{"as_of":"2026-08-09T00:16:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:1e1df308881688690d789ef0542eab53c81db40862ac77ed660fca6833f60698","coverage":[{"denominator":37,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":37,"source":"paper_references, paper_reference_links","source_observed_at":"2026-07-13T19:47:15.974727Z","state":"measured"},{"denominator":38,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":38,"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":"2026-05-10T16:32:05.581160Z","state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"arxiv_reference","source_observed_at":"2026-05-11T08:45:57.600878Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2603.23196","last_updated":"2026-07-08T14:24:44Z","snapshot_observed_at":"2026-08-04T09:43:12.488687Z","submitted_at":"2026-03-24T13:42:57Z","title":"Gaussian mixtures and non-parametric likelihoods through the lens of statistical mechanics","version":2},"cited_work":{"arxiv_id":"2603.23196","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2603.23196","snapshot_observed_at":"2026-07-09T02:19:52.061709Z","title":null,"venue":null,"work_id":"c2022d9c-3870-4cf4-84d6-f572b3ac05e6","year":2026},"citing_paper":{"arxiv_id":"2604.10899","last_updated":"2026-04-13T02:03:08Z","snapshot_observed_at":"2026-07-06T22:59:27.499664Z","submitted_at":"2026-04-13T02:03:08Z","title":"Characterisations of Kullback--Leibler approximation by finite Gaussian mixtures","version":1},"reference_index":7,"source":"arxiv_source","source_observed_at":"2026-05-10T16:32:05.581160Z"},"links":{"cited_paper":"/paper/2603.23196","citing_paper":"/paper/2604.10899"},"observation_digest":"sha256:126574d8e93d0faf7e50da1cd645ecc6324c06d776f0a5c57e124e1a409ff979","observation_id":"fb736d90-224a-453b-bca4-87a38f940492","resolution":{"observed_at":"2026-07-09T02:19:52.061709Z","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"}}],"links":{"evidence":"/evidence","html":"/paper/2603.23196/citation-record","integrity":"/paper/2603.23196/integrity","json":"/paper/2603.23196/citation-record.json","paper":"/paper/2603.23196"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-13T19:47:15.974727Z","title":"Theζ(2) limit in the random assignment problem.Random Structures & Algorithms, 18(4):381–418, 2001","venue":null,"work_id":null,"year":2001},"citing_paper":{"arxiv_id":"2603.23196","last_updated":"2026-07-08T14:24:44Z","snapshot_observed_at":"2026-08-04T09:43:12.488687Z","submitted_at":"2026-03-24T13:42:57Z","title":"Gaussian mixtures and non-parametric likelihoods through the lens of statistical mechanics","version":2},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-07-13T19:47:15.974727Z"},"links":{"citing_paper":"/paper/2603.23196"},"observation_digest":"sha256:7e904625785148e1d82062255068a7308ae6695ae9f102d0ec66294cfb42eb32","observation_id":"84f03f43-70ce-4d99-9a05-973b53aa1a42","resolution":{"observed_at":"2026-07-13T19:47:15.974727Z","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":"2026-07-13T19:47:15.974727Z","title":"Bakry, I","venue":null,"work_id":null,"year":2013},"citing_paper":{"arxiv_id":"2603.23196","last_updated":"2026-07-08T14:24:44Z","snapshot_observed_at":"2026-08-04T09:43:12.488687Z","submitted_at":"2026-03-24T13:42:57Z","title":"Gaussian mixtures and non-parametric likelihoods through the lens of statistical mechanics","version":2},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-07-13T19:47:15.974727Z"},"links":{"citing_paper":"/paper/2603.23196"},"observation_digest":"sha256:484043158431ee3add83bb1bfef153588c1baeab858fa4c585f36aa6d772e482","observation_id":"bb065048-8ad3-4e5a-a846-8fae0782332c","resolution":{"observed_at":"2026-07-13T19:47:15.974727Z","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":"2026-07-13T19:47:15.974727Z","title":"Functional inequalities for Gaussian convolutions of compactly supported mea- sures: Explicit bounds and dimension dependence.Bernoulli, 24(1):333 – 353, 2018","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2603.23196","last_updated":"2026-07-08T14:24:44Z","snapshot_observed_at":"2026-08-04T09:43:12.488687Z","submitted_at":"2026-03-24T13:42:57Z","title":"Gaussian mixtures and non-parametric likelihoods through the lens of statistical