{"as_of":"2026-08-09T13:45:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:b7fd16a5ce7d84c83f14c06dcbcc6a7a7b14aca5db36fb4e88b04f6504997491","coverage":[{"denominator":53,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":53,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-06T19:42:18.505376Z","state":"measured"},{"denominator":58,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":58,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-09T06:31:02.800959+00:00","state":"measured"},{"denominator":5,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":5,"source":"paper_references, paper_reference_links","source_observed_at":"2026-06-29T22:42:40.840261Z","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":"2026-06-29T22:44:01.353689Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2507.05107","last_updated":"2025-07-07T15:25:54Z","snapshot_observed_at":"2026-08-06T19:29:56.334273Z","submitted_at":"2025-07-07T15:25:54Z","title":"DICE: Discrete inverse continuity equation for learning population dynamics","version":1},"cited_work":{"arxiv_id":"2507.05107","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2507.05107","snapshot_observed_at":"2026-06-29T22:44:01.353689Z","title":"arXiv preprint arXiv:2507.05107 , year=","venue":null,"work_id":"beeaccd6-4242-4e11-bedc-65975569b8aa","year":2025},"citing_paper":{"arxiv_id":"2604.07671","last_updated":"2026-04-09T00:26:30Z","snapshot_observed_at":"2026-08-02T07:35:17.794393Z","submitted_at":"2026-04-09T00:26:30Z","title":"On the Unique Recovery of Transport Maps and Vector Fields from Finite Measure-Valued Data","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-05-10T18:37:44.740900Z"},"links":{"cited_paper":"/paper/2507.05107","citing_paper":"/paper/2604.07671"},"observation_digest":"sha256:859138c5232190dcb2d0831152333b2b1385431237fefe09407a34d5a977a81e","observation_id":"f36ba70e-2c93-49bb-8a03-d30ebf1feb2a","resolution":{"observed_at":"2026-05-11T00:15:53.901775Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2507.05107","last_updated":"2025-07-07T15:25:54Z","snapshot_observed_at":"2026-08-06T19:29:56.334273Z","submitted_at":"2025-07-07T15:25:54Z","title":"DICE: Discrete inverse continuity equation for learning population dynamics","version":1},"cited_work":{"arxiv_id":"2507.05107","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2507.05107","snapshot_observed_at":"2026-06-29T22:44:01.353689Z","title":"arXiv preprint arXiv:2507.05107 , year=","venue":null,"work_id":"beeaccd6-4242-4e11-bedc-65975569b8aa","year":2025},"citing_paper":{"arxiv_id":"2605.08550","last_updated":"2026-05-16T02:31:48Z","snapshot_observed_at":"2026-08-07T01:11:37.151308Z","submitted_at":"2026-05-08T23:21:17Z","title":"A Call to Lagrangian Action: Learning Population Mechanics from Temporal Snapshots","version":1},"reference_index":45,"source":"arxiv_source","source_observed_at":"2026-05-12T01:20:12.816671Z"},"links":{"cited_paper":"/paper/2507.05107","citing_paper":"/paper/2605.08550"},"observation_digest":"sha256:f7f59b4c8fd5f0538d8f396acb4f89e6a9a14fe8bda33d93bdeb937b96ffb0e7","observation_id":"8d2f7063-be73-4957-a167-d9276c1a0126","resolution":{"observed_at":"2026-05-12T08:06:27.122156Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2507.05107","last_updated":"2025-07-07T15:25:54Z","snapshot_observed_at":"2026-08-06T19:29:56.334273Z","submitted_at":"2025-07-07T15:25:54Z","title":"DICE: Discrete inverse continuity equation for learning population