{"as_of":"2026-08-23T17:01:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:cb6347f7c6c1f186c69e5d9f6db3123fb093a38876c54f5cee7ffd79cd33280f","coverage":[{"denominator":26,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":26,"source":"paper_references, paper_reference_links","source_observed_at":"2026-07-02T02:31:26.995015Z","state":"measured"},{"denominator":26,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":26,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-23T06:30:58.430688+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/2607.01167/citation-record","integrity":"/paper/2607.01167/integrity","json":"/paper/2607.01167/citation-record.json","paper":"/paper/2607.01167"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-06T09:02:13.397535Z","title":"Quasiadditivity of Riesz capacity.Math","venue":null,"work_id":"85fc3664-70d0-4fee-b9d1-85387b3742b8","year":1991},"citing_paper":{"arxiv_id":"2607.01167","last_updated":"2026-07-01T16:54:30Z","snapshot_observed_at":"2026-08-08T07:43:02.023241Z","submitted_at":"2026-07-01T16:54:30Z","title":"One-sided median porous sets and one-sided Muckenhoupt distance functions","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-07-02T02:31:26.995015Z"},"links":{"citing_paper":"/paper/2607.01167"},"observation_digest":"sha256:3b5d0d09536291ba29001084055862225307bec889dc32aec42aa1ced15f7fe9","observation_id":"f4b10887-5e8b-4966-bc3a-e12b01ace4d6","resolution":{"observed_at":"2026-07-06T09:02:13.398780Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-07-06T09:02:13.395568Z","title":"Powers of distances to lower dimen- sional sets as Muckenhoupt weights.Acta Math","venue":null,"work_id":"6f107e44-ad92-4bfe-b382-1e204864d43a","year":2014},"citing_paper":{"arxiv_id":"2607.01167","last_updated":"2026-07-01T16:54:30Z","snapshot_observed_at":"2026-08-08T07:43:02.023241Z","submitted_at":"2026-07-01T16:54:30Z","title":"One-sided median porous sets and one-sided Muckenhoupt distance functions","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-07-02T02:31:26.995015Z"},"links":{"citing_paper":"/paper/2607.01167"},"observation_digest":"sha256:82de6113c6aa20f5ac3123ad8dc9d754f21d2e9734387c8f94794f74a26a443a","observation_id":"7b01516f-ad0c-42ba-9e01-7f5f884a82df","resolution":{"observed_at":"2026-07-06T09:02:13.396936Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2406.14369","last_updated":"2024-06-20T14:42:13Z","snapshot_observed_at":"2026-08-16T13:41:04.600452Z","submitted_at":"2024-06-20T14:42:13Z","title":"Weakly porous sets and $A_1$ Muckenhoupt weights in spaces of homogeneous type","version":1},"cited_work":{"arxiv_id":"2406.14369","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2406.14369","snapshot_observed_at":"2026-07-02T02:36:26.173130Z","title":"Weakly porous sets andA1 Muckenhoupt weights in spaces of homogeneous type","venue":null,"work_id":"55815a41-e01c-48c5-bca8-d6f5f984d62b","year":2024},"citing_paper":{"arxiv_id":"2607.01167","last_updated":"2026-07-01T16:54:30Z","snapshot_observed_at":"2026-08-08T07:43:02.023241Z","submitted_at":"2026-07-01T16:54:30Z","title":"One-sided median porous sets and one-sided Muckenhoupt distance functions","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-07-02T02:31:26.995015Z"},"links":{"cited_paper":"/paper/2406.14369","citing_paper":"/paper/2607.01167"},"observation_digest":"sha256:caa8671ad51ec9b2da6a5e4e1270dddf9390f2ff46518259ffec62e9bf17a606","observation_id":"f5bdfd0f-2b0a-413a-8515-858f93b18b48","resolution":{"observed_at":"2026-07-02T02:36:26.175592Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-07-06T09:02:13.399362Z","title":"Mart´ ın-Reyes","venue":null,"work_id":"cf3be807-fa6d-4180-9595-3ad9132a9a4c","year":2025},"citing_paper":{"arxiv_id":"2607.01167","last_updated":"2026-07-01T16:54:30Z","snapshot_observed_at":"2026-08-08T07:43:02.023241Z","submitted_at":"2026-07-01T16:54:30Z","title":"One-sided median porous sets and one-sided Muckenhoupt distance functions","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-07-02T02:31:26.995015Z"},"links":{"citing_paper":"/paper/2607.01167"},"observation_digest":"sha256:a0220c0d7405868bf3950a05cc9791df82777c47bb0e4361c34d368e1068125e","observation_id":"533f3dfa-5ed0-476b-8b10-e5eed7703559","resolution":{"observed_at":"2026-07-06T09:02:13.400533Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-07-06T09:02:13.404559Z","title":"Anderson, Juha Lehrb¨ ack, Carlos Mudarra, and Antti V","venue":null,"work_id":"84f0f18c-13fe-480a-8b44-6306155d190a","year":2024},"citing_paper":{"arxiv_id":"2607.01167","last_updated":"2026-07-01T16:54:30Z","snapshot_observed_at":"2026-08-08T07:43:02.023241Z","submitted_at":"2026-07-01T16:54:30Z","title":"One-sided median porous sets and one-sided Muckenhoupt distance functions","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-07-02T02:31:26.995015Z"},"links":{"citing_paper":"/paper/2607.01167"},"observation_digest":"sha256:715e44774713b181c8adcbeed8746ff128eb0a5c601a9163135f5ae5e3288520","observation_id":"cae0e9f9-409c-4aa0-a804-1be16c8a3e1c","resolution":{"observed_at":"2026-07-06T09:02:13.406279Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-07-06T09:02:13.406836Z","title":"Neugebauer, and V","venue":null,"work_id":"83423c0a-3b05-46da-b70e-128063cb6a4e","year":1995},"citing_paper":{"arxiv_id":"2607.01167","last_updated":"2026-07-01T16:54:30Z","snapshot_observed_at":"2026-08-08T07:43:02.023241Z","submitted_at":"2026-07-01T16:54:30Z","title":"One-sided median porous sets and one-sided Muckenhoupt distance functions","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-07-02T02:31:26.995015Z"},"links":{"citing_paper":"/paper/2607.01167"},"observation_digest":"sha256:2cb5ead60691b75f003b6586638371f804f79ae6ecc5f56676b9d82d402a1d2f","observation_id":"9115a5bb-9ecc-416a-b3d2-c07fc616b852","resolution":{"observed_at":"2026-07-06T09:02:13.408221Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-07-06T09:02:13.386251Z","title":"Dur´ an and Fernando L´ opez Garc´ ıa","venue":null,"work_id":"e8348e8a-97be-46d3-83dd-b47499835737","year":2010},"citing_paper":{"arxiv_id":"2607.01167","last_updated":"2026-07-01T16:54:30Z","snapshot_observed_at":"2026-08-08T07:43:02.023241Z","submitted_at":"2026-07-01T16:54:30Z","title":"One-sided median porous sets and one-sided Muckenhoupt distance functions","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-07-02T02:31:26.995015Z"},"links":{"citing_paper":"/paper/2607.01167"},"observation_digest":"sha256:0ac42b25ddfb19fc6ffa268d0d8abfe3e3f3fb62a32732b407dc623424636d0e","observation_id":"02394afd-bc91-4c42-943f-9b5d23b21fd3","resolution":{"observed_at":"2026-07-06T09:02:13.387369Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-07-06T09:02:13.388087Z","title":"V¨ ah¨ akangas","venue":null,"work_id":"661b18f2-4b4f-4c75-a399-4c528da29089","year":2019},"citing_paper":{"arxiv_id":"2607.01167","last_updated":"2026-07-01T16:54:30Z","snapshot_observed_at":"2026-08-08T07:43:02.023241Z","submitted_at":"2026-07-01T16:54:30Z","title":"One-sided median porous sets and one-sided Muckenhoupt distance functions","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-07-02T02:31:26.995015Z"},"links":{"citing_paper":"/paper/2607.01167"},"observation_digest":"sha256:afd63788d4969feb1810b150bb3ee87b17fff7107d3adbf4f79ba2d03833bd15","observation_id":"2f2ecf23-f034-4729-a9a4-fe8f5a0ce2cf","resolution":{"observed_at":"2026-07-06T09:02:13.389260Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-07-06T09:02:13.380693Z","title":"Rubio de Francia.Weighted norm inequalities and related topics, volume 116 ofNorth-Holland Mathematics Studies","venue":null,"work_id":"3292f379-653b-4c56-acfc-48401c8407cf","year":1985},"citing_paper":{"arxiv_id":"2607.01167","last_updated":"2026-07-01T16:54:30Z","snapshot_observed_at":"2026-08-08T07:43:02.023241Z","submitted_at":"2026-07-01T16:54:30Z","title":"One-sided median porous sets and one-sided Muckenhoupt distance functions","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-07-02T02:31:26.995015Z"},"links":{"citing_paper":"/paper/2607.01167"},"observation_digest":"sha256:1ad577aba6968c8e58cfc312c6a21ef1f4c53e7c51105ea3c13bdb845ad91e69","observation_id":"975d7bfa-9350-472b-81c0-b17547436d93","resolution":{"observed_at":"2026-07-06T09:02:13.382053Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-07-06T09:02:13.382611Z","title":"New characterizations of MuckenhouptAp distance weights for p > 1.J","venue":null,"work_id":"f8c279f8-4976-4384-b300-9df87995d950","year":2026},"citing_paper":{"arxiv_id":"2607.01167","last_updated":"2026-07-01T16:54:30Z","snapshot_observed_at":"2026-08-08T07:43:02.023241Z","submitted_at":"2026-07-01T16:54:30Z","title":"One-sided median porous sets and one-sided Muckenhoupt distance functions","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-07-02T02:31:26.995015Z"},"links":{"citing_paper":"/paper/2607.01167"},"observation_digest":"sha256:2c682549290655db252c662327e14ffc45d724309ecbe95e3136d9d734d6bab0","observation_id":"8657f558-e6f4-46e8-a2c8-624f691785d8","resolution":{"observed_at":"2026-07-06T09:02:13.383889Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-07-06T09:02:13.384470Z","title":"The imbedding theorems for weighted Sobolev spaces","venue":null,"work_id":"917f8401-5715-4ac8-893a-241cb517895a","year":1991},"citing_paper":{"arxiv_id":"2607.01167","last_updated":"2026-07-01T16:54:30Z","snapshot_observed_at":"2026-08-08T07:43:02.023241Z","submitted_at":"2026-07-01T16:54:30Z","title":"One-sided median porous sets and one-sided Muckenhoupt distance functions","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-07-02T02:31:26.995015Z"},"links":{"citing_paper":"/paper/2607.01167"},"observation_digest":"sha256:78bd32332ff306cdd76ae85a7e9762fdd44d10bec7b392a6f7ddab6745b7fa0e","observation_id":"e608c37a-4b36-4bfc-8ab1-7f44f199ea99","resolution":{"observed_at":"2026-07-06T09:02:13.385713Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2606.05034","last_updated":"2026-06-03T16:00:13Z","snapshot_observed_at":"2026-08-18T12:57:03.074061Z","submitted_at":"2026-06-03T16:00:13Z","title":"Median porosity is quasiconformally