mechanics","version":2},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-07-13T19:47:15.974727Z"},"links":{"citing_paper":"/paper/2603.23196"},"observation_digest":"sha256:efd361b95846d8a01dde51e93939b4f58d1de1000a8b5abf321ae899f15dfd99","observation_id":"36ffb2a8-b129-4e30-854c-0534a7712169","resolution":{"observed_at":"2026-07-13T19:47:15.974727Z","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":"2026-07-13T19:47:15.974727Z","title":"Springer, 2006","venue":null,"work_id":null,"year":2006},"citing_paper":{"arxiv_id":"2603.23196","last_updated":"2026-07-08T14:24:44Z","snapshot_observed_at":"2026-08-04T09:43:12.488687Z","submitted_at":"2026-03-24T13:42:57Z","title":"Gaussian mixtures and non-parametric likelihoods through the lens of statistical mechanics","version":2},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-07-13T19:47:15.974727Z"},"links":{"citing_paper":"/paper/2603.23196"},"observation_digest":"sha256:b5923f821e548d2178811456b0c81e09728e45fef26fede8b57a663200e64a51","observation_id":"8849d833-0b8c-4727-bab1-83a6dcc9cd5e","resolution":{"observed_at":"2026-07-13T19:47:15.974727Z","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":"2026-07-13T19:47:15.974727Z","title":"Computer-assisted analysis of mixtures and applications, 2000","venue":null,"work_id":null,"year":2000},"citing_paper":{"arxiv_id":"2603.23196","last_updated":"2026-07-08T14:24:44Z","snapshot_observed_at":"2026-08-04T09:43:12.488687Z","submitted_at":"2026-03-24T13:42:57Z","title":"Gaussian mixtures and non-parametric likelihoods through the lens of statistical mechanics","version":2},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-07-13T19:47:15.974727Z"},"links":{"citing_paper":"/paper/2603.23196"},"observation_digest":"sha256:abd7f958c7a5790de8242b309bafa5c8a8ce03eb84079ed74304e7a036ff86e0","observation_id":"68d256b1-de75-4cd1-a7d0-8b153d3122dd","resolution":{"observed_at":"2026-07-13T19:47:15.974727Z","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":"2026-07-13T19:47:15.974727Z","title":"Boucheron, G","venue":null,"work_id":null,"year":2013},"citing_paper":{"arxiv_id":"2603.23196","last_updated":"2026-07-08T14:24:44Z","snapshot_observed_at":"2026-08-04T09:43:12.488687Z","submitted_at":"2026-03-24T13:42:57Z","title":"Gaussian mixtures and non-parametric likelihoods through the lens of statistical mechanics","version":2},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-07-13T19:47:15.974727Z"},"links":{"citing_paper":"/paper/2603.23196"},"observation_digest":"sha256:5b1db2e51cbff58e1dbcc352ebc86e741153e40aa04fe50737e6fae8cfa9e20b","observation_id":"df33c58a-6194-4b23-a2d3-a4ebdc221234","resolution":{"observed_at":"2026-07-13T19:47:15.974727Z","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":"2026-07-13T19:47:15.974727Z","title":"Oxford University Press, 02 2013","venue":null,"work_id":null,"year":2013},"citing_paper":{"arxiv_id":"2603.23196","last_updated":"2026-07-08T14:24:44Z","snapshot_observed_at":"2026-08-04T09:43:12.488687Z","submitted_at":"2026-03-24T13:42:57Z","title":"Gaussian mixtures and non-parametric likelihoods through the lens of statistical mechanics","version":2},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-07-13T19:47:15.974727Z"},"links":{"citing_paper":"/paper/2603.23196"},"observation_digest":"sha256:46d6ec8b966472a506059055a3cf2c68c3c90b90b365e3f375daa13995405f54","observation_id":"ac3b36a3-f84d-4fe5-8000-3f9e7bf0415e","resolution":{"observed_at":"2026-07-13T19:47:15.974727Z","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":"2026-07-13T19:47:15.974727Z","title":"Springer, 2014","venue":null,"work_id":null,"year":2014},"citing_paper":{"arxiv_id":"2603.23196","last_updated":"2026-07-08T14:24:44Z","snapshot_observed_at":"2026-08-04T09:43:12.488687Z","submitted_at":"2026-03-24T13:42:57Z","title":"Gaussian mixtures and non-parametric likelihoods through the lens of statistical mechanics","version":2},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-07-13T19:47:15.974727Z"},"links":{"citing_paper":"/paper/2603.23196"},"observation_digest":"sha256:20d3a03eeeead05e42050a9428e9e5840a7ee4ccd4d45930eb43161d2af7f927","observation_id":"fbb8439f-44ae-4344-96ce-2f8de4af49af","resolution":{"observed_at":"2026-07-13T19:47:15.974727Z","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":"2026-07-13T19:47:15.974727Z","title":"Consistency