{"as_of":"2026-08-06T03:01:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:60a3b70a307bdf0503ab8aa3433dc83f3620086dcdc30c820483250e4623297e","coverage":[{"denominator":32,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":32,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-01T00:12:35.271653Z","state":"measured"},{"denominator":32,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":32,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-05T06:32:48.257954+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/2607.23269/citation-record","integrity":"/paper/2607.23269/integrity","json":"/paper/2607.23269/citation-record.json","paper":"/paper/2607.23269"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T00:12:32.499969Z","title":"Asadi and N","venue":null,"work_id":null,"year":2000},"citing_paper":{"arxiv_id":"2607.23269","last_updated":"2026-07-25T16:11:15Z","snapshot_observed_at":"2026-08-01T00:12:31.459230Z","submitted_at":"2026-07-25T16:11:15Z","title":"Entropic analogues of Gr\\\"unbaum's inequality","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-01T00:12:32.499969Z"},"links":{"citing_paper":"/paper/2607.23269"},"observation_digest":"sha256:c12418c0b8ca1c91f1fd205eadfde7f395a1114ee2c929c187b1d362bf9e71cb","observation_id":"70834329-37e7-4a22-804a-6cb047c60fa5","resolution":{"observed_at":"2026-08-01T00:12:32.499969Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T00:12:32.548428Z","title":null,"venue":null,"work_id":null,"year":1997},"citing_paper":{"arxiv_id":"2607.23269","last_updated":"2026-07-25T16:11:15Z","snapshot_observed_at":"2026-08-01T00:12:31.459230Z","submitted_at":"2026-07-25T16:11:15Z","title":"Entropic analogues of Gr\\\"unbaum's inequality","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-01T00:12:32.548428Z"},"links":{"citing_paper":"/paper/2607.23269"},"observation_digest":"sha256:fa41989a77b88b9fabb8991915a8913d6513afa64f05a43de9e7226108569430","observation_id":"1fbe2eb2-2789-439d-8717-aa2b2b6ad437","resolution":{"observed_at":"2026-08-01T00:12:32.548428Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T00:12:32.599471Z","title":"Bobkov and M","venue":null,"work_id":null,"year":2011},"citing_paper":{"arxiv_id":"2607.23269","last_updated":"2026-07-25T16:11:15Z","snapshot_observed_at":"2026-08-01T00:12:31.459230Z","submitted_at":"2026-07-25T16:11:15Z","title":"Entropic analogues of Gr\\\"unbaum's inequality","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-01T00:12:32.599471Z"},"links":{"citing_paper":"/paper/2607.23269"},"observation_digest":"sha256:c98a3a636459e89b1bf889b8b5f6d2d4c3fbc2ac60d30cc4341215ab750ab43b","observation_id":"973e76a6-ffc5-4ae5-8532-bad35189e56d","resolution":{"observed_at":"2026-08-01T00:12:32.599471Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T00:12:32.671151Z","title":null,"venue":null,"work_id":null,"year":1973},"citing_paper":{"arxiv_id":"2607.23269","last_updated":"2026-07-25T16:11:15Z","snapshot_observed_at":"2026-08-01T00:12:31.459230Z","submitted_at":"2026-07-25T16:11:15Z","title":"Entropic analogues of Gr\\\"unbaum's inequality","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-01T00:12:32.671151Z"},"links":{"citing_paper":"/paper/2607.23269"},"observation_digest":"sha256:5702625318dc1b46ada14179def4f46e0053d37ec5c5ce9d050c7dbe08451180","observation_id":"7791dd03-8664-4b0c-93cc-4816574579c7","resolution":{"observed_at":"2026-08-01T00:12:32.671151Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T00:12:32.743751Z","title":"Brazitikos and C","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.23269","last_updated":"2026-07-25T16:11:15Z","snapshot_observed_at":"2026-08-01T00:12:31.459230Z","submitted_at":"2026-07-25T16:11:15Z","title":"Entropic analogues of Gr\\\"unbaum's