{"as_of":"2026-08-11T08:35:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:fc0a4104ad81904d0d8c1fa85ce235a9753dd4606022ae642b56470f11062197","coverage":[{"denominator":12,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":12,"source":"paper_references, paper_reference_links","source_observed_at":"2026-06-27T23:15:54.173394Z","state":"measured"},{"denominator":12,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":12,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-11T06:34:44.6726+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/2606.06384/citation-record","integrity":"/paper/2606.06384/integrity","json":"/paper/2606.06384/citation-record.json","paper":"/paper/2606.06384"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":"2510.06132","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-03T23:19:03.334735Z","title":"Optimal sub-Gaussian variance proxy for 3-mass distributions,","venue":null,"work_id":"37cd5e47-9783-41ee-b087-201a1fa0162f","year":2025},"citing_paper":{"arxiv_id":"2606.06384","last_updated":"2026-06-04T16:48:31Z","snapshot_observed_at":"2026-08-11T05:29:08.571860Z","submitted_at":"2026-06-04T16:48:31Z","title":"Estimation of the sub-Gaussian parameter","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-06-27T23:15:54.173394Z"},"links":{"citing_paper":"/paper/2606.06384"},"observation_digest":"sha256:acbb00ca2ef46c7b848e7135959e54900384e151c56e0cb412c51923692780c4","observation_id":"bf696724-32e7-46d7-959f-d43548a9e421","resolution":{"observed_at":"2026-07-02T15:57:06.635267Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1214/26-ecp761","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"and Shamir, R","venue":"Electronic Communications in Probability","work_id":"86a01066-c09b-4a46-8541-8b02068da5f4","year":2021},"citing_paper":{"arxiv_id":"2606.06384","last_updated":"2026-06-04T16:48:31Z","snapshot_observed_at":"2026-08-11T05:29:08.571860Z","submitted_at":"2026-06-04T16:48:31Z","title":"Estimation of the sub-Gaussian parameter","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-06-27T23:15:54.173394Z"},"links":{"citing_paper":"/paper/2606.06384"},"observation_digest":"sha256:f7fd02c2fb1a2f14cb5812b788f2a68270e71fa5d31c6dff5766d61f32c00d53","observation_id":"22829f47-e7fb-4783-9d2e-edbcf081749c","resolution":{"observed_at":"2026-06-27T23:21:23.354638Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1038/s41598-024-53346-z","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"H., Cook, H., Kuhn, M., Wyder, S., Simonovic, M., Santos, A., Doncheva, N","venue":"Scientific Reports","work_id":"ee787165-6913-4673-be5e-0aac2aea25f9","year":2017},"citing_paper":{"arxiv_id":"2606.06384","last_updated":"2026-06-04T16:48:31Z","snapshot_observed_at":"2026-08-11T05:29:08.571860Z","submitted_at":"2026-06-04T16:48:31Z","title":"Estimation of the sub-Gaussian parameter","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-06-27T23:15:54.173394Z"},"links":{"citing_paper":"/paper/2606.06384"},"observation_digest":"sha256:e587e7cad8f0b4d97a879eb625d8ee6d3b3e3e5e20cc086e084561cb793eee77","observation_id":"acd6c519-23aa-4e64-a7e6-54b67291acb3","resolution":{"observed_at":"2026-06-27T23:21:23.352955Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-27T23:15:54.173394Z","title":null,"venue":null,"work_id":null,"year":1999},"citing_paper":{"arxiv_id":"2606.06384","last_updated":"2026-06-04T16:48:31Z","snapshot_observed_at":"2026-08-11T05:29:08.571860Z","submitted_at":"2026-06-04T16:48:31Z","title":"Estimation of the sub-Gaussian parameter","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-06-27T23:15:54.173394Z"},"links":{"citing_paper":"/paper/2606.06384"},"observation_digest":"sha256:8bcb2a849df20b3ddf7296a13f0f8dbae88900fb2ec011ac7e633a0a67ddec2f","observation_id":"2179a815-ee3e-42d6-a22e-32797cafe66e","resolution":{"observed_at":"2026-06-27T23:15:54.173394Z","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":"2026-06-27T23:15:54.173394Z","title":"Then, for anyλ∈R, L(λ;P)≤ 2 λ2 loge |λ| ≤ 2 |λ|","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2606.06384","last_updated":"2026-06-04T16:48:31Z","snapshot_observed_at":"2026-08-11T05:29:08.571860Z","submitted_at":"2026-06-04T16:48:31Z","title":"Estimation of the sub-Gaussian parameter","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-06-27T23:15:54.173394Z"},"links":{"citing_paper":"/paper/2606.06384"},"observation_digest":"sha256:c30d8b6188ef0b41a51063d89a1e639f43479fd995bb80179567d448dde16e2b","observation_id":"d480e76c-bae5-40ee-bdd6-4d6428400915","resolution":{"observed_at":"2026-06-27T23:15:54.173394Z","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":"2026-06-27T23:15:54.173394Z","title":"(2025) gives exact expressions for the sub-Gaussian parameter of three-point distributions whenp≤1/6, they are still rather difficult to work with","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2606.06384","last_updated":"2026-06-04T16:48:31Z","snapshot_observed_at":"2026-08-11T05:29:08.571860Z","submitted_at":"2026-06-04T16:48:31Z","title":"Estimation of the sub-Gaussian parameter","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-06-27T23:15:54.173394Z"},"links":{"citing_paper":"/paper/2606.06384"},"observation_digest":"sha256:2aca538669637abecb1b6e9c400f106355299e54c33b20be64928a811e11736c","observation_id":"234dc101-e2a4-445a-a6e1-36bee5e95095","resolution":{"observed_at":"2026-06-27T23:15:54.173394Z","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":"2026-06-27T23:15:54.173394Z","title":"Define