of the mle under mixture models.Statistical Science, 32(1):47–63, 2017","venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2603.23196","last_updated":"2026-07-08T14:24:44Z","snapshot_observed_at":"2026-08-04T09:43:12.488687Z","submitted_at":"2026-03-24T13:42:57Z","title":"Gaussian mixtures and non-parametric likelihoods through the lens of statistical mechanics","version":2},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-07-13T19:47:15.974727Z"},"links":{"citing_paper":"/paper/2603.23196"},"observation_digest":"sha256:28d4ec9ac6ebcf22f03976f2031a1c7f4556ee283020a8caafe51d7b2755e9a0","observation_id":"f84e0062-25d6-4527-9bba-7163ef1c4ed0","resolution":{"observed_at":"2026-07-13T19:47:15.974727Z","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":"2026-07-13T19:47:15.974727Z","title":"Maximum likelihood from incomplete data via the em algorithm.Journal of the royal statistical society: series B (methodological), 39(1):1–22, 1977","venue":null,"work_id":null,"year":1977},"citing_paper":{"arxiv_id":"2603.23196","last_updated":"2026-07-08T14:24:44Z","snapshot_observed_at":"2026-08-04T09:43:12.488687Z","submitted_at":"2026-03-24T13:42:57Z","title":"Gaussian mixtures and non-parametric likelihoods through the lens of statistical mechanics","version":2},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-07-13T19:47:15.974727Z"},"links":{"citing_paper":"/paper/2603.23196"},"observation_digest":"sha256:8f040fae9f98c42f145ef48235edf76ef08d448b56f299bf5641752a54ec5a33","observation_id":"edc09536-4fa0-411f-aa14-1a5f70db189a","resolution":{"observed_at":"2026-07-13T19:47:15.974727Z","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":"2026-07-13T19:47:15.974727Z","title":"Springer Science & Business Media, 2013","venue":null,"work_id":null,"year":2013},"citing_paper":{"arxiv_id":"2603.23196","last_updated":"2026-07-08T14:24:44Z","snapshot_observed_at":"2026-08-04T09:43:12.488687Z","submitted_at":"2026-03-24T13:42:57Z","title":"Gaussian mixtures and non-parametric likelihoods through the lens of statistical mechanics","version":2},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-07-13T19:47:15.974727Z"},"links":{"citing_paper":"/paper/2603.23196"},"observation_digest":"sha256:34a10e3fe000c7d25ae3c7fc8f03b8cf12a0e0492c7755e2deb5317fee76d98d","observation_id":"9a6948d9-d45b-47a4-811e-4bbd49c03ef2","resolution":{"observed_at":"2026-07-13T19:47:15.974727Z","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":"2026-07-13T19:47:15.974727Z","title":"Fukushima, Y","venue":null,"work_id":null,"year":2010},"citing_paper":{"arxiv_id":"2603.23196","last_updated":"2026-07-08T14:24:44Z","snapshot_observed_at":"2026-08-04T09:43:12.488687Z","submitted_at":"2026-03-24T13:42:57Z","title":"Gaussian mixtures and non-parametric likelihoods through the lens of statistical mechanics","version":2},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-07-13T19:47:15.974727Z"},"links":{"citing_paper":"/paper/2603.23196"},"observation_digest":"sha256:ab7f92f92ceb2fb6897e557d7d0cf63970ec093cb85b3707e1b5af4d025d8c30","observation_id":"d7e0fd82-dbf2-4aa9-ac9f-f002a989896e","resolution":{"observed_at":"2026-07-13T19:47:15.974727Z","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":"2026-07-13T19:47:15.974727Z","title":"Posterior convergence rates of dirichlet mixtures at smooth densities","venue":null,"work_id":null,"year":2007},"citing_paper":{"arxiv_id":"2603.23196","last_updated":"2026-07-08T14:24:44Z","snapshot_observed_at":"2026-08-04T09:43:12.488687Z","submitted_at":"2026-03-24T13:42:57Z","title":"Gaussian mixtures and non-parametric likelihoods through the lens of statistical mechanics","version":2},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-07-13T19:47:15.974727Z"},"links":{"citing_paper":"/paper/2603.23196"},"observation_digest":"sha256:16a3a6eac91ff9d81ce66a4069816b0407a5621e2989366329c9dd17256c1b12","observation_id":"ea5b66d3-5cc9-4e9f-9e9d-8b9340819084","resolution":{"observed_at":"2026-07-13T19:47:15.974727Z","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":"2026-07-13T19:47:15.974727Z","title":"General maximum likelihood empirical bayes estimation of normal means.The Annals of Statistics, 37(4):1647–1684, 