dynamics","version":1},"cited_work":{"arxiv_id":"2507.05107","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2507.05107","snapshot_observed_at":"2026-06-29T22:44:01.353689Z","title":"arXiv preprint arXiv:2507.05107 , year=","venue":null,"work_id":"beeaccd6-4242-4e11-bedc-65975569b8aa","year":2025},"citing_paper":{"arxiv_id":"2605.08550","last_updated":"2026-05-16T02:31:48Z","snapshot_observed_at":"2026-08-07T01:11:37.151308Z","submitted_at":"2026-05-08T23:21:17Z","title":"A Call to Lagrangian Action: Learning Population Mechanics from Temporal Snapshots","version":2},"reference_index":45,"source":"arxiv_source","source_observed_at":"2026-05-14T20:49:26.890463Z"},"links":{"cited_paper":"/paper/2507.05107","citing_paper":"/paper/2605.08550"},"observation_digest":"sha256:9697508f8721bf376d45b8afbd0ebced1c2851fa138b9a19893935182582c333","observation_id":"daa62fc2-b4ff-4bc3-a9e8-1918280354a2","resolution":{"observed_at":"2026-05-14T20:52:59.181624Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2507.05107","last_updated":"2025-07-07T15:25:54Z","snapshot_observed_at":"2026-08-06T19:29:56.334273Z","submitted_at":"2025-07-07T15:25:54Z","title":"DICE: Discrete inverse continuity equation for learning population dynamics","version":1},"cited_work":{"arxiv_id":"2507.05107","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2507.05107","snapshot_observed_at":"2026-06-29T22:44:01.353689Z","title":"arXiv preprint arXiv:2507.05107 , year=","venue":null,"work_id":"beeaccd6-4242-4e11-bedc-65975569b8aa","year":2025},"citing_paper":{"arxiv_id":"2605.08550","last_updated":"2026-05-16T02:31:48Z","snapshot_observed_at":"2026-08-07T01:11:37.151308Z","submitted_at":"2026-05-08T23:21:17Z","title":"A Call to Lagrangian Action: Learning Population Mechanics from Temporal Snapshots","version":3},"reference_index":45,"source":"arxiv_source","source_observed_at":"2026-05-20T22:20:03.150386Z"},"links":{"cited_paper":"/paper/2507.05107","citing_paper":"/paper/2605.08550"},"observation_digest":"sha256:ff5784f6e7f67cc798dc4b613f247a00227301437f4aef2e4cac8b56d6cd2315","observation_id":"bee8af92-fdbf-46b6-941b-3053430d12b2","resolution":{"observed_at":"2026-05-20T22:23:48.127621Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2507.05107","last_updated":"2025-07-07T15:25:54Z","snapshot_observed_at":"2026-08-06T19:29:56.334273Z","submitted_at":"2025-07-07T15:25:54Z","title":"DICE: Discrete inverse continuity equation for learning population dynamics","version":1},"cited_work":{"arxiv_id":"2507.05107","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2507.05107","snapshot_observed_at":"2026-06-29T22:44:01.353689Z","title":"arXiv preprint arXiv:2507.05107 , year=","venue":null,"work_id":"beeaccd6-4242-4e11-bedc-65975569b8aa","year":2025},"citing_paper":{"arxiv_id":"2605.26285","last_updated":"2026-05-25T19:16:22Z","snapshot_observed_at":"2026-07-06T23:36:11.031436Z","submitted_at":"2026-05-25T19:16:22Z","title":"Two-Parameter Flows for Learning Population Dynamics of Physical Systems","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-06-29T22:42:40.840261Z"},"links":{"cited_paper":"/paper/2507.05107","citing_paper":"/paper/2605.26285"},"observation_digest":"sha256:510dd0c7e7f30ad6c9a8180a105a4f8190d5942590215460669b9ef0fb2918fb","observation_id":"3a9fa223-37d7-432f-bd71-fdc9ff378dc5","resolution":{"observed_at":"2026-06-29T22:44:01.355173Z","resolver_source":"arxiv_id","status":"metadata_mismatch"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}}],"links":{"evidence":"/evidence","html":"/paper/2507.05107/citation-record","integrity":"/paper/2507.05107/integrity","json":"/paper/2507.05107/citation-record.json","paper":"/paper/2507.05107"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:42:19.430291Z","title":"Marsden, and