{"as_of":"2026-08-09T00:16:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:841f4e0f30b6a1c8b6b788c1b1356f9b19ee46d4420a2076cbfea5bf036b61aa","coverage":[{"denominator":51,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":51,"source":"paper_references, paper_reference_links","source_observed_at":"2026-05-20T17:14:13.016586Z","state":"measured"},{"denominator":52,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":52,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-08T06:32:00.761636+00:00","state":"measured"},{"denominator":1,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":1,"source":"paper_references, paper_reference_links","source_observed_at":"2026-07-30T19:49:15.308488Z","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":[{"citation":{"cited_paper":{"arxiv_id":"2605.15748","last_updated":"2026-05-15T09:06:31Z","snapshot_observed_at":"2026-08-07T03:34:48.573400Z","submitted_at":"2026-05-15T09:06:31Z","title":"Quantitative stability for fractional Hardy inequalities: Rearrangement-free techniques and Emden-Fowler analysis","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2605.15748","snapshot_observed_at":"2026-07-30T19:49:15.308488Z","title":"Quantitative stability for fractional Hardy inequalities: Rearrangement-free techniques and Emden-Fowler analysis","venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2607.26830","last_updated":"2026-07-29T12:21:52Z","snapshot_observed_at":"2026-08-06T16:54:41.223324Z","submitted_at":"2026-07-29T12:21:52Z","title":"Galerkin Approximation of the Fractional Hardy Constant","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-07-30T19:49:15.308488Z"},"links":{"cited_paper":"/paper/2605.15748","citing_paper":"/paper/2607.26830"},"observation_digest":"sha256:4a3d31ab192cbc270bc8552fa5747ba805b5c6885d4377caf7d6debf381ce732","observation_id":"10ce30d5-e020-475e-9e57-7b52b3fae6d9","resolution":{"observed_at":"2026-07-30T19:49:15.308488Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"links":{"evidence":"/evidence","html":"/paper/2605.15748/citation-record","integrity":"/paper/2605.15748/integrity","json":"/paper/2605.15748/citation-record.json","paper":"/paper/2605.15748"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Chaudhuri, and M","venue":null,"work_id":"8383f9fd-fa7c-44ea-8ceb-66646ecaa74e","year":2002},"citing_paper":{"arxiv_id":"2605.15748","last_updated":"2026-05-15T09:06:31Z","snapshot_observed_at":"2026-08-07T03:34:48.573400Z","submitted_at":"2026-05-15T09:06:31Z","title":"Quantitative stability for fractional Hardy inequalities: Rearrangement-free techniques and Emden-Fowler analysis","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-05-20T17:14:13.016586Z"},"links":{"citing_paper":"/paper/2605.15748"},"observation_digest":"sha256:776b1dca1325102e99b48484a36e4643db74f66b0c21609f0106071b1145f23d","observation_id":"ebc28644-7826-4a97-b706-c15a82584bf9","resolution":{"observed_at":"2026-05-20T17:18:48.075645Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-06-05T21:23:00.469572Z","title":"Jana, and P","venue":null,"work_id":"8dd0236d-0c6c-405f-a89b-76ea55e85bc4","year":2026},"citing_paper":{"arxiv_id":"2605.15748","last_updated":"2026-05-15T09:06:31Z","snapshot_observed_at":"2026-08-07T03:34:48.573400Z","submitted_at":"2026-05-15T09:06:31Z","title":"Quantitative stability for fractional Hardy inequalities: Rearrangement-free techniques and Emden-Fowler analysis","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-05-20T17:14:13.016586Z"},"links":{"citing_paper":"/paper/2605.15748"},"observation_digest":"sha256:6e8b96ede1826a9604ab87000c99de5934c812ce46620c9f442698d4e50cb79e","observation_id":"39601bb7-0d2f-46cb-ba42-94a733613936","resolution":{"observed_at":"2026-05-20T17:18:48.031448Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-06-05T21:23:00.469572Z","title":"Roy, and V","venue":null,"work_id":"2291e242-d291-4943-8efc-aced9775b1b5","year":2026},"citing_paper":{"arxiv_id":"2605.15748","last_updated":"2026-05-15T09:06:31Z","snapshot_observed_at":"2026-08-07T03:34:48.573400Z","submitted_at":"2026-05-15T09:06:31Z","title":"Quantitative stability for fractional Hardy inequalities: Rearrangement-free techniques and Emden-Fowler analysis","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-05-20T17:14:13.016586Z"},"links":{"citing_paper":"/paper/2605.15748"},"observation_digest":"sha256:ab4b85320e2241373c8ec0ba72afc1e16633d5e321d1b667645591ff44ecaf30","observation_id":"667bbd7a-40dc-4873-86cd-a69ce6eb445c","resolution":{"observed_at":"2026-05-20T17:18:48.058236Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-06-05T21:23:00.469572Z","title":"Roy, and V","venue":null,"work_id":"5ab5ae01-be74-419d-8956-0a87b8ebacae","year":2026},"citing_paper":{"arxiv_id":"2605.15748","last_updated":"2026-05-15T09:06:31Z","snapshot_observed_at":"2026-08-07T03:34:48.573400Z","submitted_at":"2026-05-15T09:06:31Z","title":"Quantitative stability for fractional Hardy inequalities: Rearrangement-free techniques and Emden-Fowler analysis","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-05-20T17:14:13.016586Z"},"links":{"citing_paper":"/paper/2605.15748"},"observation_digest":"sha256:94265e0e01e378cfe16ba7f88a696f87387e3ac097da6129a0eff081eb7c33f3","observation_id":"236e14de-0453-4af4-b4b3-890e9aa518bd","resolution":{"observed_at":"2026-05-20T17:18:48.078956Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-06-05T21:23:00.469572Z","title":"Roy, and