2009","venue":null,"work_id":null,"year":2009},"citing_paper":{"arxiv_id":"2603.23196","last_updated":"2026-07-08T14:24:44Z","snapshot_observed_at":"2026-08-04T09:43:12.488687Z","submitted_at":"2026-03-24T13:42:57Z","title":"Gaussian mixtures and non-parametric likelihoods through the lens of statistical mechanics","version":2},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-07-13T19:47:15.974727Z"},"links":{"citing_paper":"/paper/2603.23196"},"observation_digest":"sha256:8c3c383bcab455f63ed7ad51e3f8f2a4ed1bfa12faba30fb9a2d52d2e0677b0e","observation_id":"79c127ce-b0b9-470d-b9aa-7fd544a2e527","resolution":{"observed_at":"2026-07-13T19:47:15.974727Z","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":"2026-07-13T19:47:15.974727Z","title":"Consistency of the maximum likelihood esti- mator in the presence of infinitely many incidental parameters.The Annals of Mathematical Statistics, pages 887–906, 1956","venue":null,"work_id":null,"year":1956},"citing_paper":{"arxiv_id":"2603.23196","last_updated":"2026-07-08T14:24:44Z","snapshot_observed_at":"2026-08-04T09:43:12.488687Z","submitted_at":"2026-03-24T13:42:57Z","title":"Gaussian mixtures and non-parametric likelihoods through the lens of statistical mechanics","version":2},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-07-13T19:47:15.974727Z"},"links":{"citing_paper":"/paper/2603.23196"},"observation_digest":"sha256:e573fc48453be09d6f875837d60497dcc81de69b15565f6f75207b8e8ee66adc","observation_id":"2b0735fa-1596-41cd-98a4-60fcbbd3d8be","resolution":{"observed_at":"2026-07-13T19:47:15.974727Z","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":"2026-07-13T19:47:15.974727Z","title":"Minimax bounds for estimation of normal mixtures.Bernoulli, pages 1802–1818, 2014","venue":null,"work_id":null,"year":2014},"citing_paper":{"arxiv_id":"2603.23196","last_updated":"2026-07-08T14:24:44Z","snapshot_observed_at":"2026-08-04T09:43:12.488687Z","submitted_at":"2026-03-24T13:42:57Z","title":"Gaussian mixtures and non-parametric likelihoods through the lens of statistical mechanics","version":2},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-07-13T19:47:15.974727Z"},"links":{"citing_paper":"/paper/2603.23196"},"observation_digest":"sha256:0f8ef13d7f010142e1b4956ee62e318c5978da59a377ecd995d6ab6a6874ba2c","observation_id":"af10d17d-dd29-409b-be78-8ee94dba12f9","resolution":{"observed_at":"2026-07-13T19:47:15.974727Z","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":"2026-07-13T19:47:15.974727Z","title":"Minimax bounds for estimat- ing multivariate gaussian location mixtures.Electronic Journal of Statistics, 16(1):1461–1484, 2022","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2603.23196","last_updated":"2026-07-08T14:24:44Z","snapshot_observed_at":"2026-08-04T09:43:12.488687Z","submitted_at":"2026-03-24T13:42:57Z","title":"Gaussian mixtures and non-parametric likelihoods through the lens of statistical mechanics","version":2},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-07-13T19:47:15.974727Z"},"links":{"citing_paper":"/paper/2603.23196"},"observation_digest":"sha256:eb14fe6e687caab8ac61118af0d8d26a77849b8f10bbe128daa3065515fadf56","observation_id":"86d7d8b6-5bf3-4946-9e42-858dbc84da57","resolution":{"observed_at":"2026-07-13T19:47:15.974727Z","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":"2026-07-13T19:47:15.974727Z","title":null,"venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2603.23196","last_updated":"2026-07-08T14:24:44Z","snapshot_observed_at":"2026-08-04T09:43:12.488687Z","submitted_at":"2026-03-24T13:42:57Z","title":"Gaussian mixtures and non-parametric likelihoods through the lens of statistical mechanics","version":2},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-07-13T19:47:15.974727Z"},"links":{"citing_paper":"/paper/2603.23196"},"observation_digest":"sha256:4615b9a480e4ff3c813efdf9e40d642137cb7f1c34e111f53fae032e764e7ed3","observation_id":"2a4c9f46-b882-40ae-b34f-3d8bdef23df3","resolution":{"observed_at":"2026-07-13T19:47:15.974727Z","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":"2026-07-13T19:47:15.974727Z","title":"Convex optimization, shape constraints, com- pound decisions, and empirical bayes rules.Journal of the American Statistical Association, 