{"as_of":"2026-08-10T05:07:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:37c88e1f83b841e49a9b9e4d02b0d6bbf63a249c4206bdebcd3f8c6725608426","coverage":[{"denominator":28,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":28,"source":"paper_references, paper_reference_links","source_observed_at":"2026-07-08T11:34:31.099595Z","state":"measured"},{"denominator":28,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":28,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-09T06:31:02.800959+00:00","state":"measured"},{"denominator":0,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":0,"source":"paper_references, paper_reference_links","source_observed_at":null,"state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"cited_works","source_observed_at":null,"state":"measured"}],"external_citation_measurements":[],"inbound":[],"links":{"evidence":"/evidence","html":"/paper/2607.06277/citation-record","integrity":"/paper/2607.06277/integrity","json":"/paper/2607.06277/citation-record.json","paper":"/paper/2607.06277"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-08T11:34:50.954352Z","title":null,"venue":null,"work_id":"74b12206-75df-48e4-a984-c798cab41e31","year":1990},"citing_paper":{"arxiv_id":"2607.06277","last_updated":"2026-07-07T13:43:26Z","snapshot_observed_at":"2026-08-10T02:03:51.312030Z","submitted_at":"2026-07-07T13:43:26Z","title":"Geometric transformation theorem, fundamental groups and monotone of numbers of almost Euclidean factors of geodesic balls","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-07-08T11:34:31.099595Z"},"links":{"citing_paper":"/paper/2607.06277"},"observation_digest":"sha256:98e62875f5de6796dce845b8d7414f9eada0f00ed4e1aa8ccf0e934a9a241222","observation_id":"67f108d2-42d9-4619-b4b7-5f9a2a1df1e2","resolution":{"observed_at":"2026-07-08T11:34:50.955448Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-08T11:34:50.937492Z","title":"Ambrosio, S","venue":null,"work_id":"56299642-c27e-4ce7-afd1-3fee612bae64","year":2018},"citing_paper":{"arxiv_id":"2607.06277","last_updated":"2026-07-07T13:43:26Z","snapshot_observed_at":"2026-08-10T02:03:51.312030Z","submitted_at":"2026-07-07T13:43:26Z","title":"Geometric transformation theorem, fundamental groups and monotone of numbers of almost Euclidean factors of geodesic balls","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-07-08T11:34:31.099595Z"},"links":{"citing_paper":"/paper/2607.06277"},"observation_digest":"sha256:3d42e7150625b329597220fa9b06838241ee368ece726b8c1c687303e8c7cad0","observation_id":"0798a728-b7e5-4c0d-878d-4c38e72f4272","resolution":{"observed_at":"2026-07-08T11:34:50.938748Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":"2311.12155","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-08T11:34:50.887116Z","title":"Bru` e, A","venue":null,"work_id":"132baad0-22ba-4e68-a9db-a8dfd6aa2e7c","year":2023},"citing_paper":{"arxiv_id":"2607.06277","last_updated":"2026-07-07T13:43:26Z","snapshot_observed_at":"2026-08-10T02:03:51.312030Z","submitted_at":"2026-07-07T13:43:26Z","title":"Geometric transformation theorem, fundamental groups and monotone of numbers of almost Euclidean factors of geodesic balls","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-07-08T11:34:31.099595Z"},"links":{"citing_paper":"/paper/2607.06277"},"observation_digest":"sha256:9083c98a99c82c35caa8bba8e7d6bd8e5d52ad4078ca37cabde24942ce6ef18b","observation_id":"b1e60752-e4ba-4807-afe0-8fe5da62a1b2","resolution":{"observed_at":"2026-07-08T11:34:50.889993Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-08T11:34:50.935450Z","title":"Bru` e, A","venue":null,"work_id":"4954454a-a79a-426f-9403-55f803e46e92","year":2025},"citing_paper":{"arxiv_id":"2607.06277","last_updated":"2026-07-07T13:43:26Z","snapshot_observed_at":"2026-08-10T02:03:51.312030Z","submitted_at":"2026-07-07T13:43:26Z","title":"Geometric