V","venue":null,"work_id":"c51a5181-d932-4e6a-bb29-6db16e4a91ab","year":2025},"citing_paper":{"arxiv_id":"2605.15748","last_updated":"2026-05-15T09:06:31Z","snapshot_observed_at":"2026-08-07T03:34:48.573400Z","submitted_at":"2026-05-15T09:06:31Z","title":"Quantitative stability for fractional Hardy inequalities: Rearrangement-free techniques and Emden-Fowler analysis","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-05-20T17:14:13.016586Z"},"links":{"citing_paper":"/paper/2605.15748"},"observation_digest":"sha256:7bb6538ce2555670e0fdbd34b2d71b01dcdebf1581d6c86ae556f19975354ee9","observation_id":"b36c5d87-91f9-4f4c-ba58-510efc2881fe","resolution":{"observed_at":"2026-05-20T17:18:48.034463Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-06-05T21:23:00.469572Z","title":"Akutagawa and H","venue":null,"work_id":"c8674b5b-b800-4706-9601-236254540481","year":2013},"citing_paper":{"arxiv_id":"2605.15748","last_updated":"2026-05-15T09:06:31Z","snapshot_observed_at":"2026-08-07T03:34:48.573400Z","submitted_at":"2026-05-15T09:06:31Z","title":"Quantitative stability for fractional Hardy inequalities: Rearrangement-free techniques and Emden-Fowler analysis","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-05-20T17:14:13.016586Z"},"links":{"citing_paper":"/paper/2605.15748"},"observation_digest":"sha256:64c5dcc46238e8687b51c577a2507492181fa8cc63040a765e382c04b88cdb0a","observation_id":"7e6caaa1-9371-4585-958e-677f2a83c754","resolution":{"observed_at":"2026-05-20T17:18:48.044753Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"b4d6914d-fc15-4496-a959-d73dce4cf809","year":2022},"citing_paper":{"arxiv_id":"2605.15748","last_updated":"2026-05-15T09:06:31Z","snapshot_observed_at":"2026-08-07T03:34:48.573400Z","submitted_at":"2026-05-15T09:06:31Z","title":"Quantitative stability for fractional Hardy inequalities: Rearrangement-free techniques and Emden-Fowler analysis","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-05-20T17:14:13.016586Z"},"links":{"citing_paper":"/paper/2605.15748"},"observation_digest":"sha256:bca0387e118dbd9e648bbe06dc6cc7101d316bbab1c9c1707727d77bc3f6f05a","observation_id":"1c271a34-2f39-49dc-8c2e-39f8dbb4d27a","resolution":{"observed_at":"2026-05-20T17:18:48.062299Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"45be9b2d-7811-4163-b993-feffc621ee2a","year":2022},"citing_paper":{"arxiv_id":"2605.15748","last_updated":"2026-05-15T09:06:31Z","snapshot_observed_at":"2026-08-07T03:34:48.573400Z","submitted_at":"2026-05-15T09:06:31Z","title":"Quantitative stability for fractional Hardy inequalities: Rearrangement-free techniques and Emden-Fowler analysis","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-05-20T17:14:13.016586Z"},"links":{"citing_paper":"/paper/2605.15748"},"observation_digest":"sha256:ed0190220faf4a10895a0e0be48c7be3fd8dd5c3266858a07581f0dc522af67a","observation_id":"07362f5c-f4f4-425b-a119-b2c834d585cb","resolution":{"observed_at":"2026-05-20T17:18:48.048081Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-06-05T21:23:00.469572Z","title":"Berchio, D","venue":null,"work_id":"1928c36e-566f-4c71-ac0b-f203b665d634","year":2017},"citing_paper":{"arxiv_id":"2605.15748","last_updated":"2026-05-15T09:06:31Z","snapshot_observed_at":"2026-08-07T03:34:48.573400Z","submitted_at":"2026-05-15T09:06:31Z","title":"Quantitative stability for fractional Hardy inequalities: Rearrangement-free techniques and Emden-Fowler analysis","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-05-20T17:14:13.016586Z"},"links":{"citing_paper":"/paper/2605.15748"},"observation_digest":"sha256:3cd05663780308009de03374fa373ada444de4cf0c0b41d1c85659063ff1baec","observation_id":"fcb56ebd-eeae-4212-a063-e8fafa6fc99c","resolution":{"observed_at":"2026-05-20T17:18:48.024917Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-06-05T21:23:00.469572Z","title":"Berchio, D","venue":null,"work_id":"cd8184c8-e523-405d-bcdf-0254ee6bddee","year":2020},"citing_paper":{"arxiv_id":"2605.15748","last_updated":"2026-05-15T09:06:31Z","snapshot_observed_at":"2026-08-07T03:34:48.573400Z","submitted_at":"2026-05-15T09:06:31Z","title":"Quantitative stability for fractional Hardy inequalities: Rearrangement-free techniques and Emden-Fowler analysis","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-05-20T17:14:13.016586Z"},"links":{"citing_paper":"/paper/2605.15748"},"observation_digest":"sha256:317a8a787f3f4d757aedd9ecce04fde6c3f6acede3377543a499f9aeb57fec98","observation_id":"6dab50f0-ab07-4faf-a70c-2c459f027352","resolution":{"observed_at":"2026-05-20T17:18:48.051460Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-06-05T21:23:00.469572Z","title":"Bianchi, L","venue":null,"work_id":"b2ef5e79-9d8b-4532-b0d6-be6ec9419fd3","year":2024},"citing_paper":{"arxiv_id":"2605.15748","last_updated":"2026-05-15T09:06:31Z","snapshot_observed_at":"2026-08-07T03:34:48.573400Z","submitted_at":"2026-05-15T09:06:31Z","title":"Quantitative stability for fractional Hardy inequalities: Rearrangement-free techniques and Emden-Fowler analysis","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-05-20T17:14:13.016586Z"},"links":{"citing_paper":"/paper/2605.15748"},"observation_digest":"sha256:8f173f77d11b42f3726493f9b2efd3a5e6de37c1b7cbb3550bf6a344235214f2","observation_id":"4b9d4279-09a9-41b9-994a-0c1fff0cce83","resolution":{"observed_at":"2026-05-20T17:18:48.028298Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-06-05T21:23:00.469572Z","title":"Bianchi, L","venue":null,"work_id":"6c09729d-ae94-4b32-b2e1-4381547ccc21","year":2024},"citing_paper":{"arxiv_id":"2605.15748","last_updated":"2026-05-15T09:06:31Z","snapshot_observed_at":"2026-08-07T03:34:48.573400Z","submitted_at":"2026-05-15T09:06:31Z","title":"Quantitative