109(506):674–685, 2014","venue":null,"work_id":null,"year":2014},"citing_paper":{"arxiv_id":"2603.23196","last_updated":"2026-07-08T14:24:44Z","snapshot_observed_at":"2026-08-04T09:43:12.488687Z","submitted_at":"2026-03-24T13:42:57Z","title":"Gaussian mixtures and non-parametric likelihoods through the lens of statistical mechanics","version":2},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-07-13T19:47:15.974727Z"},"links":{"citing_paper":"/paper/2603.23196"},"observation_digest":"sha256:5a588dadac1c55890b687c2ab30d03af14a65b31773e0b0201b93a6663bbe7bf","observation_id":"0e67d455-195b-424f-9aa4-649929cc8c0f","resolution":{"observed_at":"2026-07-13T19:47:15.974727Z","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":"2026-07-13T19:47:15.974727Z","title":"Number 89","venue":null,"work_id":null,"year":2001},"citing_paper":{"arxiv_id":"2603.23196","last_updated":"2026-07-08T14:24:44Z","snapshot_observed_at":"2026-08-04T09:43:12.488687Z","submitted_at":"2026-03-24T13:42:57Z","title":"Gaussian mixtures and non-parametric likelihoods through the lens of statistical mechanics","version":2},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-07-13T19:47:15.974727Z"},"links":{"citing_paper":"/paper/2603.23196"},"observation_digest":"sha256:892b1b0788ca34721c692d5cad2e982fac6870022cfa753595b1d7b912f65378","observation_id":"6e14bd7e-6b51-4d04-8ee4-ec7e59af82f6","resolution":{"observed_at":"2026-07-13T19:47:15.974727Z","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":"2026-07-13T19:47:15.974727Z","title":"Mixture models: theory, geometry, and applications","venue":null,"work_id":null,"year":1995},"citing_paper":{"arxiv_id":"2603.23196","last_updated":"2026-07-08T14:24:44Z","snapshot_observed_at":"2026-08-04T09:43:12.488687Z","submitted_at":"2026-03-24T13:42:57Z","title":"Gaussian mixtures and non-parametric likelihoods through the lens of statistical mechanics","version":2},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-07-13T19:47:15.974727Z"},"links":{"citing_paper":"/paper/2603.23196"},"observation_digest":"sha256:4e1c4b85e74615114533b06a60f7b4cb9b8d9cc0f63d67d04837d470461cbb7a","observation_id":"9b4629f3-8beb-4579-8b08-7934105fb025","resolution":{"observed_at":"2026-07-13T19:47:15.974727Z","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":"2026-07-13T19:47:15.974727Z","title":"Uniqueness of estimation and identifia- bility in mixture models.Canadian Journal of Statistics, 21(2):139–147, 1993","venue":null,"work_id":null,"year":1993},"citing_paper":{"arxiv_id":"2603.23196","last_updated":"2026-07-08T14:24:44Z","snapshot_observed_at":"2026-08-04T09:43:12.488687Z","submitted_at":"2026-03-24T13:42:57Z","title":"Gaussian mixtures and non-parametric likelihoods through the lens of statistical mechanics","version":2},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-07-13T19:47:15.974727Z"},"links":{"citing_paper":"/paper/2603.23196"},"observation_digest":"sha256:6ea31a0eae674479092f94938a95af51bf3e3fc20f144e96e1281dd7d35ad424","observation_id":"e662e0e6-e742-494f-804e-8b4c721e64ba","resolution":{"observed_at":"2026-07-13T19:47:15.974727Z","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":"2026-07-13T19:47:15.974727Z","title":"On the best approximation by finite gaussian mixtures.IEEE Transactions on Information Theory, 2025","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2603.23196","last_updated":"2026-07-08T14:24:44Z","snapshot_observed_at":"2026-08-04T09:43:12.488687Z","submitted_at":"2026-03-24T13:42:57Z","title":"Gaussian mixtures and non-parametric likelihoods through the lens of statistical mechanics","version":2},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-07-13T19:47:15.974727Z"},"links":{"citing_paper":"/paper/2603.23196"},"observation_digest":"sha256:13105b215387ebe9ef1049db41f18d1bda6f939d8a54052bf3d1c26889df193c","observation_id":"c3f62aff-b366-45f6-88d1-4021dbb1607b","resolution":{"observed_at":"2026-07-13T19:47:15.974727Z","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":"2026-07-13T19:47:15.974727Z","title":"Finite mixture models.Annual review of statistics and its application, 6(1):355–378, 2019","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2603.23196","last_updated":"2026-07-08T14:24:44Z","snapshot_observed_at":"2026-08-04T09:43:12.488687Z","submitted_at":"2026-03-24T13:42:57Z","title":"Gaussian