transformation theorem, fundamental groups and monotone of numbers of almost Euclidean factors of geodesic balls","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-07-08T11:34:31.099595Z"},"links":{"citing_paper":"/paper/2607.06277"},"observation_digest":"sha256:26eefc4c6852ac302364fb1be1137ec157f6a4a7b90344b0c66a785ad3334b34","observation_id":"ef1ccd15-e6dc-4f56-ac1d-f96db8a22638","resolution":{"observed_at":"2026-07-08T11:34:50.936763Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-08T11:34:50.952651Z","title":"Naber, D","venue":null,"work_id":"86b8cffc-3253-4d20-89a2-e1ce7b4aa54c","year":2022},"citing_paper":{"arxiv_id":"2607.06277","last_updated":"2026-07-07T13:43:26Z","snapshot_observed_at":"2026-08-10T02:03:51.312030Z","submitted_at":"2026-07-07T13:43:26Z","title":"Geometric transformation theorem, fundamental groups and monotone of numbers of almost Euclidean factors of geodesic balls","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-07-08T11:34:31.099595Z"},"links":{"citing_paper":"/paper/2607.06277"},"observation_digest":"sha256:04b9a5c88311af7e2607708c416e559465ac435a60e7e69e2828efca3a73f9de","observation_id":"a49176cc-e859-4379-843a-1db9cfd2c6dc","resolution":{"observed_at":"2026-07-08T11:34:50.953682Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-08T11:34:50.959924Z","title":"Bru´ e, E","venue":null,"work_id":"35a30656-9737-41bf-a953-873811c4ebc1","year":2023},"citing_paper":{"arxiv_id":"2607.06277","last_updated":"2026-07-07T13:43:26Z","snapshot_observed_at":"2026-08-10T02:03:51.312030Z","submitted_at":"2026-07-07T13:43:26Z","title":"Geometric transformation theorem, fundamental groups and monotone of numbers of almost Euclidean factors of geodesic balls","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-07-08T11:34:31.099595Z"},"links":{"citing_paper":"/paper/2607.06277"},"observation_digest":"sha256:be2054f661ece75a5d083c43b061ffde7fcfa905ec6e0b05d32c2092f4cb7089","observation_id":"79dbad2d-d6bc-4e4b-bd4e-25d04dbe304f","resolution":{"observed_at":"2026-07-08T11:34:50.961111Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-08T11:34:50.956092Z","title":"Cheeger, T.H","venue":null,"work_id":"775ab3e7-81e7-4ef9-a76c-e1617b6f7f09","year":1996},"citing_paper":{"arxiv_id":"2607.06277","last_updated":"2026-07-07T13:43:26Z","snapshot_observed_at":"2026-08-10T02:03:51.312030Z","submitted_at":"2026-07-07T13:43:26Z","title":"Geometric transformation theorem, fundamental groups and monotone of numbers of almost Euclidean factors of geodesic balls","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-07-08T11:34:31.099595Z"},"links":{"citing_paper":"/paper/2607.06277"},"observation_digest":"sha256:718195ebd50e9792fc62328389a4b3ecc222d835f37c34096a70f68578a4bf71","observation_id":"15c0f970-a389-4906-9e8c-4705cfc136fa","resolution":{"observed_at":"2026-07-08T11:34:50.957450Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-08T11:34:50.961742Z","title":"Cheeger, T.H","venue":null,"work_id":"0a3bfabf-9e60-4855-b4c8-ac4e826b5370","year":1997},"citing_paper":{"arxiv_id":"2607.06277","last_updated":"2026-07-07T13:43:26Z","snapshot_observed_at":"2026-08-10T02:03:51.312030Z","submitted_at":"2026-07-07T13:43:26Z","title":"Geometric transformation theorem, fundamental groups and monotone of numbers of almost Euclidean factors of geodesic