Tudor Ratiu","venue":null,"work_id":"426d7dba-d474-4fd3-b0d9-f0e3d3ae93f4","year":1988},"citing_paper":{"arxiv_id":"2507.05107","last_updated":"2025-07-07T15:25:54Z","snapshot_observed_at":"2026-08-06T19:29:56.334273Z","submitted_at":"2025-07-07T15:25:54Z","title":"DICE: Discrete inverse continuity equation for learning population dynamics","version":1},"reference_index":1,"source":"arxiv_source","source_observed_at":"2026-08-06T19:42:18.244251Z"},"links":{"citing_paper":"/paper/2507.05107"},"observation_digest":"sha256:5eb74107d988bf6242ecb05bafea1d6632f9ca04000d805e375fa3f064486bab","observation_id":"92aa8f0e-31ae-458a-acd2-250aff115b2e","resolution":{"observed_at":"2026-08-06T19:42:19.435202Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-06T19:42:18.250069Z","title":"Albergo and Eric Vanden-Eijnden","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2507.05107","last_updated":"2025-07-07T15:25:54Z","snapshot_observed_at":"2026-08-06T19:29:56.334273Z","submitted_at":"2025-07-07T15:25:54Z","title":"DICE: Discrete inverse continuity equation for learning population dynamics","version":1},"reference_index":2,"source":"arxiv_source","source_observed_at":"2026-08-06T19:42:18.250069Z"},"links":{"citing_paper":"/paper/2507.05107"},"observation_digest":"sha256:0121192b1a84e86ca60c792c3389aa39d1511e39d308fc8e6b100055bc2a1bd3","observation_id":"5ec4e842-96cf-4c13-a9f9-6ca9266ac8b3","resolution":{"observed_at":"2026-08-06T19:42:18.250069Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2303.08797","last_updated":"2025-10-09T00:43:44Z","snapshot_observed_at":"2026-07-06T15:03:52.079498Z","submitted_at":"2023-03-15T17:43:42Z","title":"Stochastic Interpolants: A Unifying Framework for Flows and Diffusions","version":4},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2303.08797","snapshot_observed_at":"2026-08-06T19:42:18.254800Z","title":"Albergo, Nicholas M","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2507.05107","last_updated":"2025-07-07T15:25:54Z","snapshot_observed_at":"2026-08-06T19:29:56.334273Z","submitted_at":"2025-07-07T15:25:54Z","title":"DICE: Discrete inverse continuity equation for learning population dynamics","version":1},"reference_index":3,"source":"arxiv_source","source_observed_at":"2026-08-06T19:42:18.254800Z"},"links":{"cited_paper":"/paper/2303.08797","citing_paper":"/paper/2507.05107"},"observation_digest":"sha256:2ecafdded11b5164e49144abc334329a23070798f561ee6f986cbe50b3ec4205","observation_id":"a749a958-13b9-496b-afa7-c13f1788a948","resolution":{"observed_at":"2026-08-06T19:42:18.254800Z","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":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:42:19.400564Z","title":"Alligood, Tim D","venue":null,"work_id":"6a5b12d0-3245-49be-95d6-b7744b497f5f","year":1996},"citing_paper":{"arxiv_id":"2507.05107","last_updated":"2025-07-07T15:25:54Z","snapshot_observed_at":"2026-08-06T19:29:56.334273Z","submitted_at":"2025-07-07T15:25:54Z","title":"DICE: Discrete inverse continuity equation for learning population dynamics","version":1},"reference_index":4,"source":"arxiv_source","source_observed_at":"2026-08-06T19:42:18.260470Z"},"links":{"citing_paper":"/paper/2507.05107"},"observation_digest":"sha256:e1a3d9ceeda54d177330f7592ace996a5aec3b805db4a9b19564786299df5a13","observation_id":"1c35f2a1-37a4-4983-84cc-5632a48fd537","resolution":{"observed_at":"2026-08-06T19:42:19.405323Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:42:19.383851Z","title":"Gradient