mixtures and non-parametric likelihoods through the lens of statistical mechanics","version":2},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-07-13T19:47:15.974727Z"},"links":{"citing_paper":"/paper/2603.23196"},"observation_digest":"sha256:6db71d082cd3d8555d1a03ba45e1545b1e62dea8e72ecbd18ff7fe260523156b","observation_id":"7411be49-d53a-46de-b663-5b5811c10752","resolution":{"observed_at":"2026-07-13T19:47:15.974727Z","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":"2026-07-13T19:47:15.974727Z","title":"A conjecture on random bipartite matching.arXiv preprint cond- mat/9801176, 1998","venue":null,"work_id":null,"year":1998},"citing_paper":{"arxiv_id":"2603.23196","last_updated":"2026-07-08T14:24:44Z","snapshot_observed_at":"2026-08-04T09:43:12.488687Z","submitted_at":"2026-03-24T13:42:57Z","title":"Gaussian mixtures and non-parametric likelihoods through the lens of statistical mechanics","version":2},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-07-13T19:47:15.974727Z"},"links":{"citing_paper":"/paper/2603.23196"},"observation_digest":"sha256:ed837d4ef8933acfe8d6b6472752c5375ca4e257f5c83ea09f87a1710fccc43d","observation_id":"6cade4a5-4b7b-4d13-af39-2b29183b151b","resolution":{"observed_at":"2026-07-13T19:47:15.974727Z","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":"2026-07-13T19:47:15.974727Z","title":"Consistency of maximum likelihood estimators for certain non- parametric families, in particular: mixtures.Journal of Statistical Planning and Inference, 19(2):137–158, 1988","venue":null,"work_id":null,"year":1988},"citing_paper":{"arxiv_id":"2603.23196","last_updated":"2026-07-08T14:24:44Z","snapshot_observed_at":"2026-08-04T09:43:12.488687Z","submitted_at":"2026-03-24T13:42:57Z","title":"Gaussian mixtures and non-parametric likelihoods through the lens of statistical mechanics","version":2},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-07-13T19:47:15.974727Z"},"links":{"citing_paper":"/paper/2603.23196"},"observation_digest":"sha256:e58af4c89c77a523ead2e646cadf4c4b030cf43d3180aeb74e2e6ff9b4e7b96e","observation_id":"ee4948d3-6d7e-4860-936b-39fc5e1b7632","resolution":{"observed_at":"2026-07-13T19:47:15.974727Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2008.08244","last_updated":"2020-09-07T01:10:12Z","snapshot_observed_at":"2026-07-06T09:48:15.927807Z","submitted_at":"2020-08-19T03:39:13Z","title":"Self-regularizing Property of Nonparametric Maximum Likelihood Estimator in Mixture Models","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2008.08244","snapshot_observed_at":"2026-07-13T19:47:15.974727Z","title":"Self-regularizing property of nonpara- metric maximum likelihood estimator in mixture models.arXiv preprint arXiv:2008.08244, 2020","venue":null,"work_id":null,"year":2008},"citing_paper":{"arxiv_id":"2603.23196","last_updated":"2026-07-08T14:24:44Z","snapshot_observed_at":"2026-08-04T09:43:12.488687Z","submitted_at":"2026-03-24T13:42:57Z","title":"Gaussian mixtures and non-parametric likelihoods through the lens of statistical mechanics","version":2},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-07-13T19:47:15.974727Z"},"links":{"cited_paper":"/paper/2008.08244","citing_paper":"/paper/2603.23196"},"observation_digest":"sha256:34de7e55b64f2c93c3c5d9cf6d42554d3cd2ebd9b8d6ecf648275fd2ea35c490","observation_id":"b8de649d-7d26-42b3-9e7f-585169c12241","resolution":{"observed_at":"2026-07-13T19:47:15.974727Z","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":"2026-07-13T19:47:15.974727Z","title":"A generalization of the method of maximum likelihood- estimating a mixing distribution","venue":null,"work_id":null,"year":1950},"citing_paper":{"arxiv_id":"2603.23196","last_updated":"2026-07-08T14:24:44Z","snapshot_observed_at":"2026-08-04T09:43:12.488687Z","submitted_at":"2026-03-24T13:42:57Z","title":"Gaussian mixtures and non-parametric likelihoods through the lens of statistical mechanics","version":2},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-07-13T19:47:15.974727Z"},"links":{"citing_paper":"/paper/2603.23196"},"observation_digest":"sha256:5370e48a502df95ea2b8f984b32bb1370bda4fece8f121e0739d576bf6a4e0ef","observation_id":"a411d379-c733-4e82-bb84-3cb35727ddca","resolution":{"observed_at":"2026-07-13T19:47:15.974727Z","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":"2026-07-13T19:47:15.974727Z","title":"On