inequality","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-01T00:12:32.743751Z"},"links":{"citing_paper":"/paper/2607.23269"},"observation_digest":"sha256:067dbc8982471846a28f3b41bc430c6ef914c0df72e7ea09d97cea1bd2bbd812","observation_id":"97833ae0-5363-4226-a3af-8d38896983ba","resolution":{"observed_at":"2026-08-01T00:12:32.743751Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T00:12:32.809431Z","title":"Chadjiconstantinidis and A","venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2607.23269","last_updated":"2026-07-25T16:11:15Z","snapshot_observed_at":"2026-08-01T00:12:31.459230Z","submitted_at":"2026-07-25T16:11:15Z","title":"Entropic analogues of Gr\\\"unbaum's inequality","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-01T00:12:32.809431Z"},"links":{"citing_paper":"/paper/2607.23269"},"observation_digest":"sha256:e68cf1974f2fad31934bf56431ddb9ae88a52d1a74ebfea667f8577e07429d65","observation_id":"e63d3b7c-7599-4ec1-8cfc-71ed744b1dc3","resolution":{"observed_at":"2026-08-01T00:12:32.809431Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T00:12:32.877723Z","title":"Cordero-Erausquin, M","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.23269","last_updated":"2026-07-25T16:11:15Z","snapshot_observed_at":"2026-08-01T00:12:31.459230Z","submitted_at":"2026-07-25T16:11:15Z","title":"Entropic analogues of Gr\\\"unbaum's inequality","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-01T00:12:32.877723Z"},"links":{"citing_paper":"/paper/2607.23269"},"observation_digest":"sha256:a98d73aae3637a3e17d6bc32fd5501e402bd3ff42ed0cb8bb5d517e4a4991758","observation_id":"af262ae2-df43-49e1-80c8-9a65241cdb29","resolution":{"observed_at":"2026-08-01T00:12:32.877723Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T00:12:32.923225Z","title":"Costa and T","venue":null,"work_id":null,"year":1984},"citing_paper":{"arxiv_id":"2607.23269","last_updated":"2026-07-25T16:11:15Z","snapshot_observed_at":"2026-08-01T00:12:31.459230Z","submitted_at":"2026-07-25T16:11:15Z","title":"Entropic analogues of Gr\\\"unbaum's inequality","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-01T00:12:32.923225Z"},"links":{"citing_paper":"/paper/2607.23269"},"observation_digest":"sha256:e4263bb0536d32346b51d936c08f9439a41812d3e179af170a63725e521666d8","observation_id":"f0f403c0-f45e-499e-b408-498e4785ff74","resolution":{"observed_at":"2026-08-01T00:12:32.923225Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T00:12:33.007248Z","title":null,"venue":null,"work_id":null,"year":2006},"citing_paper":{"arxiv_id":"2607.23269","last_updated":"2026-07-25T16:11:15Z","snapshot_observed_at":"2026-08-01T00:12:31.459230Z","submitted_at":"2026-07-25T16:11:15Z","title":"Entropic analogues of Gr\\\"unbaum's inequality","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-01T00:12:33.007248Z"},"links":{"citing_paper":"/paper/2607.23269"},"observation_digest":"sha256:ddb3228e2081339440c29bd022a06a65b611cb10510871c8d3aa69a6ac4419c2","observation_id":"d40d226c-fa8d-4e95-a5a2-acd9750902cd","resolution":{"observed_at":"2026-08-01T00:12:33.007248Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T00:12:33.173927Z","title":"Dembo, T","venue":null,"work_id":null,"year":1991},"citing_paper":{"arxiv_id":"2607.23269","last_updated":"2026-07-25T16:11:15Z","snapshot_observed_at":"2026-08-01T00:12:31.459230Z","submitted_at":"2026-07-25T16:11:15Z","title":"Entropic analogues of Gr\\\"unbaum's inequality","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-01T00:12:33.173927Z"},"links":{"citing_paper":"/paper/2607.23269"},"observation_digest":"sha256:b61a2c6ad00c6e6ec807687faa757095ea365bb2c11da99a393feb1b58fdde79","observation_id":"d5418fc8-38f7-44a9-87e3-5ff43962dbed","resolution":{"observed_at":"2026-08-01T00:12:33.173927Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T00:12:33.315137Z","title":"Ebrahimi","venue":null,"work_id":null,"year":1996},"citing_paper":{"arxiv_id":"2607.23269","last_updated":"2026-07-25T16:11:15Z","snapshot_observed_at":"2026-08-01T00:12:31.459230Z","submitted_at":"2026-07-25T16:11:15Z","title":"Entropic