balls","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-07-08T11:34:31.099595Z"},"links":{"citing_paper":"/paper/2607.06277"},"observation_digest":"sha256:e501f4378a759ec4a73bd3b5cbc3b98070456155d7f329415cb0a01067f222a1","observation_id":"da15d34c-71ba-44b5-9899-8b04efe01758","resolution":{"observed_at":"2026-07-08T11:34:50.963153Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-08T11:34:50.963754Z","title":"Cheeger, W","venue":null,"work_id":"a6a7c1d9-1f4a-45bf-9192-fd5020c79326","year":2021},"citing_paper":{"arxiv_id":"2607.06277","last_updated":"2026-07-07T13:43:26Z","snapshot_observed_at":"2026-08-10T02:03:51.312030Z","submitted_at":"2026-07-07T13:43:26Z","title":"Geometric transformation theorem, fundamental groups and monotone of numbers of almost Euclidean factors of geodesic balls","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-07-08T11:34:31.099595Z"},"links":{"citing_paper":"/paper/2607.06277"},"observation_digest":"sha256:2f45ebc28c8b603c4c63127c054a8f2f3b4cbb8462779348c0fb5ea3d7f51e4b","observation_id":"9b3faf77-e124-49a1-9a05-3b0edd797408","resolution":{"observed_at":"2026-07-08T11:34:50.964919Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-08T11:34:50.943402Z","title":"Cheeger, A","venue":null,"work_id":"6743460a-6484-4c66-a6ae-0ea7b7a61cfc","year":2015},"citing_paper":{"arxiv_id":"2607.06277","last_updated":"2026-07-07T13:43:26Z","snapshot_observed_at":"2026-08-10T02:03:51.312030Z","submitted_at":"2026-07-07T13:43:26Z","title":"Geometric transformation theorem, fundamental groups and monotone of numbers of almost Euclidean factors of geodesic balls","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-07-08T11:34:31.099595Z"},"links":{"citing_paper":"/paper/2607.06277"},"observation_digest":"sha256:e38c7e88c618cf533aa41485755590d8b60b68f4c992fee4f4b97bafe0aaf5d4","observation_id":"1291c3d9-61f5-4f7d-8697-baeb5ad8591c","resolution":{"observed_at":"2026-07-08T11:34:50.944648Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-08T11:34:50.933503Z","title":"Colding, A","venue":null,"work_id":"c4d4ed43-e95c-4a09-bd82-57fa5e1b1dd9","year":2013},"citing_paper":{"arxiv_id":"2607.06277","last_updated":"2026-07-07T13:43:26Z","snapshot_observed_at":"2026-08-10T02:03:51.312030Z","submitted_at":"2026-07-07T13:43:26Z","title":"Geometric transformation theorem, fundamental groups and monotone of numbers of almost Euclidean factors of geodesic balls","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-07-08T11:34:31.099595Z"},"links":{"citing_paper":"/paper/2607.06277"},"observation_digest":"sha256:c48739040742c9aa6b987c2503d0ea8e5804604655b53f916f2fbf7eb9e70b40","observation_id":"5395c36c-0c13-4e69-89bd-a3ee90f1d382","resolution":{"observed_at":"2026-07-08T11:34:50.934804Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-08T11:34:50.925525Z","title":"Cohn-Vossen","venue":null,"work_id":"5a8a97c3-9b4c-45ff-b721-c40597876054","year":1935},"citing_paper":{"arxiv_id":"2607.06277","last_updated":"2026-07-07T13:43:26Z","snapshot_observed_at":"2026-08-10T02:03:51.312030Z","submitted_at":"2026-07-07T13:43:26Z","title":"Geometric transformation theorem, fundamental groups and monotone of numbers of almost Euclidean factors of geodesic balls","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-07-08T11:34:31.099595Z"},"links":{"citing_paper":"/paper/2607.06277"},"observation_digest":"sha256:235636ef8c31e7156993edf1f49ccee996e35d5f294f54a90bf44532e8767c2b","observation_id":"8c8282a8-0cc9-435b-b21f-30a29fdef7f0","resolution":{"observed_at":"2026-07-08T11:34:50.927021Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-08T11:34:50.958222Z","title":"Huang, X","venue":null,"work_id":"469a651e-cba1-4954-a08d-e1501053c1a1","year":2024},"citing_paper":{"arxiv_id":"2607.06277","last_updated":"2026-07-07T13:43:26Z","snapshot_observed_at":"2026-08-10T02:03:51.312030Z","submitted_at":"2026-07-07T13:43:26Z","title":"Geometric transformation theorem, fundamental groups and monotone of numbers of almost Euclidean factors of geodesic