Flows","venue":null,"work_id":"c8ff90c8-4211-41ec-a1da-96d8ea819ca0","year":2005},"citing_paper":{"arxiv_id":"2507.05107","last_updated":"2025-07-07T15:25:54Z","snapshot_observed_at":"2026-08-06T19:29:56.334273Z","submitted_at":"2025-07-07T15:25:54Z","title":"DICE: Discrete inverse continuity equation for learning population dynamics","version":1},"reference_index":5,"source":"arxiv_source","source_observed_at":"2026-08-06T19:42:18.265524Z"},"links":{"citing_paper":"/paper/2507.05107"},"observation_digest":"sha256:7565a8815cc1ed247aab3f1d5d0683501d921a17ca0e8a8ddca45a65a0281d70","observation_id":"0932cb23-5117-4b2f-a884-98688470f23a","resolution":{"observed_at":"2026-08-06T19:42:19.389060Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:42:19.362533Z","title":"A simple proof of the Poincaré inequality for a large class of probability measures","venue":null,"work_id":"7fc21e7d-7df5-4ec2-a9e5-af2ad771253d","year":2008},"citing_paper":{"arxiv_id":"2507.05107","last_updated":"2025-07-07T15:25:54Z","snapshot_observed_at":"2026-08-06T19:29:56.334273Z","submitted_at":"2025-07-07T15:25:54Z","title":"DICE: Discrete inverse continuity equation for learning population dynamics","version":1},"reference_index":6,"source":"arxiv_source","source_observed_at":"2026-08-06T19:42:18.272657Z"},"links":{"citing_paper":"/paper/2507.05107"},"observation_digest":"sha256:529c18deb067c43f4d1258c656c49f13144daff185e69f681fd7e03a620045ab","observation_id":"d96147ca-5255-47a1-ae07-8143fc43a6a5","resolution":{"observed_at":"2026-08-06T19:42:19.369749Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:42:19.345191Z","title":"A computational fluid mechanics solution to the Monge - Kantorovich mass transfer problem","venue":null,"work_id":"09a84e7a-631b-4d13-a25b-c80ec47d978a","year":2000},"citing_paper":{"arxiv_id":"2507.05107","last_updated":"2025-07-07T15:25:54Z","snapshot_observed_at":"2026-08-06T19:29:56.334273Z","submitted_at":"2025-07-07T15:25:54Z","title":"DICE: Discrete inverse continuity equation for learning population dynamics","version":1},"reference_index":7,"source":"arxiv_source","source_observed_at":"2026-08-06T19:42:18.278097Z"},"links":{"citing_paper":"/paper/2507.05107"},"observation_digest":"sha256:3cd227011381b072ec860f1c2680e781b4e5dab2d65b16dadff26b22da77f376","observation_id":"4d804532-5e84-4a9e-9bf1-ea2c93faaff4","resolution":{"observed_at":"2026-08-06T19:42:19.351333Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:42:19.327246Z","title":"Gallouët, and François-Xavier Vialard","venue":null,"work_id":"f299a279-d7af-4515-ae62-4409c4361579","year":2019},"citing_paper":{"arxiv_id":"2507.05107","last_updated":"2025-07-07T15:25:54Z","snapshot_observed_at":"2026-08-06T19:29:56.334273Z","submitted_at":"2025-07-07T15:25:54Z","title":"DICE: Discrete inverse continuity equation for learning population dynamics","version":1},"reference_index":8,"source":"arxiv_source","source_observed_at":"2026-08-06T19:42:18.282394Z"},"links":{"citing_paper":"/paper/2507.05107"},"observation_digest":"sha256:ad03a465f3f27dd8c28e8c16807692d218f2c9282471ae4b897690f06a30a446","observation_id":"c1a9034e-1a03-4f34-b583-b1c08b923708","resolution":{"observed_at":"2026-08-06T19:42:19.332578Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:42:19.309352Z","title":"A survey of projection-based model reduction methods for parametric dynamical