links":{"citing_paper":"/paper/2507.00342"},"observation_digest":"sha256:2b03fea1d04b6f6b8765907e7d39f34ebe1c1dcea498cce4a82fa408bcc0fe9f","observation_id":"97d2999c-583f-4a91-a94c-3f9991be7b9b","resolution":{"observed_at":"2026-08-06T21:34:01.853304Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T21:34:01.657024Z","title":"Shen, X.-H","venue":null,"work_id":"45d95a49-bd65-401b-935f-952944361f2c","year":1998},"citing_paper":{"arxiv_id":"2507.00342","last_updated":"2025-07-01T00:43:21Z","snapshot_observed_at":"2026-08-06T21:15:52.769122Z","submitted_at":"2025-07-01T00:43:21Z","title":"Complete two-sided $\\delta$-stable minimal hypersurfaces in $\\mathbf R^{n+1}$","version":1},"reference_index":39,"source":"pdf_text","source_observed_at":"2026-08-06T21:33:58.639975Z"},"links":{"citing_paper":"/paper/2507.00342"},"observation_digest":"sha256:c54d9e3f6c346b496409fefcf41b47931a9ad50b09dbfa945542ebe0dc7fcfa4","observation_id":"a571d123-c435-41e5-ba3e-fd6eb62a4198","resolution":{"observed_at":"2026-08-06T21:34:01.695706Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T21:34:01.488306Z","title":null,"venue":null,"work_id":"6d9a26e7-31a2-45cc-a8fc-74cd83b8f5b4","year":2009},"citing_paper":{"arxiv_id":"2507.00342","last_updated":"2025-07-01T00:43:21Z","snapshot_observed_at":"2026-08-06T21:15:52.769122Z","submitted_at":"2025-07-01T00:43:21Z","title":"Complete two-sided $\\delta$-stable minimal hypersurfaces in $\\mathbf R^{n+1}$","version":1},"reference_index":40,"source":"pdf_text","source_observed_at":"2026-08-06T21:33:58.727079Z"},"links":{"citing_paper":"/paper/2507.00342"},"observation_digest":"sha256:7e99988178099bdf1ef99732d1aeadaf3261fc7a874e71a0ef08cd48eb9fec7c","observation_id":"a72446a8-7e10-49d9-abef-15641c064ddc","resolution":{"observed_at":"2026-08-06T21:34:01.568566Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T21:34:01.352480Z","title":null,"venue":null,"work_id":"00c9afba-f711-4b0d-9e37-833b19b9d6cc","year":1968},"citing_paper":{"arxiv_id":"2507.00342","last_updated":"2025-07-01T00:43:21Z","snapshot_observed_at":"2026-08-06T21:15:52.769122Z","submitted_at":"2025-07-01T00:43:21Z","title":"Complete two-sided $\\delta$-stable minimal hypersurfaces in $\\mathbf R^{n+1}$","version":1},"reference_index":41,"source":"pdf_text","source_observed_at":"2026-08-06T21:33:58.786066Z"},"links":{"citing_paper":"/paper/2507.00342"},"observation_digest":"sha256:d67c58fd5c00814fd6dd2d74aba5693ae266ed1303af31882bf0440c1f961a9f","observation_id":"7329d25b-a32b-43a4-88fa-63cec02ab707","resolution":{"observed_at":"2026-08-06T21:34:01.413850Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T21:34:00.203159Z","title":null,"venue":null,"work_id":"22f24a0f-ed47-45db-83c2-b8ca7b816011","year":2009},"citing_paper":{"arxiv_id":"2507.00342","last_updated":"2025-07-01T00:43:21Z","snapshot_observed_at":"2026-08-06T21:15:52.769122Z","submitted_at":"2025-07-01T00:43:21Z","title":"Complete two-sided $\\delta$-stable minimal hypersurfaces in $\\mathbf R^{n+1}$","version":1},"reference_index":42,"source":"pdf_text","source_observed_at":"2026-08-06T21:33:58.822772Z"},"links":{"citing_paper":"/paper/2507.00342"},"observation_digest":"sha256:069d2c32c83c7298e8575102d14efd8f823c280c38849bd9524b44e57962618a","observation_id":"93a56395-ec03-4ac2-8a7a-c83df08701ff","resolution":{"observed_at":"2026-08-06T21:34:00.807200Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T21:33:59.713069Z","title":"White, Introduction to minimal surface theory, Geome tric analysis, IAS/Park