invariant","version":1},"cited_work":{"arxiv_id":"2606.05034","doi":null,"metadata_source":"pith","pith_arxiv_id":"2606.05034","snapshot_observed_at":"2026-07-02T02:36:26.166638Z","title":"Median porosity is quasiconformally invariant","venue":"math.CA","work_id":"1c59e1ca-964e-4067-8f38-3a9f2a5e72cd","year":2026},"citing_paper":{"arxiv_id":"2607.01167","last_updated":"2026-07-01T16:54:30Z","snapshot_observed_at":"2026-08-08T07:43:02.023241Z","submitted_at":"2026-07-01T16:54:30Z","title":"One-sided median porous sets and one-sided Muckenhoupt distance functions","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-07-02T02:31:26.995015Z"},"links":{"cited_paper":"/paper/2606.05034","citing_paper":"/paper/2607.01167"},"observation_digest":"sha256:e802b4a1614f855b9cc00267ffe6d1a2c53adab58e5b06531025066250fda1f4","observation_id":"1d617469-08e2-425d-8116-6e2a0ac06ecf","resolution":{"observed_at":"2026-07-02T02:36:26.168194Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-07-06T09:02:13.391843Z","title":"American Mathematical Society, Providence, RI, 2021","venue":null,"work_id":"57fe68a4-c647-4528-965e-41f82a14077a","year":2021},"citing_paper":{"arxiv_id":"2607.01167","last_updated":"2026-07-01T16:54:30Z","snapshot_observed_at":"2026-08-08T07:43:02.023241Z","submitted_at":"2026-07-01T16:54:30Z","title":"One-sided median porous sets and one-sided Muckenhoupt distance functions","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-07-02T02:31:26.995015Z"},"links":{"citing_paper":"/paper/2607.01167"},"observation_digest":"sha256:98c4d9236d2b5a8ec45421eaf45dca20de646ff1e8635491655dce3daf0ebe34","observation_id":"ad71b4e6-5279-46b6-b69e-70b7ed5541b2","resolution":{"observed_at":"2026-07-06T09:02:13.393066Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-07-06T09:02:13.402790Z","title":"Parabolic weighted norm inequalities and partial differential equations","venue":null,"work_id":"65a8d720-48cc-43a4-84bb-6270d9c23eb7","year":2016},"citing_paper":{"arxiv_id":"2607.01167","last_updated":"2026-07-01T16:54:30Z","snapshot_observed_at":"2026-08-08T07:43:02.023241Z","submitted_at":"2026-07-01T16:54:30Z","title":"One-sided median porous sets and one-sided Muckenhoupt distance functions","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-07-02T02:31:26.995015Z"},"links":{"citing_paper":"/paper/2607.01167"},"observation_digest":"sha256:9d59eda1c3b2cb9c8f70c3e5b214ed0ed4c1339f59a0da18e71a5684c2a8f113","observation_id":"a74ecd26-423b-4a81-931f-bafaea795c6f","resolution":{"observed_at":"2026-07-06T09:02:13.404001Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2604.12561","last_updated":"2026-04-14T10:43:07Z","snapshot_observed_at":"2026-08-09T20:07:16.235330Z","submitted_at":"2026-04-14T10:43:07Z","title":"Parabolic weak porosity and parabolic Muckenhoupt distance functions","version":1},"cited_work":{"arxiv_id":"2604.12561","doi":null,"metadata_source":"pith","pith_arxiv_id":"2604.12561","snapshot_observed_at":"2026-07-02T02:36:26.176984Z","title":"Parabolic weak porosity and parabolic Muckenhoupt distance functions","venue":"math.CA","work_id":"f29292bf-58a3-4eba-b5b5-6a23dd6cedc8","year":2026},"citing_paper":{"arxiv_id":"2607.01167","last_updated":"2026-07-01T16:54:30Z","snapshot_observed_at":"2026-08-08T07:43:02.023241Z","submitted_at":"2026-07-01T16:54:30Z","title":"One-sided median porous sets and one-sided Muckenhoupt distance