systems","venue":null,"work_id":"228bba84-3c62-45ae-951d-8996f0f86c96","year":2015},"citing_paper":{"arxiv_id":"2507.05107","last_updated":"2025-07-07T15:25:54Z","snapshot_observed_at":"2026-08-06T19:29:56.334273Z","submitted_at":"2025-07-07T15:25:54Z","title":"DICE: Discrete inverse continuity equation for learning population dynamics","version":1},"reference_index":9,"source":"arxiv_source","source_observed_at":"2026-08-06T19:42:18.286803Z"},"links":{"citing_paper":"/paper/2507.05107"},"observation_digest":"sha256:2a2c7e4710c15155bb9cf2c03a445f5b7480f7f7ffe586bc31d897f864312480","observation_id":"74c9e192-2714-4170-9ffc-fb7395fabe89","resolution":{"observed_at":"2026-08-06T19:42:19.314522Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:42:19.288912Z","title":"Parametric model reduction of mean-field and stochastic systems via higher-order action matching","venue":null,"work_id":"1192bdd0-ad12-427b-9b0a-1560d3c02669","year":2024},"citing_paper":{"arxiv_id":"2507.05107","last_updated":"2025-07-07T15:25:54Z","snapshot_observed_at":"2026-08-06T19:29:56.334273Z","submitted_at":"2025-07-07T15:25:54Z","title":"DICE: Discrete inverse continuity equation for learning population dynamics","version":1},"reference_index":10,"source":"arxiv_source","source_observed_at":"2026-08-06T19:42:18.291627Z"},"links":{"citing_paper":"/paper/2507.05107"},"observation_digest":"sha256:be059e316ee340f2e0527c178664f33accc633d40b76d6b23715726652aafca0","observation_id":"4166a84d-fd5f-45c5-b770-725f2efbc6b7","resolution":{"observed_at":"2026-08-06T19:42:19.296246Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:42:19.269539Z","title":"A registration method for reduced basis problems using linear optimal transport","venue":null,"work_id":"6a427bbf-2fc6-4157-aaa3-83e12eec2691","year":2024},"citing_paper":{"arxiv_id":"2507.05107","last_updated":"2025-07-07T15:25:54Z","snapshot_observed_at":"2026-08-06T19:29:56.334273Z","submitted_at":"2025-07-07T15:25:54Z","title":"DICE: Discrete inverse continuity equation for learning population dynamics","version":1},"reference_index":11,"source":"arxiv_source","source_observed_at":"2026-08-06T19:42:18.296374Z"},"links":{"citing_paper":"/paper/2507.05107"},"observation_digest":"sha256:9ec33e86fece931164f1457343be31206cc449a4b040222f2f43ec537db735a9","observation_id":"c332b139-6ea3-409c-9dd5-716a61b5f5e5","resolution":{"observed_at":"2026-08-06T19:42:19.275012Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:42:19.248960Z","title":"Supervised training of conditional Monge maps","venue":null,"work_id":"fbcce03f-56f4-45f2-acad-34a4437192fd","year":2022},"citing_paper":{"arxiv_id":"2507.05107","last_updated":"2025-07-07T15:25:54Z","snapshot_observed_at":"2026-08-06T19:29:56.334273Z","submitted_at":"2025-07-07T15:25:54Z","title":"DICE: Discrete inverse continuity equation for learning population dynamics","version":1},"reference_index":12,"source":"arxiv_source","source_observed_at":"2026-08-06T19:42:18.301058Z"},"links":{"citing_paper":"/paper/2507.05107"},"observation_digest":"sha256:7828e906685f8f7922c9fb3376bed71850455667bf337bbe4f0cd4160d063f25","observation_id":"50d3e388-713f-4bb3-a904-71cb38514ed7","resolution":{"observed_at":"2026-08-06T19:42:19.256595Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:42:19.229727Z","title":"Proximal optimal transport modeling of population dynamics","venue":null,"work_id":"1a4a97f3-05f6-4dbc-b86a-1d71564a7b5f","year":2022},"citing_paper":{"arxiv_id":"2507.05107","last_updated":"2025-07-07T15:25:54Z","snapshot_observed_at":"2026-08-06T19:29:56.334273Z","submitted_at":"2025-07-07T15:25:54Z","title":"DICE: Discrete inverse continuity equation for learning population dynamics","version":1},"reference_index":13,"source":"arxiv_source","source_observed_at":"2026-08-06T19:42:18.305642Z"},"links":{"citing_paper":"/paper/2507.05107"},"observation_digest":"sha256:98214e076cd40ce3872a2c8285ac85967ad1a3430febd6b1fbb3b77d6a7df0f2","observation_id":"48ce603d-4af8-4fa1-b547-a2607b0be7df","resolution":{"observed_at":"2026-08-06T19:42:19.235104Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:42:19.212222Z","title":"Deep momentum multi-marginal S chr\\\" o dinger bridge","venue":null,"work_id":"47c1c7f4-29e8-4ba5-890e-a43a9caf2ab9","year":2023},"citing_paper":{"arxiv_id":"2507.05107","last_updated":"2025-07-07T15:25:54Z","snapshot_observed_at":"2026-08-06T19:29:56.334273Z","submitted_at":"2025-07-07T15:25:54Z","title":"DICE: Discrete inverse continuity equation for learning population dynamics","version":1},"reference_index":14,"source":"arxiv_source","source_observed_at":"2026-08-06T19:42:18.310412Z"},"links":{"citing_paper":"/paper/2507.05107"},"observation_digest":"sha256:355e848a3ebd8c587fb663588f4907023422df044574098d9a45835bdcf51f3c","observation_id":"7b183162-8293-4ed5-adc8-485fca84a895","resolution":{"observed_at":"2026-08-06T19:42:19.217487Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:42:19.193320Z","title":"Fast and smooth interpolation on wasserstein space","venue":null,"work_id":"ddeff643-7ee5-4868-ade8-537f7ca32884","year":2021},"citing_paper":{"arxiv_id":"2507.05107","last_updated":"2025-07-07T15:25:54Z","snapshot_observed_at":"2026-08-06T19:29:56.334273Z","submitted_at":"2025-07-07T15:25:54Z","title":"DICE: Discrete inverse continuity equation for learning population dynamics","version":1},"reference_index":15,"source":"arxiv_source","source_observed_at":"2026-08-06T19:42:18.314988Z"},"links":{"citing_paper":"/paper/2507.05107"},"observation_digest":"sha256:4886ebf7f062ce561dc54358c8839bb5cbad39e8f71e7435c370e22283dba5f1","observation_id":"da343cd0-2d11-4a26-8f79-3621ad047ef2","resolution":{"observed_at":"2026-08-06T19:42:19.198551Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:42:19.169464Z","title":"Nonlinear model reduction on metric spaces","venue":null,"work_id":"83b5b23a-0890-4bb1-8195-463b3aac7dbb","year":2020},"citing_paper":{"arxiv_id":"2507.05107","last_updated":"2025-07-07T15:25:54Z","snapshot_observed_at":"2026-08-06T19:29:56.334273Z","submitted_at":"2025-07-07T15:25:54Z","title":"DICE: Discrete inverse continuity equation for learning population dynamics","version":1},"reference_index":16,"source":"arxiv_source","source_observed_at":"2026-08-06T19:42:18.320224Z"},"links":{"citing_paper":"/paper/2507.05107"},"observation_digest":"sha256:4c7579c16b4e671be1880ebbaf943de6b3cf81e97abaacc539fc9b0baf2ac468","observation_id":"ff37be7c-a28e-4004-be8f-ae3bd370ddf6","resolution":{"observed_at":"2026-08-06T19:42:19.174849Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:42:19.151412Z","title":"Second order analysis on ( P _2(M), W_2 )","venue":null,"work_id":"a35e6cbb-3381-47ca-bea4-38f71a5f5947","year":2011},"citing_paper":{"arxiv_id":"2507.05107","last_updated":"2025-07-07T15:25:54Z","snapshot_observed_at":"2026-08-06T19:29:56.334273Z","submitted_at":"2025-07-07T15:25:54Z","title":"DICE: Discrete inverse continuity equation for learning population