balls","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-07-08T11:34:31.099595Z"},"links":{"citing_paper":"/paper/2607.06277"},"observation_digest":"sha256:3078f6fc092f67d03fc8ae40d824c161a0fd3db69daa499c7ef839bfa6641188","observation_id":"659099bd-9195-49ec-8835-8e948c63bf5a","resolution":{"observed_at":"2026-07-08T11:34:50.959372Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2502.03259","last_updated":"2025-02-05T15:16:36Z","snapshot_observed_at":"2026-08-09T16:23:13.190628Z","submitted_at":"2025-02-05T15:16:36Z","title":"Nonnegative Ricci Curvature, Euclidean Volume Growth, and the Fundamental Groups of Open $4$-Manifolds","version":1},"cited_work":{"arxiv_id":"2502.03259","doi":null,"metadata_source":"pith","pith_arxiv_id":"2502.03259","snapshot_observed_at":"2026-07-08T11:34:50.901680Z","title":"Nonnegative Ricci Curvature, Euclidean Volume Growth, and the Fundamental Groups of Open $4$-Manifolds","venue":"math.DG","work_id":"abcb6d35-d88d-4804-961f-40d7d546d5ac","year":2025},"citing_paper":{"arxiv_id":"2607.06277","last_updated":"2026-07-07T13:43:26Z","snapshot_observed_at":"2026-08-10T02:03:51.312030Z","submitted_at":"2026-07-07T13:43:26Z","title":"Geometric transformation theorem, fundamental groups and monotone of numbers of almost Euclidean factors of geodesic balls","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-07-08T11:34:31.099595Z"},"links":{"cited_paper":"/paper/2502.03259","citing_paper":"/paper/2607.06277"},"observation_digest":"sha256:e38db039b187268a0b18b5f43b1fb2aad2cf9f5eb723d80389a883d1f2071715","observation_id":"4cb09c7b-11bc-4958-85c4-746a71d1cb31","resolution":{"observed_at":"2026-07-08T11:34:50.903336Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1515/crelle-2024-0089","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":null,"venue":"Journal für die reine und angewandte Mathematik (Crelles Journal)","work_id":"e8108923-5fa0-456a-a271-f9b79d9810d7","year":2025},"citing_paper":{"arxiv_id":"2607.06277","last_updated":"2026-07-07T13:43:26Z","snapshot_observed_at":"2026-08-10T02:03:51.312030Z","submitted_at":"2026-07-07T13:43:26Z","title":"Geometric transformation theorem, fundamental groups and monotone of numbers of almost Euclidean factors of geodesic balls","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-07-08T11:34:31.099595Z"},"links":{"citing_paper":"/paper/2607.06277"},"observation_digest":"sha256:7ea2bf1abf8700eb263f5629cfa0c3e1d99aca42c4c16a0c27973deb9e141228","observation_id":"8abc4e06-cd49-4fb4-b04a-3a7ccd3aaecc","resolution":{"observed_at":"2026-07-08T11:34:50.883608Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-07-11T00:19:35.169542+00:00","source":"crossref_status_cache"},{"observed_at":"2026-07-11T00:19:35.169542+00:00","source":"openalex_status_cache"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-08T11:34:50.948878Z","title":null,"venue":null,"work_id":"ca9843f8-2aeb-47da-8f6c-3be0a7d838cf","year":1986},"citing_paper":{"arxiv_id":"2607.06277","last_updated":"2026-07-07T13:43:26Z","snapshot_observed_at":"2026-08-10T02:03:51.312030Z","submitted_at":"2026-07-07T13:43:26Z","title":"Geometric transformation theorem, fundamental groups and monotone of numbers of almost Euclidean factors of geodesic balls","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-07-08T11:34:31.099595Z"},"links":{"citing_paper":"/paper/2607.06277"},"observation_digest":"sha256:32d784941ced001ca2a33de65bd78bbab4d0720154143e6103f28da9d4224dfe","observation_id":"c2730e7a-e54c-4c2b-85a9-deda6f6ff940","resolution":{"observed_at":"2026-07-08T11:34:50.950281Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-08T11:34:50.939605Z","title":null,"venue":null,"work_id":"6cf7e88c-b94e-4469-ac19-6d9c2cdf02c2","year":2013},"citing_paper":{"arxiv_id":"2607.06277","last_updated":"2026-07-07T13:43:26Z","snapshot_observed_at":"2026-08-10T02:03:51.312030Z","submitted_at":"2026-07-07T13:43:26Z","title":"Geometric