functions","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-07-02T02:31:26.995015Z"},"links":{"cited_paper":"/paper/2604.12561","citing_paper":"/paper/2607.01167"},"observation_digest":"sha256:f8c7b8bb4fe4bf7c1003c1edad5477ee958d315e65629a114b8a42236dfc6ef7","observation_id":"fd622136-6e00-4634-aabe-f61381b67f92","resolution":{"observed_at":"2026-07-02T02:36:26.178701Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-07-06T09:02:13.401140Z","title":"V¨ ah¨ akangas","venue":null,"work_id":"a1423571-0678-428a-a83d-f92b3584567c","year":2016},"citing_paper":{"arxiv_id":"2607.01167","last_updated":"2026-07-01T16:54:30Z","snapshot_observed_at":"2026-08-08T07:43:02.023241Z","submitted_at":"2026-07-01T16:54:30Z","title":"One-sided median porous sets and one-sided Muckenhoupt distance functions","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-07-02T02:31:26.995015Z"},"links":{"citing_paper":"/paper/2607.01167"},"observation_digest":"sha256:a8a34c05452192e6c1a5179c9c9e0e1cb2ac764cdcfefda7458ca8fd1ec0d1bd","observation_id":"af3cb321-7a86-43c5-b49d-538074cf1632","resolution":{"observed_at":"2026-07-06T09:02:13.402231Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-07-06T09:02:13.375465Z","title":"Mart´ ın-Reyes and Alberto de la Torre","venue":null,"work_id":"48b125c4-4063-47f7-9d56-b5aaa4cca0e7","year":1994},"citing_paper":{"arxiv_id":"2607.01167","last_updated":"2026-07-01T16:54:30Z","snapshot_observed_at":"2026-08-08T07:43:02.023241Z","submitted_at":"2026-07-01T16:54:30Z","title":"One-sided median porous sets and one-sided Muckenhoupt distance functions","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-07-02T02:31:26.995015Z"},"links":{"citing_paper":"/paper/2607.01167"},"observation_digest":"sha256:99542e56b13d943f5e52765caafea224020ee33b192d168bc4c82053c61d774c","observation_id":"57939f47-f9c6-4af3-8762-71ebf5ab4346","resolution":{"observed_at":"2026-07-06T09:02:13.376790Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-07-06T09:02:13.369094Z","title":"Mart´ ın-Reyes, Pedro Ortega Salvador, and Alberto de la Torre","venue":null,"work_id":"6e495ceb-0754-4a81-a72c-17f1a1eb1a9c","year":1990},"citing_paper":{"arxiv_id":"2607.01167","last_updated":"2026-07-01T16:54:30Z","snapshot_observed_at":"2026-08-08T07:43:02.023241Z","submitted_at":"2026-07-01T16:54:30Z","title":"One-sided median porous sets and one-sided Muckenhoupt distance functions","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-07-02T02:31:26.995015Z"},"links":{"citing_paper":"/paper/2607.01167"},"observation_digest":"sha256:06523a32db592a4bce1833290463aaa0d4eb9b1d8bc83a15b053902a14486409","observation_id":"f3d8b101-0578-40f0-9b29-505bc2ddf7fb","resolution":{"observed_at":"2026-07-06T09:02:13.370404Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-07-06T09:02:13.371027Z","title":"Mart´ ın-Reyes, Luboˇ s Pick, and Alberto de la Torre","venue":null,"work_id":"7a1ce85d-72c8-4a0d-a96e-8c25a2f0e950","year":1993},"citing_paper":{"arxiv_id":"2607.01167","last_updated":"2026-07-01T16:54:30Z","snapshot_observed_at":"2026-08-08T07:43:02.023241Z","submitted_at":"2026-07-01T16:54:30Z","title":"One-sided median porous sets and one-sided Muckenhoupt distance functions","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-07-02T02:31:26.995015Z"},"links":{"citing_paper":"/paper/2607.01167"},"observation_digest":"sha256:512b94008f000ad1f0ee27031ee19f9394f431e6571d0237744bee454f57aff7","observation_id":"f8a8c7fa-a4b8-4619-b9ca-dcaf812d6bd4","resolution":{"observed_at":"2026-07-06T09:02:13.372371Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-07-06T09:02:13.367218Z","title":"Weak