analogues of Gr\\\"unbaum's inequality","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-01T00:12:33.315137Z"},"links":{"citing_paper":"/paper/2607.23269"},"observation_digest":"sha256:4fe4f86f8f7e389d9ebb34aae1e7910d8ffa35ca14149baed328222842ef47b4","observation_id":"c868e99f-54d2-4424-800a-ef6d5d39bdd0","resolution":{"observed_at":"2026-08-01T00:12:33.315137Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T00:12:33.463850Z","title":"Ebrahimi","venue":null,"work_id":null,"year":1997},"citing_paper":{"arxiv_id":"2607.23269","last_updated":"2026-07-25T16:11:15Z","snapshot_observed_at":"2026-08-01T00:12:31.459230Z","submitted_at":"2026-07-25T16:11:15Z","title":"Entropic analogues of Gr\\\"unbaum's inequality","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-01T00:12:33.463850Z"},"links":{"citing_paper":"/paper/2607.23269"},"observation_digest":"sha256:33ba9c6d190ca492f47d12fa4780dc637ff28a12253ceaf83b08458a51076655","observation_id":"48b35262-9274-4e3f-b459-c69447b4ba9a","resolution":{"observed_at":"2026-08-01T00:12:33.463850Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T00:12:33.581899Z","title":"Eskenazis and L","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2607.23269","last_updated":"2026-07-25T16:11:15Z","snapshot_observed_at":"2026-08-01T00:12:31.459230Z","submitted_at":"2026-07-25T16:11:15Z","title":"Entropic analogues of Gr\\\"unbaum's inequality","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-01T00:12:33.581899Z"},"links":{"citing_paper":"/paper/2607.23269"},"observation_digest":"sha256:a1516af123d236916eb912d8dc18382c4c03a5acc042e212213fd42dc9de47f5","observation_id":"95b13b0e-4255-4e31-ad6a-30e6c4c0c944","resolution":{"observed_at":"2026-08-01T00:12:33.581899Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T00:12:33.655980Z","title":"Eskenazis, P","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2607.23269","last_updated":"2026-07-25T16:11:15Z","snapshot_observed_at":"2026-08-01T00:12:31.459230Z","submitted_at":"2026-07-25T16:11:15Z","title":"Entropic analogues of Gr\\\"unbaum's inequality","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-01T00:12:33.655980Z"},"links":{"citing_paper":"/paper/2607.23269"},"observation_digest":"sha256:b88d132920ba0c0de32a1125b5226c869469963002f1de4e1b049602db7cf939","observation_id":"cc03ab49-c9fb-4eb8-9449-cf6f0afb2c27","resolution":{"observed_at":"2026-08-01T00:12:33.655980Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T00:12:33.740164Z","title":"Fradelizi","venue":null,"work_id":null,"year":1997},"citing_paper":{"arxiv_id":"2607.23269","last_updated":"2026-07-25T16:11:15Z","snapshot_observed_at":"2026-08-01T00:12:31.459230Z","submitted_at":"2026-07-25T16:11:15Z","title":"Entropic analogues of Gr\\\"unbaum's inequality","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-01T00:12:33.740164Z"},"links":{"citing_paper":"/paper/2607.23269"},"observation_digest":"sha256:0e65c3c7d1d820f0f6ea8ad6b2ab00baca481e2c9549b9cd630ffd5e5d9f847f","observation_id":"7e7a4679-3b06-4128-a17c-f6fa6ef800ae","resolution":{"observed_at":"2026-08-01T00:12:33.740164Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T00:12:33.830806Z","title":"Fradelizi, L","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.23269","last_updated":"2026-07-25T16:11:15Z","snapshot_observed_at":"2026-08-01T00:12:31.459230Z","submitted_at":"2026-07-25T16:11:15Z","title":"Entropic analogues of Gr\\\"unbaum's inequality","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-01T00:12:33.830806Z"},"links":{"citing_paper":"/paper/2607.23269"},"observation_digest":"sha256:e306af7147d0697187177e14b3a64ac9fd627a1b3e4546dad429bb472c688e89","observation_id":"b0d5cc66-ded0-47ad-9751-86fe2414b872","resolution":{"observed_at":"2026-08-01T00:12:33.830806Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T00:12:33.921871Z","title":"Fradelizi, Y","venue":null,"work_id":null,"year":2010},"citing_paper":{"arxiv_id":"2607.23269","last_updated":"2026-07-25T16:11:15Z","snapshot_observed_at":"2026-08-01T00:12:31.459230Z","submitted_at":"2026-07-25T16:11:15Z","title":"Entropic