transformation theorem, fundamental groups and monotone of numbers of almost Euclidean factors of geodesic balls","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-07-08T11:34:31.099595Z"},"links":{"citing_paper":"/paper/2607.06277"},"observation_digest":"sha256:f3a9a31465a1d7fa3b5c687c258639493098bbc3263ba4049fef14d2878dc925","observation_id":"f97daa82-e854-4c87-a76c-d2922c58a9f1","resolution":{"observed_at":"2026-07-08T11:34:50.940836Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-08T11:34:50.950953Z","title":null,"venue":null,"work_id":"f5fef1d5-dca3-4ca5-b067-935e0cf1fedd","year":1968},"citing_paper":{"arxiv_id":"2607.06277","last_updated":"2026-07-07T13:43:26Z","snapshot_observed_at":"2026-08-10T02:03:51.312030Z","submitted_at":"2026-07-07T13:43:26Z","title":"Geometric transformation theorem, fundamental groups and monotone of numbers of almost Euclidean factors of geodesic balls","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-07-08T11:34:31.099595Z"},"links":{"citing_paper":"/paper/2607.06277"},"observation_digest":"sha256:43ac6849d9fe4f7ff84a43a2a9265614dc5ea2ed6dd49c69875165b76ce7e4a8","observation_id":"2051770d-ca05-49d1-9710-921d3ace87d8","resolution":{"observed_at":"2026-07-08T11:34:50.952011Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-08T11:34:50.931324Z","title":"Mondino, A","venue":null,"work_id":"4b590cfd-45e2-430d-bc58-6d1540676df4","year":2019},"citing_paper":{"arxiv_id":"2607.06277","last_updated":"2026-07-07T13:43:26Z","snapshot_observed_at":"2026-08-10T02:03:51.312030Z","submitted_at":"2026-07-07T13:43:26Z","title":"Geometric transformation theorem, fundamental groups and monotone of numbers of almost Euclidean factors of geodesic balls","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-07-08T11:34:31.099595Z"},"links":{"citing_paper":"/paper/2607.06277"},"observation_digest":"sha256:2f1002ffd109b39ddb62bb520189c6e9eb3589e4d62df3d8545433c3bdb1cd61","observation_id":"af20ef46-136b-482c-91e1-a2620418bda5","resolution":{"observed_at":"2026-07-08T11:34:50.932857Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-08T11:34:50.922905Z","title":"Kapovitch, B","venue":null,"work_id":"5a5f8c90-0d62-4863-bf95-911eecf1d653","year":null},"citing_paper":{"arxiv_id":"2607.06277","last_updated":"2026-07-07T13:43:26Z","snapshot_observed_at":"2026-08-10T02:03:51.312030Z","submitted_at":"2026-07-07T13:43:26Z","title":"Geometric transformation theorem, fundamental groups and monotone of numbers of almost Euclidean factors of geodesic balls","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-07-08T11:34:31.099595Z"},"links":{"citing_paper":"/paper/2607.06277"},"observation_digest":"sha256:6aa0fe4cfb1cf4e422206ea217e767d2401770d0695348b5ae4487ede7b340d6","observation_id":"89d459d9-94a1-4525-8410-fadd0adc7cef","resolution":{"observed_at":"2026-07-08T11:34:50.924686Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1809.10220","last_updated":"2019-01-31T03:30:58Z","snapshot_observed_at":"2026-08-06T15:39:05.096880Z","submitted_at":"2018-09-26T20:33:59Z","title":"Nonnegative Ricci curvature, almost stability at infinity, and structure of fundamental groups","version":2},"cited_work":{"arxiv_id":"1809.10220","doi":null,"metadata_source":"pith","pith_arxiv_id":"1809.10220","snapshot_observed_at":"2026-07-08T11:34:50.898003Z","title":"Nonnegative Ricci curvature, almost stability at infinity, and structure of fundamental groups","venue":"math.DG","work_id":"277cd8fd-5e8d-4481-9a19-fc611dd5b371","year":2018},"citing_paper":{"arxiv_id":"2607.06277","last_updated":"2026-07-07T13:43:26Z","snapshot_observed_at":"2026-08-10T02:03:51.312030Z","submitted_at":"2026-07-07T13:43:26Z","title":"Geometric