stability for fractional Hardy inequalities: Rearrangement-free techniques and Emden-Fowler analysis","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-05-20T17:14:13.016586Z"},"links":{"citing_paper":"/paper/2605.15748"},"observation_digest":"sha256:b80a7300905e8d12fb8a6acb510a1a5822d57ee5a3af2ecf62ed364c80b98347","observation_id":"b28a947b-6dcc-4cd2-b92f-920df1e27c76","resolution":{"observed_at":"2026-05-20T17:18:48.054709Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-06-05T21:23:00.469572Z","title":"Bianchi, G","venue":null,"work_id":"939c4fc7-929a-4057-b87a-cbb2229430d8","year":2026},"citing_paper":{"arxiv_id":"2605.15748","last_updated":"2026-05-15T09:06:31Z","snapshot_observed_at":"2026-08-07T03:34:48.573400Z","submitted_at":"2026-05-15T09:06:31Z","title":"Quantitative stability for fractional Hardy inequalities: Rearrangement-free techniques and Emden-Fowler analysis","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-05-20T17:14:13.016586Z"},"links":{"citing_paper":"/paper/2605.15748"},"observation_digest":"sha256:fff4781ad28398c2cce5d7b690bb5454636251265ae116aa37d1a6d93008f6fe","observation_id":"c8963c63-1848-4c61-890e-5d03d723ecde","resolution":{"observed_at":"2026-05-20T17:18:48.065618Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-06-05T21:23:00.469572Z","title":"Bogdan and B","venue":null,"work_id":"f6529d7a-72f8-4a60-a660-f6ce15ef4248","year":2011},"citing_paper":{"arxiv_id":"2605.15748","last_updated":"2026-05-15T09:06:31Z","snapshot_observed_at":"2026-08-07T03:34:48.573400Z","submitted_at":"2026-05-15T09:06:31Z","title":"Quantitative stability for fractional Hardy inequalities: Rearrangement-free techniques and Emden-Fowler analysis","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-05-20T17:14:13.016586Z"},"links":{"citing_paper":"/paper/2605.15748"},"observation_digest":"sha256:51a7a67cd54713ce8d2bb944235b379bf5b2f43f19995b6f40f17513537e7c79","observation_id":"5bf902f8-207e-4f70-b2a6-51c8907aa763","resolution":{"observed_at":"2026-05-20T17:18:48.068982Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-06-05T21:23:00.469572Z","title":"Bogdan, T","venue":null,"work_id":"921b2566-acbc-497a-8892-d28c58d32635","year":2022},"citing_paper":{"arxiv_id":"2605.15748","last_updated":"2026-05-15T09:06:31Z","snapshot_observed_at":"2026-08-07T03:34:48.573400Z","submitted_at":"2026-05-15T09:06:31Z","title":"Quantitative stability for fractional Hardy inequalities: Rearrangement-free techniques and Emden-Fowler analysis","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-05-20T17:14:13.016586Z"},"links":{"citing_paper":"/paper/2605.15748"},"observation_digest":"sha256:7942b55caea9b41f41d8e651656cc45fa07d2b263b9e7c26b0b0d19512725069","observation_id":"48651ada-81a4-4554-9a02-3bfdbd9207e9","resolution":{"observed_at":"2026-05-20T17:18:48.041476Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-06-05T21:23:00.469572Z","title":"Brasco and E","venue":null,"work_id":"a734e13e-9f91-4fd1-bc94-33a81fa5a019","year":2018},"citing_paper":{"arxiv_id":"2605.15748","last_updated":"2026-05-15T09:06:31Z","snapshot_observed_at":"2026-08-07T03:34:48.573400Z","submitted_at":"2026-05-15T09:06:31Z","title":"Quantitative stability for fractional Hardy inequalities: Rearrangement-free techniques and Emden-Fowler analysis","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-05-20T17:14:13.016586Z"},"links":{"citing_paper":"/paper/2605.15748"},"observation_digest":"sha256:f6b12c43f8c2d0d31bdbcfbe77cce511d462d3bf0a1a707bfc32957aa19b36e0","observation_id":"345afbde-1617-404a-b5a3-45699793a869","resolution":{"observed_at":"2026-05-20T17:18:48.037672Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-06-05T21:23:00.469572Z","title":"Carron,In´ egalit´ es de Hardy sur les vari´ et´ es riemanniennes non-compactes, J","venue":null,"work_id":"443400f2-da67-48ff-a997-65e08af51ce5","year":1997},"citing_paper":{"arxiv_id":"2605.15748","last_updated":"2026-05-15T09:06:31Z","snapshot_observed_at":"2026-08-07T03:34:48.573400Z","submitted_at":"2026-05-15T09:06:31Z","title":"Quantitative stability for fractional Hardy inequalities: Rearrangement-free techniques and Emden-Fowler analysis","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-05-20T17:14:13.016586Z"},"links":{"citing_paper":"/paper/2605.15748"},"observation_digest":"sha256:b76781963709f0996e29d3b08b00b3eb41ab03cdda22951661f083a60dcd4e0b","observation_id":"ab05babb-ed66-4b3d-a87b-da52f37b46d1","resolution":{"observed_at":"2026-05-20T17:18:48.082483Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"79c752e9-4fbb-4d44-a6fa-fe8e8d6246be","year":2023},"citing_paper":{"arxiv_id":"2605.15748","last_updated":"2026-05-15T09:06:31Z","snapshot_observed_at":"2026-08-07T03:34:48.573400Z","submitted_at":"2026-05-15T09:06:31Z","title":"Quantitative stability for fractional Hardy inequalities: Rearrangement-free techniques and Emden-Fowler analysis","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-05-20T17:14:13.016586Z"},"links":{"citing_paper":"/paper/2605.15748"},"observation_digest":"sha256:4505e90d7bdbb0b716cacf2951ab4bd540d10adfdae92e7963d2ace9d538fd09","observation_id":"9c4efc7e-a6f2-45db-a188-8a03049e0794","resolution":{"observed_at":"2026-05-20T17:18:48.071974Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"3787ba8d-b169-4568-bacf-82be1754e635","year":2024},"citing_paper":{"arxiv_id":"2605.15748","last_updated":"2026-05-15T09:06:31Z","snapshot_observed_at":"2026-08-07T03:34:48.573400Z","submitted_at":"2026-05-15T09:06:31Z","title":"Quantitative