analogues of Gr\\\"unbaum's inequality","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-01T00:12:33.921871Z"},"links":{"citing_paper":"/paper/2607.23269"},"observation_digest":"sha256:402a7e511fcb3b571f8448cb539eb68aea23c8b350fb6b898bbc67d03cac5979","observation_id":"791fa6b1-fbb3-4b51-b1c5-aba6b4ca1be9","resolution":{"observed_at":"2026-08-01T00:12:33.921871Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T00:12:34.004580Z","title":"Fradelizi and O","venue":null,"work_id":null,"year":2006},"citing_paper":{"arxiv_id":"2607.23269","last_updated":"2026-07-25T16:11:15Z","snapshot_observed_at":"2026-08-01T00:12:31.459230Z","submitted_at":"2026-07-25T16:11:15Z","title":"Entropic analogues of Gr\\\"unbaum's inequality","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-01T00:12:34.004580Z"},"links":{"citing_paper":"/paper/2607.23269"},"observation_digest":"sha256:e32f8fd0aa3c727bb2a01d12e9a9aed1205b4b7a548be663569042024398d13b","observation_id":"f17e017e-2878-43eb-b57f-d319b612e6b4","resolution":{"observed_at":"2026-08-01T00:12:34.004580Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T00:12:34.064630Z","title":"Fradelizi, D","venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2607.23269","last_updated":"2026-07-25T16:11:15Z","snapshot_observed_at":"2026-08-01T00:12:31.459230Z","submitted_at":"2026-07-25T16:11:15Z","title":"Entropic analogues of Gr\\\"unbaum's inequality","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-01T00:12:34.064630Z"},"links":{"citing_paper":"/paper/2607.23269"},"observation_digest":"sha256:5b0625ab0de022e8517c40cce062fa96e207c110a23309ab15d230d296c4ce44","observation_id":"f8c47b6b-4c15-466b-8ddd-a476088cd422","resolution":{"observed_at":"2026-08-01T00:12:34.064630Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T00:12:34.170169Z","title":"Fradelizi, J","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2607.23269","last_updated":"2026-07-25T16:11:15Z","snapshot_observed_at":"2026-08-01T00:12:31.459230Z","submitted_at":"2026-07-25T16:11:15Z","title":"Entropic analogues of Gr\\\"unbaum's inequality","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-01T00:12:34.170169Z"},"links":{"citing_paper":"/paper/2607.23269"},"observation_digest":"sha256:5c396e96beb8f0d7ce44f33afd0014922f1ca6504ab8192ea70574601b02abeb","observation_id":"4f6f85c6-a6a9-45f8-8f04-506be6ca96dc","resolution":{"observed_at":"2026-08-01T00:12:34.170169Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T00:12:34.279324Z","title":"Fradelizi, M","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2607.23269","last_updated":"2026-07-25T16:11:15Z","snapshot_observed_at":"2026-08-01T00:12:31.459230Z","submitted_at":"2026-07-25T16:11:15Z","title":"Entropic analogues of Gr\\\"unbaum's inequality","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-01T00:12:34.279324Z"},"links":{"citing_paper":"/paper/2607.23269"},"observation_digest":"sha256:ff6036b8dca551a390e4224b96825e59f6634b469fdd9854b2c0c6a9c4588112","observation_id":"9e5e7c38-5f26-4338-9f00-e1c1963f61a0","resolution":{"observed_at":"2026-08-01T00:12:34.279324Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T00:12:34.341218Z","title":"Fradelizi and M","venue":null,"work_id":null,"year":2008},"citing_paper":{"arxiv_id":"2607.23269","last_updated":"2026-07-25T16:11:15Z","snapshot_observed_at":"2026-08-01T00:12:31.459230Z","submitted_at":"2026-07-25T16:11:15Z","title":"Entropic analogues of Gr\\\"unbaum's inequality","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-01T00:12:34.341218Z"},"links":{"citing_paper":"/paper/2607.23269"},"observation_digest":"sha256:c6a3759e91d794ec1a965e50719890dd6ba39cfb02e64861fe769f1ef1811985","observation_id":"93d8523e-7dbf-4328-bb01-bc86147db86e","resolution":{"observed_at":"2026-08-01T00:12:34.341218Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T00:12:34.445168Z","title":"Gr¨ unbaum","venue":null,"work_id":null,"year":1960},"citing_paper":{"arxiv_id":"2607.23269","last_updated":"2026-07-25T16:11:15Z","snapshot_observed_at":"2026-08-01T00:12:31.459230Z","submitted_at":"2026-07-25T16:11:15Z","title":"Entropic analogues of Gr\\\"unbaum's inequality","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-01T00:12:34.445168Z"},"links":{"citing_paper":"/paper/2607.23269"},"observation_digest":"sha256:bbfafea06a3f3a655cc46a8c59011708e7b82fc9a9ea41f8d9e0d543ee04f3b6","observation_id":"09a2b463-fee0-4d81-956c-bbe1d15d1fe7","resolution":{"observed_at":"2026-08-01T00:12:34.445168Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T00:12:34.500628Z","title":"Klartag and J","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.23269","last_updated":"2026-07-25T16:11:15Z","snapshot_observed_at":"2026-08-01T00:12:31.459230Z","submitted_at":"2026-07-25T16:11:15Z","title":"Entropic analogues of Gr\\\"unbaum's inequality","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-01T00:12:34.500628Z"},"links":{"citing_paper":"/paper/2607.23269"},"observation_digest":"sha256:65e9b21d6b4172c4cad8a48a881c2878384a3ade00a471a5164866cf2b260379","observation_id":"b1a3f073-bccb-4d0c-9eeb-4b6e8deb51ed","resolution":{"observed_at":"2026-08-01T00:12:34.500628Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T00:12:34.578232Z","title":"Klartag and O","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.23269","last_updated":"2026-07-25T16:11:15Z","snapshot_observed_at":"2026-08-01T00:12:31.459230Z","submitted_at":"2026-07-25T16:11:15Z","title":"Entropic analogues of Gr\\\"unbaum's inequality","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-01T00:12:34.578232Z"},"links":{"citing_paper":"/paper/2607.23269"},"observation_digest":"sha256:69210eee37e4c68193fcf57c0f8d1c56f6e525fd10b077f88ff927de7b0680e7","observation_id":"ad0d2bef-3f5d-4507-8c6b-82ac7d002221","resolution":{"observed_at":"2026-08-01T00:12:34.578232Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T00:12:34.689234Z","title":null,"venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2607.23269","last_updated":"2026-07-25T16:11:15Z","snapshot_observed_at":"2026-08-01T00:12:31.459230Z","submitted_at":"2026-07-25T16:11:15Z","title":"Entropic analogues of Gr\\\"unbaum's inequality","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-01T00:12:34.689234Z"},"links":{"citing_paper":"/paper/2607.23269"},"observation_digest":"sha256:cc66652b08541bb9c21412f99695a9f8926dba6ea127219452808930b63c4107","observation_id":"6b30db3a-3e1b-42e7-bfec-9287cba5c954","resolution":{"observed_at":"2026-08-01T00:12:34.689234Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T00:12:34.800925Z","title":"Lov´ asz and S","venue":null,"work_id":null,"year":2007},"citing_paper":{"arxiv_id":"2607.23269","last_updated":"2026-07-25T16:11:15Z","snapshot_observed_at":"2026-08-01T00:12:31.459230Z","submitted_at":"2026-07-25T16:11:15Z","title":"Entropic analogues of Gr\\\"unbaum's inequality","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-01T00:12:34.800925Z"},"links":{"citing_paper":"/paper/2607.23269"},"observation_digest":"sha256:0d1f927c820de9623590bc5e53dafa625b277c4d9afca6f22adab2924779b8cf","observation_id":"c9ae8ed1-cfb3-4ab4-a04c-731d296cee21","resolution":{"observed_at":"2026-08-01T00:12:34.800925Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T00:12:34.872260Z","title":"Melbourne, P","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.23269","last_updated":"2026-07-25T16:11:15Z","snapshot_observed_at":"2026-08-01T00:12:31.459230Z","submitted_at":"2026-07-25T16:11:15Z","title":"Entropic analogues of Gr\\\"unbaum's