transformation theorem, fundamental groups and monotone of numbers of almost Euclidean factors of geodesic balls","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-07-08T11:34:31.099595Z"},"links":{"cited_paper":"/paper/1809.10220","citing_paper":"/paper/2607.06277"},"observation_digest":"sha256:fedefb5ddfaff84a13e7d705785722b88677c653dda45833f17afb4646ba5dd1","observation_id":"0027b3af-e5b6-41a7-848c-48fdae5835cd","resolution":{"observed_at":"2026-07-08T11:34:50.899623Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-08T11:34:50.946812Z","title":null,"venue":null,"work_id":"f5b51cc6-d4bc-4cee-940e-408fa8f5edfa","year":2019},"citing_paper":{"arxiv_id":"2607.06277","last_updated":"2026-07-07T13:43:26Z","snapshot_observed_at":"2026-08-10T02:03:51.312030Z","submitted_at":"2026-07-07T13:43:26Z","title":"Geometric transformation theorem, fundamental groups and monotone of numbers of almost Euclidean factors of geodesic balls","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-07-08T11:34:31.099595Z"},"links":{"citing_paper":"/paper/2607.06277"},"observation_digest":"sha256:af3399728a1e8a426aab79263c961a317a961592957816c0c782bd3a89c31c7e","observation_id":"19bd6026-57dd-4bde-8474-85875d92aea4","resolution":{"observed_at":"2026-07-08T11:34:50.948075Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-08T11:34:50.920594Z","title":null,"venue":null,"work_id":"0916085d-3367-4dc1-aefc-42da105c34ae","year":2020},"citing_paper":{"arxiv_id":"2607.06277","last_updated":"2026-07-07T13:43:26Z","snapshot_observed_at":"2026-08-10T02:03:51.312030Z","submitted_at":"2026-07-07T13:43:26Z","title":"Geometric transformation theorem, fundamental groups and monotone of numbers of almost Euclidean factors of geodesic balls","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-07-08T11:34:31.099595Z"},"links":{"citing_paper":"/paper/2607.06277"},"observation_digest":"sha256:14d7800b36d26570a1507a16afe88980a71100806e37851a98e272c32e97d687","observation_id":"7c5d33b1-bf35-4b4c-99ba-45e00464c3fa","resolution":{"observed_at":"2026-07-08T11:34:50.921970Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-08T11:34:50.929542Z","title":null,"venue":null,"work_id":"b54bcbf7-25be-4ba5-b83b-de1cae38c4fb","year":2020},"citing_paper":{"arxiv_id":"2607.06277","last_updated":"2026-07-07T13:43:26Z","snapshot_observed_at":"2026-08-10T02:03:51.312030Z","submitted_at":"2026-07-07T13:43:26Z","title":"Geometric transformation theorem, fundamental groups and monotone of numbers of almost Euclidean factors of geodesic balls","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-07-08T11:34:31.099595Z"},"links":{"citing_paper":"/paper/2607.06277"},"observation_digest":"sha256:0ffca318a9b5aed4f8f924bf4a682cd8548e794be9abe254de895c2455f1e6f2","observation_id":"4ccf9be1-d5f6-4c91-b62b-10a16d64581e","resolution":{"observed_at":"2026-07-08T11:34:50.930740Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-08T11:34:50.945196Z","title":null,"venue":null,"work_id":"f1defff2-2fa3-47d4-9faa-d3335ec9ea53","year":2022},"citing_paper":{"arxiv_id":"2607.06277","last_updated":"2026-07-07T13:43:26Z","snapshot_observed_at":"2026-08-10T02:03:51.312030Z","submitted_at":"2026-07-07T13:43:26Z","title":"Geometric transformation theorem, fundamental groups and monotone of numbers of almost Euclidean factors of geodesic balls","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-07-08T11:34:31.099595Z"},"links":{"citing_paper":"/paper/2607.06277"},"observation_digest":"sha256:61759701fc166e4d650f0382250ebae3f7766ab104e842c22ba77c2ca9d212fa","observation_id":"3c6f4dc5-fc84-487d-80ca-1ef6285ed8c1","resolution":{"observed_at":"2026-07-08T11:34:50.946204Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1808.02329","last_updated":"2018-09-11T00:33:35Z","snapshot_observed_at":"2026-07-06T06:54:28.175614Z","submitted_at":"2018-08-07T12:52:57Z","title":"Ricci