stability for fractional Hardy inequalities: Rearrangement-free techniques and Emden-Fowler analysis","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-05-20T17:14:13.016586Z"},"links":{"citing_paper":"/paper/2605.15748"},"observation_digest":"sha256:80679c6dfde9f8600de8059aa05bec4ff1d47ef340220ee086283b8566519093","observation_id":"38e22057-6bf6-4963-afab-24b5e48797d4","resolution":{"observed_at":"2026-05-20T17:18:48.234550Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"3cdb6a2f-7fe9-4685-9a13-0d74391ab399","year":2026},"citing_paper":{"arxiv_id":"2605.15748","last_updated":"2026-05-15T09:06:31Z","snapshot_observed_at":"2026-08-07T03:34:48.573400Z","submitted_at":"2026-05-15T09:06:31Z","title":"Quantitative stability for fractional Hardy inequalities: Rearrangement-free techniques and Emden-Fowler analysis","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-05-20T17:14:13.016586Z"},"links":{"citing_paper":"/paper/2605.15748"},"observation_digest":"sha256:95e20f291f2bc81273c7dbd7f0fe4a254f4f34342b6de0cab67a989ed3ca7740","observation_id":"8d22fc3b-6612-4408-87ff-9841bc624e8f","resolution":{"observed_at":"2026-05-20T17:18:48.140273Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-06-05T21:23:00.469572Z","title":"Chen and R","venue":null,"work_id":"9312bb53-26b8-41b5-9cf4-c7d5639a7edd","year":2003},"citing_paper":{"arxiv_id":"2605.15748","last_updated":"2026-05-15T09:06:31Z","snapshot_observed_at":"2026-08-07T03:34:48.573400Z","submitted_at":"2026-05-15T09:06:31Z","title":"Quantitative stability for fractional Hardy inequalities: Rearrangement-free techniques and Emden-Fowler analysis","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-05-20T17:14:13.016586Z"},"links":{"citing_paper":"/paper/2605.15748"},"observation_digest":"sha256:e7778ae21ca3223ea1928e70b55048b99b22fd37676a75ef6ce7fdde08940d77","observation_id":"b68fcf37-8793-496e-99be-427d45048d5d","resolution":{"observed_at":"2026-05-20T17:18:48.136331Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-06-05T21:23:00.469572Z","title":"Cianchi and A","venue":null,"work_id":"a51c1335-4933-4d41-9b07-4a1108398c38","year":2008},"citing_paper":{"arxiv_id":"2605.15748","last_updated":"2026-05-15T09:06:31Z","snapshot_observed_at":"2026-08-07T03:34:48.573400Z","submitted_at":"2026-05-15T09:06:31Z","title":"Quantitative stability for fractional Hardy inequalities: Rearrangement-free techniques and Emden-Fowler analysis","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-05-20T17:14:13.016586Z"},"links":{"citing_paper":"/paper/2605.15748"},"observation_digest":"sha256:aecd4c3d4a4debb8783d94621f115db0a3aaca52f8ad2a957d5288420c34f286","observation_id":"6d05094d-6d0a-4e85-8250-ce38efd89aa1","resolution":{"observed_at":"2026-05-20T17:18:48.128949Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-06-05T21:23:00.469572Z","title":"Cinti and F","venue":null,"work_id":"e8d2e11e-cbd5-4907-be1d-6108187fb2b7","year":2024},"citing_paper":{"arxiv_id":"2605.15748","last_updated":"2026-05-15T09:06:31Z","snapshot_observed_at":"2026-08-07T03:34:48.573400Z","submitted_at":"2026-05-15T09:06:31Z","title":"Quantitative stability for fractional Hardy inequalities: Rearrangement-free techniques and Emden-Fowler analysis","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-05-20T17:14:13.016586Z"},"links":{"citing_paper":"/paper/2605.15748"},"observation_digest":"sha256:789fd7eb29ddf28ba14edb24eae963690f5872a874bea8fd9f34032c5430825d","observation_id":"9e3971ac-2af6-4e48-916d-b16b69584667","resolution":{"observed_at":"2026-05-20T17:18:48.121378Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-06-05T21:23:00.469572Z","title":"Csat´ o and P","venue":null,"work_id":"0b0fa1dc-ed37-4935-b750-7a26c3846a69","year":2026},"citing_paper":{"arxiv_id":"2605.15748","last_updated":"2026-05-15T09:06:31Z","snapshot_observed_at":"2026-08-07T03:34:48.573400Z","submitted_at":"2026-05-15T09:06:31Z","title":"Quantitative stability for fractional Hardy inequalities: Rearrangement-free techniques and Emden-Fowler analysis","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-05-20T17:14:13.016586Z"},"links":{"citing_paper":"/paper/2605.15748"},"observation_digest":"sha256:65b83f6d9f02746ac06a931e16212f8795d6b650213d51a14b44f1d5a5e17edf","observation_id":"ad847def-43d9-403c-a97e-f44b4a780fcf","resolution":{"observed_at":"2026-05-20T17:18:48.117333Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-06-05T21:23:00.469572Z","title":"De Nitti, F","venue":null,"work_id":"e99e2047-17f5-4f2f-956b-8fac4e0d81f6","year":2025},"citing_paper":{"arxiv_id":"2605.15748","last_updated":"2026-05-15T09:06:31Z","snapshot_observed_at":"2026-08-07T03:34:48.573400Z","submitted_at":"2026-05-15T09:06:31Z","title":"Quantitative stability for fractional Hardy inequalities: Rearrangement-free techniques and Emden-Fowler analysis","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-05-20T17:14:13.016586Z"},"links":{"citing_paper":"/paper/2605.15748"},"observation_digest":"sha256:7fa6266ffc011697ef86d2282a4d19a3132432d312b9787dfd1fa84b6d83595c","observation_id":"3500b041-b164-4a2b-902e-fbe624c7f1db","resolution":{"observed_at":"2026-05-20T17:18:48.113433Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-06-05T21:23:00.469572Z","title":"Di