the nonparametric maximum likelihood estimator for gaussian location mixture densities with application to gaussian denoising.The Annals of Statistics, 48(2):738–762, 2020","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2603.23196","last_updated":"2026-07-08T14:24:44Z","snapshot_observed_at":"2026-08-04T09:43:12.488687Z","submitted_at":"2026-03-24T13:42:57Z","title":"Gaussian mixtures and non-parametric likelihoods through the lens of statistical mechanics","version":2},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-07-13T19:47:15.974727Z"},"links":{"citing_paper":"/paper/2603.23196"},"observation_digest":"sha256:ecbf8beabf09e0ca27bfe5afe8f9e6288d04ad4a06ebacedec3b1e0abf50ce51","observation_id":"0752b1c9-2dad-4154-bf28-18134557cf03","resolution":{"observed_at":"2026-07-13T19:47:15.974727Z","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":"2026-07-13T19:47:15.974727Z","title":"Multivariate, heteroscedastic empirical bayes via nonparametric maximum likelihood.Journal of the Royal Statistical Society Series B: Statistical Methodology, 87(1):1–32, 05 2024","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2603.23196","last_updated":"2026-07-08T14:24:44Z","snapshot_observed_at":"2026-08-04T09:43:12.488687Z","submitted_at":"2026-03-24T13:42:57Z","title":"Gaussian mixtures and non-parametric likelihoods through the lens of statistical mechanics","version":2},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-07-13T19:47:15.974727Z"},"links":{"citing_paper":"/paper/2603.23196"},"observation_digest":"sha256:a6f26303d8ab33380657863a262a8d5344724cd96dd3280587adf7ec624731f6","observation_id":"bc4e6dc0-5123-4b7b-a80c-964b604b0bfc","resolution":{"observed_at":"2026-07-13T19:47:15.974727Z","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":"2026-07-13T19:47:15.974727Z","title":"Finite mixture distributions., 1981","venue":null,"work_id":null,"year":1981},"citing_paper":{"arxiv_id":"2603.23196","last_updated":"2026-07-08T14:24:44Z","snapshot_observed_at":"2026-08-04T09:43:12.488687Z","submitted_at":"2026-03-24T13:42:57Z","title":"Gaussian mixtures and non-parametric likelihoods through the lens of statistical mechanics","version":2},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-07-13T19:47:15.974727Z"},"links":{"citing_paper":"/paper/2603.23196"},"observation_digest":"sha256:06c539f589ae312cd2142f85403f0c2239ff07a77b4c57dd0b6a805624502bcd","observation_id":"8245d101-9ef6-43b5-8a29-386d84b0daab","resolution":{"observed_at":"2026-07-13T19:47:15.974727Z","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":"2026-07-13T19:47:15.974727Z","title":"Cambridge university press, 2000","venue":null,"work_id":null,"year":2000},"citing_paper":{"arxiv_id":"2603.23196","last_updated":"2026-07-08T14:24:44Z","snapshot_observed_at":"2026-08-04T09:43:12.488687Z","submitted_at":"2026-03-24T13:42:57Z","title":"Gaussian mixtures and non-parametric likelihoods through the lens of statistical mechanics","version":2},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-07-13T19:47:15.974727Z"},"links":{"citing_paper":"/paper/2603.23196"},"observation_digest":"sha256:dfa078b63a583b5c29f7902595b75d5b4750b6ac60a5b9791d7a4a99e8cdd804","observation_id":"9a7f5ff3-f5ff-489b-a637-20d5a403aca8","resolution":{"observed_at":"2026-07-13T19:47:15.974727Z","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":"2026-07-13T19:47:15.974727Z","title":"Probability inequalities for likelihood ratios and convergence rates of sieve mles.The Annals of Statistics, pages 339– 362, 1995","venue":null,"work_id":null,"year":1995},"citing_paper":{"arxiv_id":"2603.23196","last_updated":"2026-07-08T14:24:44Z","snapshot_observed_at":"2026-08-04T09:43:12.488687Z","submitted_at":"2026-03-24T13:42:57Z","title":"Gaussian mixtures and non-parametric likelihoods through the lens of statistical mechanics","version":2},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-07-13T19:47:15.974727Z"},"links":{"citing_paper":"/paper/2603.23196"},"observation_digest":"sha256:77799cc84de74a394d48245219340f0742d0c15fe980e830a0d048ba6b4b580d","observation_id":"9d6b5216-4a63-4001-a5cd-daa31d8ea365","resolution":{"observed_at":"2026-07-13T19:47:15.974727Z","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":"2026-07-13T19:47:15.974727Z","title":"Statistical