City","venue":null,"work_id":"ef7fa36b-7e5f-4a35-8cff-fd2fd240c5e6","year":2015},"citing_paper":{"arxiv_id":"2507.00342","last_updated":"2025-07-01T00:43:21Z","snapshot_observed_at":"2026-08-06T21:15:52.769122Z","submitted_at":"2025-07-01T00:43:21Z","title":"Complete two-sided $\\delta$-stable minimal hypersurfaces in $\\mathbf R^{n+1}$","version":1},"reference_index":43,"source":"pdf_text","source_observed_at":"2026-08-06T21:33:58.901894Z"},"links":{"citing_paper":"/paper/2507.00342"},"observation_digest":"sha256:8f2510817f4011a9b14c5e739aa500f7eb607eb02b57005a0df9bdf7884eda25","observation_id":"4a5bb294-1436-4056-9ffd-5b418e428512","resolution":{"observed_at":"2026-08-06T21:33:59.842635Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2301.02730","last_updated":"2024-09-30T15:02:51Z","snapshot_observed_at":"2026-07-06T14:38:13.498613Z","submitted_at":"2023-01-06T22:23:39Z","title":"Dimension constraints in some problems involving intermediate curvature","version":2},"cited_work":{"arxiv_id":"2301.02730","doi":null,"metadata_source":"pith","pith_arxiv_id":"2301.02730","snapshot_observed_at":"2026-08-06T21:33:59.156871Z","title":"Dimension constraints in some problems involving intermediate curvature","venue":"math.DG","work_id":"5c0e1f8b-39f6-42f6-aec5-fe781220b778","year":2023},"citing_paper":{"arxiv_id":"2507.00342","last_updated":"2025-07-01T00:43:21Z","snapshot_observed_at":"2026-08-06T21:15:52.769122Z","submitted_at":"2025-07-01T00:43:21Z","title":"Complete two-sided $\\delta$-stable minimal hypersurfaces in $\\mathbf R^{n+1}$","version":1},"reference_index":44,"source":"pdf_text","source_observed_at":"2026-08-06T21:33:58.985835Z"},"links":{"cited_paper":"/paper/2301.02730","citing_paper":"/paper/2507.00342"},"observation_digest":"sha256:8f908db497e56df3132e6345b085b7b80b725b58e7f0b9038bee4dada15748ba","observation_id":"03dbaef2-1fd2-4f1d-a3ea-64847e6f2935","resolution":{"observed_at":"2026-08-06T21:33:59.196234Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T21:33:59.570032Z","title":"δ-STABLE MINIMAL HYPERSURF ACES 24 Qing-Ming Cheng Ma thema tical Science Research Center, Chongqing University of Technology, Chongqing 400054, P","venue":null,"work_id":"174c50df-8f78-4c4d-b7ff-6f0dca04f45a","year":2021},"citing_paper":{"arxiv_id":"2507.00342","last_updated":"2025-07-01T00:43:21Z","snapshot_observed_at":"2026-08-06T21:15:52.769122Z","submitted_at":"2025-07-01T00:43:21Z","title":"Complete two-sided $\\delta$-stable minimal hypersurfaces in $\\mathbf R^{n+1}$","version":1},"reference_index":45,"source":"pdf_text","source_observed_at":"2026-08-06T21:33:59.051985Z"},"links":{"citing_paper":"/paper/2507.00342"},"observation_digest":"sha256:298e55e6972cb177cdff705bcebecef449114325c0f6874b3f27bad51f2202ae","observation_id":"a34d5102-7d4c-470c-bcc7-4886673b55dd","resolution":{"observed_at":"2026-08-06T21:33:59.629653Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2507.00342","last_updated":"2025-07-01T00:43:21Z","latest_version":1,"primary_category":"math.DG","snapshot_observed_at":"2026-08-06T21:15:52.769122Z","submitted_at":"2025-07-01T00:43:21Z","title":"Complete two-sided $\\delta$-stable minimal hypersurfaces in $\\mathbf R^{n+1}$"},"reference_resolution":{"displayed":45,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":20,"verified_exact":3,"verified_fuzzy":22},"total_outbound_references":45},"refusal":"A citation records a reference. It does not transfer a finding from one paper to another.","schema":"pith.paper-citation-record.v1","standing_sources":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"thesis":"As of 7 August 2026, this Paper Citation Record lists 45 of 45 outbound references and 0 inbound Pith citation observations for arXiv:2507.00342."}