inequality","version":1},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-01T00:12:34.872260Z"},"links":{"citing_paper":"/paper/2607.23269"},"observation_digest":"sha256:61caa09a7b4e4912bfce8812e4dd6b2ae4e81ea0908a26f618558fa3b9f83cff","observation_id":"cd23d7b2-89e9-4f02-bad7-2e6a49102783","resolution":{"observed_at":"2026-08-01T00:12:34.872260Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T00:12:34.984032Z","title":null,"venue":null,"work_id":null,"year":1987},"citing_paper":{"arxiv_id":"2607.23269","last_updated":"2026-07-25T16:11:15Z","snapshot_observed_at":"2026-08-01T00:12:31.459230Z","submitted_at":"2026-07-25T16:11:15Z","title":"Entropic analogues of Gr\\\"unbaum's inequality","version":1},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-01T00:12:34.984032Z"},"links":{"citing_paper":"/paper/2607.23269"},"observation_digest":"sha256:d88e07374029dd223c65171b567eee994d48afc479923d05cbdc4a58c96b009e","observation_id":"6d0f015d-a881-4971-b779-a750c176dc48","resolution":{"observed_at":"2026-08-01T00:12:34.984032Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T00:12:35.079710Z","title":"Moharana and S","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2607.23269","last_updated":"2026-07-25T16:11:15Z","snapshot_observed_at":"2026-08-01T00:12:31.459230Z","submitted_at":"2026-07-25T16:11:15Z","title":"Entropic analogues of Gr\\\"unbaum's inequality","version":1},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-01T00:12:35.079710Z"},"links":{"citing_paper":"/paper/2607.23269"},"observation_digest":"sha256:0fb051c57db2378852fd87a3f6ef20699b1bd17431187e124ae065188c890c69","observation_id":"fb1ae008-7760-486a-bfbd-9b05437dc557","resolution":{"observed_at":"2026-08-01T00:12:35.079710Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T00:12:35.174557Z","title":null,"venue":null,"work_id":null,"year":2004},"citing_paper":{"arxiv_id":"2607.23269","last_updated":"2026-07-25T16:11:15Z","snapshot_observed_at":"2026-08-01T00:12:31.459230Z","submitted_at":"2026-07-25T16:11:15Z","title":"Entropic analogues of Gr\\\"unbaum's inequality","version":1},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-01T00:12:35.174557Z"},"links":{"citing_paper":"/paper/2607.23269"},"observation_digest":"sha256:cf4f814c27aba8245ee4980b90d7aee5356d7d0aafc5e93c0d12d8b32f43f837","observation_id":"c01f9031-f294-4ab0-b958-fb7d099eda2c","resolution":{"observed_at":"2026-08-01T00:12:35.174557Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T00:12:35.271653Z","title":"Zardasht, S","venue":null,"work_id":null,"year":2015},"citing_paper":{"arxiv_id":"2607.23269","last_updated":"2026-07-25T16:11:15Z","snapshot_observed_at":"2026-08-01T00:12:31.459230Z","submitted_at":"2026-07-25T16:11:15Z","title":"Entropic analogues of Gr\\\"unbaum's inequality","version":1},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-01T00:12:35.271653Z"},"links":{"citing_paper":"/paper/2607.23269"},"observation_digest":"sha256:111241f2f9766272217aa050d04f4cfee2cae7f09db4fb4a0624103995422a58","observation_id":"d85b83be-397a-489d-822c-89a19fa1ff6c","resolution":{"observed_at":"2026-08-01T00:12:35.271653Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2607.23269","last_updated":"2026-07-25T16:11:15Z","latest_version":1,"primary_category":"math.PR","snapshot_observed_at":"2026-08-01T00:12:31.459230Z","submitted_at":"2026-07-25T16:11:15Z","title":"Entropic analogues of Gr\\\"unbaum's inequality"},"reference_resolution":{"displayed":32,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":32,"verified_exact":0,"verified_fuzzy":0},"total_outbound_references":32},"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":"2026-08-05T06:32:48.257954+00:00","source":"crossref"},{"observed_at":"2026-08-05T06:32:44.755628+00:00","source":"retraction_watch"}],"thesis":"As of 6 August 2026, this Paper Citation Record lists 32 of 32 outbound references and 0 inbound Pith citation observations for arXiv:2607.23269."}