curvature and isometric actions with scaling nonvanishing property","version":3},"cited_work":{"arxiv_id":"1808.02329","doi":null,"metadata_source":"pith","pith_arxiv_id":"1808.02329","snapshot_observed_at":"2026-07-08T11:34:50.892249Z","title":"Ricci curvature and isometric actions with scaling nonvanishing property","venue":"math.DG","work_id":"3d599bc5-9927-4d33-b7c3-3dd6459b86a1","year":2018},"citing_paper":{"arxiv_id":"2607.06277","last_updated":"2026-07-07T13:43:26Z","snapshot_observed_at":"2026-08-10T02:03:51.312030Z","submitted_at":"2026-07-07T13:43:26Z","title":"Geometric transformation theorem, fundamental groups and monotone of numbers of almost Euclidean factors of geodesic balls","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-07-08T11:34:31.099595Z"},"links":{"cited_paper":"/paper/1808.02329","citing_paper":"/paper/2607.06277"},"observation_digest":"sha256:5772a15be7df0949590b5ce89864b6e5e456a378ffe8c73257e4a0f0b15795c3","observation_id":"29d3f786-8a68-4692-85cc-a23a5ebdc374","resolution":{"observed_at":"2026-07-08T11:34:50.896433Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-08T11:34:50.927663Z","title":null,"venue":null,"work_id":"729926f4-463d-40b8-adfc-e3e8fc8e66ed","year":1999},"citing_paper":{"arxiv_id":"2607.06277","last_updated":"2026-07-07T13:43:26Z","snapshot_observed_at":"2026-08-10T02:03:51.312030Z","submitted_at":"2026-07-07T13:43:26Z","title":"Geometric transformation theorem, fundamental groups and monotone of numbers of almost Euclidean factors of geodesic balls","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-07-08T11:34:31.099595Z"},"links":{"citing_paper":"/paper/2607.06277"},"observation_digest":"sha256:d58b809bd1dec4f3803d38f9769d28cdabac680fed1add2f5e82305cea894c60","observation_id":"448ad640-2c0c-4f7b-8b14-acc3d7c92776","resolution":{"observed_at":"2026-07-08T11:34:50.928907Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-08T11:34:50.941630Z","title":null,"venue":null,"work_id":"ffafe280-7026-49b9-a789-6866e88c6c46","year":2000},"citing_paper":{"arxiv_id":"2607.06277","last_updated":"2026-07-07T13:43:26Z","snapshot_observed_at":"2026-08-10T02:03:51.312030Z","submitted_at":"2026-07-07T13:43:26Z","title":"Geometric transformation theorem, fundamental groups and monotone of numbers of almost Euclidean factors of geodesic balls","version":1},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-07-08T11:34:31.099595Z"},"links":{"citing_paper":"/paper/2607.06277"},"observation_digest":"sha256:d56f2ef0a48d0bb3ce9498c21bf11a335f2f81ab6c79df94c3e0c48aa7aa13a8","observation_id":"e7c2142f-a3f4-4b21-a534-6493e741517e","resolution":{"observed_at":"2026-07-08T11:34:50.942672Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2607.06277","last_updated":"2026-07-07T13:43:26Z","latest_version":1,"primary_category":"math.DG","snapshot_observed_at":"2026-08-10T02:03:51.312030Z","submitted_at":"2026-07-07T13:43:26Z","title":"Geometric transformation theorem, fundamental groups and monotone of numbers of almost Euclidean factors of geodesic balls"},"reference_resolution":{"displayed":28,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":10,"verified_exact":5,"verified_fuzzy":13},"total_outbound_references":28},"refusal":"A citation records a reference. It does not transfer a finding from one paper to another.","schema":"pith.paper-citation-record.v1","standing_sources":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"thesis":"As of 10 August 2026, this Paper Citation Record lists 28 of 28 outbound references and 0 inbound Pith citation observations for arXiv:2607.06277."}