Nezza, G","venue":null,"work_id":"6408cd6c-89b9-40f2-9db7-018e528aa5a7","year":2012},"citing_paper":{"arxiv_id":"2605.15748","last_updated":"2026-05-15T09:06:31Z","snapshot_observed_at":"2026-08-07T03:34:48.573400Z","submitted_at":"2026-05-15T09:06:31Z","title":"Quantitative stability for fractional Hardy inequalities: Rearrangement-free techniques and Emden-Fowler analysis","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-05-20T17:14:13.016586Z"},"links":{"citing_paper":"/paper/2605.15748"},"observation_digest":"sha256:3b15a74c11862f1bab7738cb2c482388cbbccc68a84d97d69dfb6e6fa0f61bad","observation_id":"267d6a66-9a6e-427d-af65-700ce71addeb","resolution":{"observed_at":"2026-05-20T17:18:48.124891Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2410.21039","last_updated":"2025-04-24T23:28:08Z","snapshot_observed_at":"2026-07-06T19:40:48.425432Z","submitted_at":"2024-10-28T13:57:22Z","title":"Scale-Dependent Poincar\\'{e} inequalities, log-Sobolev inequality and the stability of the Heisenberg Uncertainty Principle on the hyperbolic space","version":4},"cited_work":{"arxiv_id":"2410.21039","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2410.21039","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"3fcd285b-d69c-45a6-983e-098d882aa812","year":2024},"citing_paper":{"arxiv_id":"2605.15748","last_updated":"2026-05-15T09:06:31Z","snapshot_observed_at":"2026-08-07T03:34:48.573400Z","submitted_at":"2026-05-15T09:06:31Z","title":"Quantitative stability for fractional Hardy inequalities: Rearrangement-free techniques and Emden-Fowler analysis","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-05-20T17:14:13.016586Z"},"links":{"cited_paper":"/paper/2410.21039","citing_paper":"/paper/2605.15748"},"observation_digest":"sha256:c623897b6bd3626aeff8179971d553157e550cab53a85bb28501a4fdf77ff56e","observation_id":"d48b11da-cb7b-41a5-94f0-4192c8665b7b","resolution":{"observed_at":"2026-05-20T17:18:47.470634Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"3e813eb5-0d14-4a87-9308-77d1e91dcea5","year":2026},"citing_paper":{"arxiv_id":"2605.15748","last_updated":"2026-05-15T09:06:31Z","snapshot_observed_at":"2026-08-07T03:34:48.573400Z","submitted_at":"2026-05-15T09:06:31Z","title":"Quantitative stability for fractional Hardy inequalities: Rearrangement-free techniques and Emden-Fowler analysis","version":1},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-05-20T17:14:13.016586Z"},"links":{"citing_paper":"/paper/2605.15748"},"observation_digest":"sha256:4732d9fc8c83e7d3c5a8f64fd1873507bcc924129f104c87dee5e636e90305e9","observation_id":"e21703b1-5ed1-4a22-b595-4b2dc102a2cc","resolution":{"observed_at":"2026-05-20T17:18:48.109580Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-06-05T21:23:00.469572Z","title":"Dyda,A fractional order Hardy inequality, Illinois J","venue":null,"work_id":"282027c9-b425-4e0b-83b6-c2f0c8f320d7","year":2004},"citing_paper":{"arxiv_id":"2605.15748","last_updated":"2026-05-15T09:06:31Z","snapshot_observed_at":"2026-08-07T03:34:48.573400Z","submitted_at":"2026-05-15T09:06:31Z","title":"Quantitative stability for fractional Hardy inequalities: Rearrangement-free techniques and Emden-Fowler analysis","version":1},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-05-20T17:14:13.016586Z"},"links":{"citing_paper":"/paper/2605.15748"},"observation_digest":"sha256:933976be8d5f73d75cfba92d0c452d596f9e88d789a21f6a5c9a21ccecf4fffa","observation_id":"46b37f14-810f-43c7-9ddd-ebcc0972f9cf","resolution":{"observed_at":"2026-05-20T17:18:48.105185Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-06-05T21:23:00.469572Z","title":"Dyda and M","venue":null,"work_id":"7fca7fbe-cd1e-454d-bf00-0228a114b963","year":2024},"citing_paper":{"arxiv_id":"2605.15748","last_updated":"2026-05-15T09:06:31Z","snapshot_observed_at":"2026-08-07T03:34:48.573400Z","submitted_at":"2026-05-15T09:06:31Z","title":"Quantitative stability for fractional Hardy inequalities: Rearrangement-free techniques and Emden-Fowler analysis","version":1},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-05-20T17:14:13.016586Z"},"links":{"citing_paper":"/paper/2605.15748"},"observation_digest":"sha256:5cc1a2879a2be0d84897bd4c55891c8561e235f52c5bbf306890d92cce8b60ea","observation_id":"9c9a4d74-055a-4889-9947-1db297e544c1","resolution":{"observed_at":"2026-05-20T17:18:48.097982Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-06-05T21:23:00.469572Z","title":"Dyda and M","venue":null,"work_id":"8b0bf4ec-ccb4-413d-a3b1-b876672e9d3f","year":2024},"citing_paper":{"arxiv_id":"2605.15748","last_updated":"2026-05-15T09:06:31Z","snapshot_observed_at":"2026-08-07T03:34:48.573400Z","submitted_at":"2026-05-15T09:06:31Z","title":"Quantitative stability for fractional Hardy inequalities: Rearrangement-free techniques and Emden-Fowler analysis","version":1},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-05-20T17:14:13.016586Z"},"links":{"citing_paper":"/paper/2605.15748"},"observation_digest":"sha256:96c0aa6a4cac1b09b6e0da26c7c166a2764861873632c397392f9913aeb27211","observation_id":"8764b939-ff1c-41ea-ba4e-653a71d36c39","resolution":{"observed_at":"2026-05-20T17:18:48.094788Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"713f14c6-024d-422c-b10c-5eb0cf40811f","year":2023},"citing_paper":{"arxiv_id":"2605.15748","last_updated":"2026-05-15T09:06:31Z","snapshot_observed_at":"2026-08-07T03:34:48.573400Z","submitted_at":"2026-05-15T09:06:31Z","title":"Quantitative