q0 = 1 2 and qn := q0 + 1/(4√n)","venue":null,"work_id":null,"year":2002},"citing_paper":{"arxiv_id":"2606.06384","last_updated":"2026-06-04T16:48:31Z","snapshot_observed_at":"2026-08-11T05:29:08.571860Z","submitted_at":"2026-06-04T16:48:31Z","title":"Estimation of the sub-Gaussian parameter","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-06-27T23:15:54.173394Z"},"links":{"citing_paper":"/paper/2606.06384"},"observation_digest":"sha256:08f1cb9fbc81a3cbfa5a68017b22003ceda6b09802713cd5e41221462d8196b9","observation_id":"416427b9-123f-4c11-a948-ac8b51367080","resolution":{"observed_at":"2026-06-27T23:15:54.173394Z","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":"2026-06-27T23:15:54.173394Z","title":"As for its empirical analogueLn, first let λ∗ ∈ Λ∗(P )","venue":null,"work_id":null,"year":2012},"citing_paper":{"arxiv_id":"2606.06384","last_updated":"2026-06-04T16:48:31Z","snapshot_observed_at":"2026-08-11T05:29:08.571860Z","submitted_at":"2026-06-04T16:48:31Z","title":"Estimation of the sub-Gaussian parameter","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-06-27T23:15:54.173394Z"},"links":{"citing_paper":"/paper/2606.06384"},"observation_digest":"sha256:7088619fdfb74d3637e291fcea22104a5d8f66de1799239953d45247e122012e","observation_id":"3f248c2d-e748-4874-87c8-259e7dd909c8","resolution":{"observed_at":"2026-06-27T23:15:54.173394Z","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":"2026-06-27T23:15:54.173394Z","title":null,"venue":null,"work_id":null,"year":2012},"citing_paper":{"arxiv_id":"2606.06384","last_updated":"2026-06-04T16:48:31Z","snapshot_observed_at":"2026-08-11T05:29:08.571860Z","submitted_at":"2026-06-04T16:48:31Z","title":"Estimation of the sub-Gaussian parameter","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-06-27T23:15:54.173394Z"},"links":{"citing_paper":"/paper/2606.06384"},"observation_digest":"sha256:2a6624849f7a9997ecbe637bde3eac85a337014a12f3424853324802639234e4","observation_id":"c3698ce0-a59d-4341-bab2-bd87049aa4e5","resolution":{"observed_at":"2026-06-27T23:15:54.173394Z","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":"2026-06-27T23:15:54.173394Z","title":"Moreover, ifCn is made larger thanC, then we must have˜ξ2 n(P) =ξ 2 ∗(P)for allP∈ P(Ξ, C 0, r−)","venue":null,"work_id":null,"year":1961},"citing_paper":{"arxiv_id":"2606.06384","last_updated":"2026-06-04T16:48:31Z","snapshot_observed_at":"2026-08-11T05:29:08.571860Z","submitted_at":"2026-06-04T16:48:31Z","title":"Estimation of the sub-Gaussian parameter","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-06-27T23:15:54.173394Z"},"links":{"citing_paper":"/paper/2606.06384"},"observation_digest":"sha256:9e59e9be71ba744e4041a1c4e8ce488cb60e4e6a51fca566a9c8a4ac1c21f65d","observation_id":"f1f8bfa5-868b-49d7-a418-0d0c8cc8255b","resolution":{"observed_at":"2026-06-27T23:15:54.173394Z","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":"2026-06-27T23:15:54.173394Z","title":"Provided n be large enough, λ will be contained in[−Cn, Cn], and by a law of large numbers for infinite means (Durrett (2019), Theorem 2.3.8), ˜Mn(λ) a.s","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2606.06384","last_updated":"2026-06-04T16:48:31Z","snapshot_observed_at":"2026-08-11T05:29:08.571860Z","submitted_at":"2026-06-04T16:48:31Z","title":"Estimation of the sub-Gaussian parameter","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-06-27T23:15:54.173394Z"},"links":{"citing_paper":"/paper/2606.06384"},"observation_digest":"sha256:86813946846de1a80e89b07299ada32fdc5ab465ab46ed782c35d340a414998f","observation_id":"17efe6eb-43c2-433a-80d3-9c6066cbdeb5","resolution":{"observed_at":"2026-06-27T23:15:54.173394Z","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":"2026-06-27T23:15:54.173394Z","title":"Note that∆ n = |X(n) − ¯X| ∨ |X (1) − ¯X|","venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2606.06384","last_updated":"2026-06-04T16:48:31Z","snapshot_observed_at":"2026-08-11T05:29:08.571860Z","submitted_at":"2026-06-04T16:48:31Z","title":"Estimation of the sub-Gaussian parameter","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-06-27T23:15:54.173394Z"},"links":{"citing_paper":"/paper/2606.06384"},"observation_digest":"sha256:4ddfb6df2f0e6da9f5160933e0c078c564866b8f4eb8ecd6f49ff92fdb9b8f52","observation_id":"c6e51784-a119-4b50-9e7e-526803834f23","resolution":{"observed_at":"2026-06-27T23:15:54.173394Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2606.06384","last_updated":"2026-06-04T16:48:31Z","latest_version":1,"primary_category":"math.ST","snapshot_observed_at":"2026-08-11T05:29:08.571860Z","submitted_at":"2026-06-04T16:48:31Z","title":"Estimation of the sub-Gaussian parameter"},"reference_resolution":{"displayed":12,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":9,"verified_exact":3,"verified_fuzzy":0},"total_outbound_references":12},"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":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"thesis":"As of 11 August 2026, this Paper Citation Record lists 12 of 12 outbound references and 0 inbound Pith citation observations for arXiv:2606.06384."}