porosity on metric measure spaces.Proc","venue":null,"work_id":"c9fec9ff-33ef-4850-a4f9-60a6d9899a80","year":2025},"citing_paper":{"arxiv_id":"2607.01167","last_updated":"2026-07-01T16:54:30Z","snapshot_observed_at":"2026-08-08T07:43:02.023241Z","submitted_at":"2026-07-01T16:54:30Z","title":"One-sided median porous sets and one-sided Muckenhoupt distance functions","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-07-02T02:31:26.995015Z"},"links":{"citing_paper":"/paper/2607.01167"},"observation_digest":"sha256:001539979782cc22cf79ae8436d40dccadd8fa55ef83c59827b6351eed46e7e0","observation_id":"abf10907-9f2e-4539-9489-f9de023a9872","resolution":{"observed_at":"2026-07-06T09:02:13.368465Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2507.21020","last_updated":"2025-09-04T17:32:27Z","snapshot_observed_at":"2026-08-13T14:33:39.933689Z","submitted_at":"2025-07-28T17:42:19Z","title":"Medians, Oscillations, and Distance Functions","version":2},"cited_work":{"arxiv_id":"2507.21020","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2507.21020","snapshot_observed_at":"2026-07-02T11:26:54.771446Z","title":"Pasquariello and I","venue":null,"work_id":"e050e7e3-5fd8-4764-8eb9-ff4248759926","year":2025},"citing_paper":{"arxiv_id":"2607.01167","last_updated":"2026-07-01T16:54:30Z","snapshot_observed_at":"2026-08-08T07:43:02.023241Z","submitted_at":"2026-07-01T16:54:30Z","title":"One-sided median porous sets and one-sided Muckenhoupt distance functions","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-07-02T02:31:26.995015Z"},"links":{"cited_paper":"/paper/2507.21020","citing_paper":"/paper/2607.01167"},"observation_digest":"sha256:2796a866919ebb9a598486060dee5283b4fc3d1da10a86cc8e7a36faec97b157","observation_id":"e954a0b9-7b8a-42af-8810-22f87af0a661","resolution":{"observed_at":"2026-07-02T02:36:26.175771Z","resolver_source":"arxiv_id","status":"metadata_mismatch"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-07-06T09:02:13.365232Z","title":"Medians, continuity, and vanishing oscillation.Studia Math., 213(3):227–242, 2012","venue":null,"work_id":"4f5dba9c-6033-42c6-ae5b-61802c68e59c","year":2012},"citing_paper":{"arxiv_id":"2607.01167","last_updated":"2026-07-01T16:54:30Z","snapshot_observed_at":"2026-08-08T07:43:02.023241Z","submitted_at":"2026-07-01T16:54:30Z","title":"One-sided median porous sets and one-sided Muckenhoupt distance functions","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-07-02T02:31:26.995015Z"},"links":{"citing_paper":"/paper/2607.01167"},"observation_digest":"sha256:62dcc3dc4f3cd6b2c2dd5dae1704c69e0cda7514ba3bc0aeccce9d6a4d008e91","observation_id":"11543539-a8c7-4d49-9c35-7ddc949d416d","resolution":{"observed_at":"2026-07-06T09:02:13.366623Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-07-06T09:02:13.372944Z","title":"Weighted inequalities for the one-sided Hardy-Littlewood maximal functions.Trans","venue":null,"work_id":"126160ee-e725-42da-b158-e434692d94b2","year":1986},"citing_paper":{"arxiv_id":"2607.01167","last_updated":"2026-07-01T16:54:30Z","snapshot_observed_at":"2026-08-08T07:43:02.023241Z","submitted_at":"2026-07-01T16:54:30Z","title":"One-sided median porous sets and one-sided Muckenhoupt distance