physics of inference: Thresh- olds and algorithms.Advances in Physics, 65(5):453–552, 2016","venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2603.23196","last_updated":"2026-07-08T14:24:44Z","snapshot_observed_at":"2026-08-04T09:43:12.488687Z","submitted_at":"2026-03-24T13:42:57Z","title":"Gaussian mixtures and non-parametric likelihoods through the lens of statistical mechanics","version":2},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-07-13T19:47:15.974727Z"},"links":{"citing_paper":"/paper/2603.23196"},"observation_digest":"sha256:06f5476c0c137cda140df632fc5b65461fe44d35344335731c88e2f33d18d416","observation_id":"b3b4381a-7286-407e-b869-14f836992d07","resolution":{"observed_at":"2026-07-13T19:47:15.974727Z","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":"2026-07-13T19:47:15.974727Z","title":"Generalized maximum likelihood estimation of normal mixture densities.Statistica Sinica, pages 1297–1318, 2009","venue":null,"work_id":null,"year":2009},"citing_paper":{"arxiv_id":"2603.23196","last_updated":"2026-07-08T14:24:44Z","snapshot_observed_at":"2026-08-04T09:43:12.488687Z","submitted_at":"2026-03-24T13:42:57Z","title":"Gaussian mixtures and non-parametric likelihoods through the lens of statistical mechanics","version":2},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-07-13T19:47:15.974727Z"},"links":{"citing_paper":"/paper/2603.23196"},"observation_digest":"sha256:54b7e8f1431fb27fa0f61e5e4e37ac1cab4fc38184883a079d2720bae8f6762c","observation_id":"a78c1309-82b9-4bbe-8b76-484dd2038d9e","resolution":{"observed_at":"2026-07-13T19:47:15.974727Z","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":"2026-07-13T19:47:15.974727Z","title":"On efficient and scalable computation of the nonparametric maximum likelihood estimator in mixture models.Journal of Machine Learning Research, 25(8):1–46, 2024","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2603.23196","last_updated":"2026-07-08T14:24:44Z","snapshot_observed_at":"2026-08-04T09:43:12.488687Z","submitted_at":"2026-03-24T13:42:57Z","title":"Gaussian mixtures and non-parametric likelihoods through the lens of statistical mechanics","version":2},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-07-13T19:47:15.974727Z"},"links":{"citing_paper":"/paper/2603.23196"},"observation_digest":"sha256:76d14f3f6297f094c355b689188719910a280ad0d18b867802817ca0dd94e9d8","observation_id":"df71ebe6-be92-43e1-b5da-5ad5eabaee92","resolution":{"observed_at":"2026-07-13T19:47:15.974727Z","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":"2026-07-13T19:47:15.974727Z","title":"Deep autoencoding gaussian mixture model for unsuper- vised anomaly detection","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2603.23196","last_updated":"2026-07-08T14:24:44Z","snapshot_observed_at":"2026-08-04T09:43:12.488687Z","submitted_at":"2026-03-24T13:42:57Z","title":"Gaussian mixtures and non-parametric likelihoods through the lens of statistical mechanics","version":2},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-07-13T19:47:15.974727Z"},"links":{"citing_paper":"/paper/2603.23196"},"observation_digest":"sha256:6d8bcf2e5a08e01916905ba3d1e7d21c118f784630e48f7f0c7ce092e3969f9b","observation_id":"3764cad4-7d12-49d2-93ab-71a2075bd4fa","resolution":{"observed_at":"2026-07-13T19:47:15.974727Z","resolver_source":null,"status":"malformed_identifier"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2603.23196","last_updated":"2026-07-08T14:24:44Z","latest_version":2,"primary_category":"math.ST","snapshot_observed_at":"2026-08-04T09:43:12.488687Z","submitted_at":"2026-03-24T13:42:57Z","title":"Gaussian mixtures and non-parametric likelihoods through the lens of statistical mechanics"},"reference_resolution":{"displayed":37,"state_counts":{"malformed_identifier":1,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":36,"verified_exact":0,"verified_fuzzy":0},"total_outbound_references":37},"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 37 of 37 outbound references and 1 inbound Pith citation observation for arXiv:2603.23196."}