stability for fractional Hardy inequalities: Rearrangement-free techniques and Emden-Fowler analysis","version":1},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-05-20T17:14:13.016586Z"},"links":{"citing_paper":"/paper/2605.15748"},"observation_digest":"sha256:9f9d1ef62bbc7a8eb3228e892a6e2aa94896ea9c444fe9ac6db8c46ecbb42ce8","observation_id":"fb0e50a4-d132-4828-b0b7-0400bf387aef","resolution":{"observed_at":"2026-05-20T17:18:48.091340Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"509cbe63-a78d-45d8-997f-26f4fcfddd05","year":2023},"citing_paper":{"arxiv_id":"2605.15748","last_updated":"2026-05-15T09:06:31Z","snapshot_observed_at":"2026-08-07T03:34:48.573400Z","submitted_at":"2026-05-15T09:06:31Z","title":"Quantitative stability for fractional Hardy inequalities: Rearrangement-free techniques and Emden-Fowler analysis","version":1},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-05-20T17:14:13.016586Z"},"links":{"citing_paper":"/paper/2605.15748"},"observation_digest":"sha256:ad0a2b90d40963380868e755002ad7d37a7bf49f6a2e527ba3a05d398e7126f3","observation_id":"d1ffc61f-38b7-42c5-a999-b17ddc20ffc5","resolution":{"observed_at":"2026-05-20T17:18:48.087557Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"1b97434b-bc01-4dad-8aae-e0b2c3e807fd","year":2010},"citing_paper":{"arxiv_id":"2605.15748","last_updated":"2026-05-15T09:06:31Z","snapshot_observed_at":"2026-08-07T03:34:48.573400Z","submitted_at":"2026-05-15T09:06:31Z","title":"Quantitative stability for fractional Hardy inequalities: Rearrangement-free techniques and Emden-Fowler analysis","version":1},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-05-20T17:14:13.016586Z"},"links":{"citing_paper":"/paper/2605.15748"},"observation_digest":"sha256:3330d88794c306b2a04a2cec25a3d2b649be019b62a68fe7aff32902f68f99a9","observation_id":"2850aa0c-dea1-433c-bd5c-d8b2dc99ecd3","resolution":{"observed_at":"2026-05-20T17:18:48.230800Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-06-05T21:23:00.469572Z","title":"Figalli and Y","venue":null,"work_id":"06fb13e4-843d-4183-8637-111483995321","year":2022},"citing_paper":{"arxiv_id":"2605.15748","last_updated":"2026-05-15T09:06:31Z","snapshot_observed_at":"2026-08-07T03:34:48.573400Z","submitted_at":"2026-05-15T09:06:31Z","title":"Quantitative stability for fractional Hardy inequalities: Rearrangement-free techniques and Emden-Fowler analysis","version":1},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-05-20T17:14:13.016586Z"},"links":{"citing_paper":"/paper/2605.15748"},"observation_digest":"sha256:3ea79292db368ad701eafe7f261d122650187779c91b7c3abefabec148549a30","observation_id":"6625f8e3-75b4-43f7-8c88-9ee312dcbbc0","resolution":{"observed_at":"2026-05-20T17:18:48.226246Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-06-05T21:23:00.469572Z","title":"Flynn, N","venue":null,"work_id":"203df910-9a85-4afe-88cf-bc6dcf98c6eb","year":2023},"citing_paper":{"arxiv_id":"2605.15748","last_updated":"2026-05-15T09:06:31Z","snapshot_observed_at":"2026-08-07T03:34:48.573400Z","submitted_at":"2026-05-15T09:06:31Z","title":"Quantitative stability for fractional Hardy inequalities: Rearrangement-free techniques and Emden-Fowler analysis","version":1},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-05-20T17:14:13.016586Z"},"links":{"citing_paper":"/paper/2605.15748"},"observation_digest":"sha256:42a00ae00bca0126e2bc95591ed46d7aaa5d05596c1de16a31e4fa0a33ae2748","observation_id":"e927f52c-e01c-422e-911f-bef84d263b03","resolution":{"observed_at":"2026-05-20T17:18:48.222898Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-06-05T21:23:00.469572Z","title":"1, 259–288","venue":null,"work_id":"b66eb510-53ab-4123-a7f8-cc327304620f","year":1931},"citing_paper":{"arxiv_id":"2605.15748","last_updated":"2026-05-15T09:06:31Z","snapshot_observed_at":"2026-08-07T03:34:48.573400Z","submitted_at":"2026-05-15T09:06:31Z","title":"Quantitative stability for fractional Hardy inequalities: Rearrangement-free techniques and Emden-Fowler analysis","version":1},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-05-20T17:14:13.016586Z"},"links":{"citing_paper":"/paper/2605.15748"},"observation_digest":"sha256:4fa8b5900d6e5b7092bbf40fb85f1fc2520777333d5ad49215e62ff8cbaedeab","observation_id":"840ddfa3-e2be-4e9d-8c4d-f64d9736c6b1","resolution":{"observed_at":"2026-05-20T17:18:48.219401Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"db7e3cd8-6871-4fb4-b921-27eebed46ccc","year":2008},"citing_paper":{"arxiv_id":"2605.15748","last_updated":"2026-05-15T09:06:31Z","snapshot_observed_at":"2026-08-07T03:34:48.573400Z","submitted_at":"2026-05-15T09:06:31Z","title":"Quantitative stability for fractional Hardy inequalities: Rearrangement-free techniques and Emden-Fowler analysis","version":1},"reference_index":38,"source":"pdf_text","source_observed_at":"2026-05-20T17:14:13.016586Z"},"links":{"citing_paper":"/paper/2605.15748"},"observation_digest":"sha256:d6d3cb969636fbaf987779c2b18dd8e4f750db097ba6153088fce532c84d635d","observation_id":"821e8058-11f1-4fac-aa44-9183cb8cd2d0","resolution":{"observed_at":"2026-05-20T17:18:48.216074Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"4e0d9973-6681-45a7-8395-fc381bc2fd25","year":2008},"citing_paper":{"arxiv_id":"2605.15748","last_updated":"2026-05-15T09:06:31Z","snapshot_observed_at":"2026-08-07T03:34:48.573400Z","submitted_at":"2026-05-15T09:06:31Z","title":"Quantitative stability for fractional Hardy inequalities: Rearrangement-free