functions","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-07-02T02:31:26.995015Z"},"links":{"citing_paper":"/paper/2607.01167"},"observation_digest":"sha256:85af586e95368cf368ea181a22e15fd677d3d97a3138b4ea6e96f0d76f48e242","observation_id":"aa0cc9b8-eb4c-4277-9c1f-d9ca57e4c8fa","resolution":{"observed_at":"2026-07-06T09:02:13.374662Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-07-06T09:02:13.377388Z","title":"Porosity, dimension, and local entropies: a survey.Rev","venue":null,"work_id":"7e80c6a3-5262-4409-9cb0-7eabf0beac92","year":2011},"citing_paper":{"arxiv_id":"2607.01167","last_updated":"2026-07-01T16:54:30Z","snapshot_observed_at":"2026-08-08T07:43:02.023241Z","submitted_at":"2026-07-01T16:54:30Z","title":"One-sided median porous sets and one-sided Muckenhoupt distance functions","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-07-02T02:31:26.995015Z"},"links":{"citing_paper":"/paper/2607.01167"},"observation_digest":"sha256:8c8540f66a3e315f2ea2635c6756acef751b624ee8e8215e135c35be627db6d0","observation_id":"8975c6cc-fb0e-4b8d-876b-da17b110c970","resolution":{"observed_at":"2026-07-06T09:02:13.380119Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-07-06T09:02:13.389988Z","title":"Springer-Verlag, Berlin, 1989","venue":null,"work_id":"52464165-97ac-4151-a1cb-671cb0815ff8","year":1989},"citing_paper":{"arxiv_id":"2607.01167","last_updated":"2026-07-01T16:54:30Z","snapshot_observed_at":"2026-08-08T07:43:02.023241Z","submitted_at":"2026-07-01T16:54:30Z","title":"One-sided median porous sets and one-sided Muckenhoupt distance functions","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-07-02T02:31:26.995015Z"},"links":{"citing_paper":"/paper/2607.01167"},"observation_digest":"sha256:4485a99d767cd8d8be2876c70696f1bbfeece1c1ea6c02a3b3917de58f1cb785","observation_id":"398850f6-73bf-4285-9449-f183d847dd9e","resolution":{"observed_at":"2026-07-06T09:02:13.391294Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-07-06T09:02:13.393708Z","title":null,"venue":null,"work_id":"5f10864b-5911-4055-be72-8376f288645c","year":2003},"citing_paper":{"arxiv_id":"2607.01167","last_updated":"2026-07-01T16:54:30Z","snapshot_observed_at":"2026-08-08T07:43:02.023241Z","submitted_at":"2026-07-01T16:54:30Z","title":"One-sided median porous sets and one-sided Muckenhoupt distance functions","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-07-02T02:31:26.995015Z"},"links":{"citing_paper":"/paper/2607.01167"},"observation_digest":"sha256:6594a1d078f36fa770cbdaf8f41bab994cf084a7d045999b68262bf63b172ab2","observation_id":"10572cc4-f676-43ca-9597-dc19952b90bc","resolution":{"observed_at":"2026-07-06T09:02:13.394883Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2607.01167","last_updated":"2026-07-01T16:54:30Z","latest_version":1,"primary_category":"math.CA","snapshot_observed_at":"2026-08-08T07:43:02.023241Z","submitted_at":"2026-07-01T16:54:30Z","title":"One-sided median porous sets and one-sided Muckenhoupt distance functions"},"reference_resolution":{"displayed":26,"state_counts":{"malformed_identifier":0,"metadata_mismatch":1,"parse_uncertain":0,"unresolved":1,"verified_exact":3,"verified_fuzzy":21},"total_outbound_references":26},"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":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"thesis":"As of 23 August 2026, this Paper Citation Record lists 26 of 26 outbound references and 0 inbound Pith citation observations for arXiv:2607.01167."}