techniques and Emden-Fowler analysis","version":1},"reference_index":39,"source":"pdf_text","source_observed_at":"2026-05-20T17:14:13.016586Z"},"links":{"citing_paper":"/paper/2605.15748"},"observation_digest":"sha256:411c6fce5734dd0732816783f1274592b1920f51dad00632d959e94368ff74f5","observation_id":"e620a083-7529-40e1-9ed1-52eb7081dfb3","resolution":{"observed_at":"2026-05-20T17:18:48.211883Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"298fa488-8fe5-403d-bad9-fb7b951e3d73","year":2010},"citing_paper":{"arxiv_id":"2605.15748","last_updated":"2026-05-15T09:06:31Z","snapshot_observed_at":"2026-08-07T03:34:48.573400Z","submitted_at":"2026-05-15T09:06:31Z","title":"Quantitative stability for fractional Hardy inequalities: Rearrangement-free techniques and Emden-Fowler analysis","version":1},"reference_index":40,"source":"pdf_text","source_observed_at":"2026-05-20T17:14:13.016586Z"},"links":{"citing_paper":"/paper/2605.15748"},"observation_digest":"sha256:413818f800514cde5834490e88bc644db38a8f0f8d6256be6f037b51232f9671","observation_id":"2f3ee799-9f31-4a98-9199-6b3e4968291b","resolution":{"observed_at":"2026-05-20T17:18:48.207517Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"70482491-25f1-4cdc-8f25-e0adbee4c0db","year":2018},"citing_paper":{"arxiv_id":"2605.15748","last_updated":"2026-05-15T09:06:31Z","snapshot_observed_at":"2026-08-07T03:34:48.573400Z","submitted_at":"2026-05-15T09:06:31Z","title":"Quantitative stability for fractional Hardy inequalities: Rearrangement-free techniques and Emden-Fowler analysis","version":1},"reference_index":41,"source":"pdf_text","source_observed_at":"2026-05-20T17:14:13.016586Z"},"links":{"citing_paper":"/paper/2605.15748"},"observation_digest":"sha256:46f042302b01c86d5d796ccd0e988694d2fe004e52145b76b5c9e390a73a78dc","observation_id":"91b1e6b9-4476-4038-8dfc-925d7173a252","resolution":{"observed_at":"2026-05-20T17:18:48.203289Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-06-05T21:23:00.469572Z","title":"Grafakos,Classical Fourier analysis, third ed., Graduate Texts in Mathematics, vol","venue":null,"work_id":"69bc7d81-b404-4fe5-83af-9c08da8dedb8","year":2014},"citing_paper":{"arxiv_id":"2605.15748","last_updated":"2026-05-15T09:06:31Z","snapshot_observed_at":"2026-08-07T03:34:48.573400Z","submitted_at":"2026-05-15T09:06:31Z","title":"Quantitative stability for fractional Hardy inequalities: Rearrangement-free techniques and Emden-Fowler analysis","version":1},"reference_index":42,"source":"pdf_text","source_observed_at":"2026-05-20T17:14:13.016586Z"},"links":{"citing_paper":"/paper/2605.15748"},"observation_digest":"sha256:1bf8b75967d012639c6801b74362a2e225b04fb6c467f98cd58cf4a545a47640","observation_id":"38ee495e-bcd8-4859-a339-4cf68d76d950","resolution":{"observed_at":"2026-05-20T17:18:48.197572Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-06-05T21:23:00.469572Z","title":"H¨ ormander,The analysis of linear partial differential operators","venue":null,"work_id":"d4ef7c53-22af-4279-928c-35ef585b1a8f","year":2007},"citing_paper":{"arxiv_id":"2605.15748","last_updated":"2026-05-15T09:06:31Z","snapshot_observed_at":"2026-08-07T03:34:48.573400Z","submitted_at":"2026-05-15T09:06:31Z","title":"Quantitative stability for fractional Hardy inequalities: Rearrangement-free techniques and Emden-Fowler analysis","version":1},"reference_index":43,"source":"pdf_text","source_observed_at":"2026-05-20T17:14:13.016586Z"},"links":{"citing_paper":"/paper/2605.15748"},"observation_digest":"sha256:a98b5788fc04bc02b696f632840ac50002640dfd51446182849fd13aad6c76e6","observation_id":"3992c1d1-66fc-455c-9c7b-d66e6b1ff4c4","resolution":{"observed_at":"2026-05-20T17:18:48.176364Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-06-05T21:23:00.469572Z","title":"Ihnatsyeva, K","venue":null,"work_id":"a5cba339-d4cb-428d-8b0e-82372ac96e36","year":2025},"citing_paper":{"arxiv_id":"2605.15748","last_updated":"2026-05-15T09:06:31Z","snapshot_observed_at":"2026-08-07T03:34:48.573400Z","submitted_at":"2026-05-15T09:06:31Z","title":"Quantitative stability for fractional Hardy inequalities: Rearrangement-free techniques and Emden-Fowler analysis","version":1},"reference_index":44,"source":"pdf_text","source_observed_at":"2026-05-20T17:14:13.016586Z"},"links":{"citing_paper":"/paper/2605.15748"},"observation_digest":"sha256:e78c1aa775c8aabf60908ecaebc422c2d4d57d2acc0b676c7349987b652e4081","observation_id":"342d4241-28dc-4c0b-8cea-cb9caa35d078","resolution":{"observed_at":"2026-05-20T17:18:48.172189Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-06-05T21:23:00.469572Z","title":"Kijaczko and V","venue":null,"work_id":"0682dbc7-b6d6-4238-b20a-d9456752a3c6","year":2026},"citing_paper":{"arxiv_id":"2605.15748","last_updated":"2026-05-15T09:06:31Z","snapshot_observed_at":"2026-08-07T03:34:48.573400Z","submitted_at":"2026-05-15T09:06:31Z","title":"Quantitative stability for fractional Hardy inequalities: Rearrangement-free techniques and Emden-Fowler analysis","version":1},"reference_index":45,"source":"pdf_text","source_observed_at":"2026-05-20T17:14:13.016586Z"},"links":{"citing_paper":"/paper/2605.15748"},"observation_digest":"sha256:29f608627870935c86b1e66f8985bf33db38a6c1f637e05dd8b25378575c0917","observation_id":"7b545d22-b7fc-44c1-8706-22adf994de04","resolution":{"observed_at":"2026-05-20T17:18:48.166204Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"1d6682aa-9a80-4e00-a14d-037352abc05d","year":1965},"citing_paper":{"arxiv_id":"2605.15748","last_updated":"2026-05-15T09:06:31Z","snapshot_observed_at":"2026-08-07T03:34:48.573400Z","submitted_at":"2026-05-15T09:06:31Z","title":"Quantitative stability for fractional Hardy inequalities: Rearrangement-free techniques and Emden-Fowler analysis","version":1},"reference_index":46,"source":"pdf_text","source_observed_at":"2026-05-20T17:14:13.016586Z"},"links":{"citing_paper":"/paper/2605.15748"},"observation_digest":"sha256:f642541ac1162ea637c013af5b93e641e991de5e9a2674c93232586187ccb4eb","observation_id":"44345b89-6d57-484f-ac9a-51c0729b5956","resolution":{"observed_at":"2026-05-20T17:18:48.162606Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"3fed271e-6219-4768-b6a3-241371851857","year":2026},"citing_paper":{"arxiv_id":"2605.15748","last_updated":"2026-05-15T09:06:31Z","snapshot_observed_at":"2026-08-07T03:34:48.573400Z","submitted_at":"2026-05-15T09:06:31Z","title":"Quantitative stability for fractional Hardy inequalities: Rearrangement-free techniques and Emden-Fowler analysis","version":1},"reference_index":47,"source":"pdf_text","source_observed_at":"2026-05-20T17:14:13.016586Z"},"links":{"citing_paper":"/paper/2605.15748"},"observation_digest":"sha256:6297254777cc1eeea7960393961a2e62bcc98504de0baa6a1cfd7830dfa9a858","observation_id":"6213d8b8-cf40-46a5-8b9e-7c6cf60511d7","resolution":{"observed_at":"2026-05-20T17:18:48.158088Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-06-05T21:23:00.469572Z","title":"Loss and C","venue":null,"work_id":"2dfdf530-fe95-44af-acde-f4cb4bf91410","year":2010},"citing_paper":{"arxiv_id":"2605.15748","last_updated":"2026-05-15T09:06:31Z","snapshot_observed_at":"2026-08-07T03:34:48.573400Z","submitted_at":"2026-05-15T09:06:31Z","title":"Quantitative stability for fractional Hardy inequalities: Rearrangement-free techniques and Emden-Fowler analysis","version":1},"reference_index":48,"source":"pdf_text","source_observed_at":"2026-05-20T17:14:13.016586Z"},"links":{"citing_paper":"/paper/2605.15748"},"observation_digest":"sha256:080d0fb46c5870936f4bda262e3586fde79fb57ebc83fb35b6d64700f4e3705b","observation_id":"de3a33f8-af89-44ae-9b75-99125dda1967","resolution":{"observed_at":"2026-05-20T17:18:48.154614Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-06-05T21:23:00.469572Z","title":"Mouhot, E","venue":null,"work_id":"4e376a7c-6a9d-47ae-9a05-cd9095da554f","year":2011},"citing_paper":{"arxiv_id":"2605.15748","last_updated":"2026-05-15T09:06:31Z","snapshot_observed_at":"2026-08-07T03:34:48.573400Z","submitted_at":"2026-05-15T09:06:31Z","title":"Quantitative stability for fractional Hardy inequalities: Rearrangement-free techniques and Emden-Fowler analysis","version":1},"reference_index":49,"source":"pdf_text","source_observed_at":"2026-05-20T17:14:13.016586Z"},"links":{"citing_paper":"/paper/2605.15748"},"observation_digest":"sha256:81c89c810c4ff9a622d01439585592771a8a10bf0cd76a5321a7dd4aef7f15bd","observation_id":"e92f501b-1203-4cec-9062-b5edcbe41eaf","resolution":{"observed_at":"2026-05-20T17:18:48.151290Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-06-05T21:23:00.469572Z","title":"Sahu,Weighted fractional Hardy inequalities with singularity on any flat submanifold, J","venue":null,"work_id":"24f7cab4-cccf-49dd-892f-bf136126c239","year":2025},"citing_paper":{"arxiv_id":"2605.15748","last_updated":"2026-05-15T09:06:31Z","snapshot_observed_at":"2026-08-07T03:34:48.573400Z","submitted_at":"2026-05-15T09:06:31Z","title":"Quantitative stability for fractional Hardy inequalities: Rearrangement-free techniques and Emden-Fowler analysis","version":1},"reference_index":50,"source":"pdf_text","source_observed_at":"2026-05-20T17:14:13.016586Z"},"links":{"citing_paper":"/paper/2605.15748"},"observation_digest":"sha256:2f5a88ce609656fd1290bf9e7a3b1579716312a8ffc85cf21d0a623245e8133a","observation_id":"0753a0d2-9d81-4523-a3f1-13c2afdb9fe5","resolution":{"observed_at":"2026-05-20T17:18:48.147892Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"dcc1540d-0c05-4ed0-bbe6-41eb6fa23b9f","year":1993},"citing_paper":{"arxiv_id":"2605.15748","last_updated":"2026-05-15T09:06:31Z","snapshot_observed_at":"2026-08-07T03:34:48.573400Z","submitted_at":"2026-05-15T09:06:31Z","title":"Quantitative stability for fractional Hardy inequalities: Rearrangement-free techniques and Emden-Fowler analysis","version":1},"reference_index":51,"source":"pdf_text","source_observed_at":"2026-05-20T17:14:13.016586Z"},"links":{"citing_paper":"/paper/2605.15748"},"observation_digest":"sha256:9d6870e6f22ccdbf274109d937c5aea0b76b8d9da7140db5c0c0d44d3a1e0d2a","observation_id":"55695aee-3231-449e-8718-f971e2297bd4","resolution":{"observed_at":"2026-05-20T17:18:48.143882Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2605.15748","last_updated":"2026-05-15T09:06:31Z","latest_version":1,"primary_category":"math.AP","snapshot_observed_at":"2026-08-07T03:34:48.573400Z","submitted_at":"2026-05-15T09:06:31Z","title":"Quantitative stability for fractional Hardy inequalities: Rearrangement-free techniques and Emden-Fowler analysis"},"reference_resolution":{"displayed":51,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":16,"verified_exact":1,"verified_fuzzy":34},"total_outbound_references":51},"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":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"thesis":"As of 9 August 2026, this Paper Citation Record lists 51 of 51 outbound references and 1 inbound Pith citation observation for arXiv:2605.15748."}