dynamics","version":1},"reference_index":17,"source":"arxiv_source","source_observed_at":"2026-08-06T19:42:18.324923Z"},"links":{"citing_paper":"/paper/2507.05107"},"observation_digest":"sha256:87b62ae26562adbb8fc84dad44e43a423a6509c645fd6e425650667bde757d1c","observation_id":"428ee039-f59b-484e-9e38-230877022ff7","resolution":{"observed_at":"2026-08-06T19:42:19.156757Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:42:19.132130Z","title":"Trudinger","venue":null,"work_id":"19875b71-63c4-4642-be4d-988abed166d2","year":2001},"citing_paper":{"arxiv_id":"2507.05107","last_updated":"2025-07-07T15:25:54Z","snapshot_observed_at":"2026-08-06T19:29:56.334273Z","submitted_at":"2025-07-07T15:25:54Z","title":"DICE: Discrete inverse continuity equation for learning population dynamics","version":1},"reference_index":18,"source":"arxiv_source","source_observed_at":"2026-08-06T19:42:18.329740Z"},"links":{"citing_paper":"/paper/2507.05107"},"observation_digest":"sha256:d8c4f6cf53f8707c639d086be64fe16a7b7878b29921d2769a33ade489188deb","observation_id":"056336b6-8059-4c02-9aa9-3b0b08d4d4e1","resolution":{"observed_at":"2026-08-06T19:42:19.137012Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2503.00530","last_updated":"2025-03-01T15:12:01Z","snapshot_observed_at":"2026-08-07T17:37:10.254539Z","submitted_at":"2025-03-01T15:12:01Z","title":"Trajectory Inference with Smooth Schr\\\"odinger Bridges","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2503.00530","snapshot_observed_at":"2026-08-06T19:42:18.336827Z","title":"Trajectory inference with smooth Schrödinger bridges","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2507.05107","last_updated":"2025-07-07T15:25:54Z","snapshot_observed_at":"2026-08-06T19:29:56.334273Z","submitted_at":"2025-07-07T15:25:54Z","title":"DICE: Discrete inverse continuity equation for learning population dynamics","version":1},"reference_index":19,"source":"arxiv_source","source_observed_at":"2026-08-06T19:42:18.336827Z"},"links":{"cited_paper":"/paper/2503.00530","citing_paper":"/paper/2507.05107"},"observation_digest":"sha256:8405c4f2a51c8200bb9435940ffd3efcc56c227afeadbbaafa0213cff5c18fca","observation_id":"82cc4f49-6f28-4686-8ec1-1e86afb803cc","resolution":{"observed_at":"2026-08-06T19:42:18.336827Z","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":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:42:19.114499Z","title":"Mapping of coherent structures in parameterized flows by learning optimal transportation with Gaussian models","venue":null,"work_id":"10e35598-1122-4bc4-8ddf-6242f7b20367","year":2022},"citing_paper":{"arxiv_id":"2507.05107","last_updated":"2025-07-07T15:25:54Z","snapshot_observed_at":"2026-08-06T19:29:56.334273Z","submitted_at":"2025-07-07T15:25:54Z","title":"DICE: Discrete inverse continuity equation for learning population dynamics","version":1},"reference_index":20,"source":"arxiv_source","source_observed_at":"2026-08-06T19:42:18.342047Z"},"links":{"citing_paper":"/paper/2507.05107"},"observation_digest":"sha256:1d1dd799558ba54012e6b6e0ec348a3bca5236ad615c9dcbe9fb1df76fec27bf","observation_id":"e3f5236a-c4f3-498d-8c2b-970d8872682b","resolution":{"observed_at":"2026-08-06T19:42:19.119466Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:42:19.098854Z","title":"The variational formulation of the Fokker -- Planck equation","venue":null,"work_id":"9e4eb05b-c8a4-48c6-8481-2fdced27727d","year":1998},"citing_paper":{"arxiv_id":"2507.05107","last_updated":"2025-07-07T15:25:54Z","snapshot_observed_at":"2026-08-06T19:29:56.334273Z","submitted_at":"2025-07-07T15:25:54Z","title":"DICE: Discrete inverse continuity equation for learning population dynamics","version":1},"reference_index":21,"source":"arxiv_source","source_observed_at":"2026-08-06T19:42:18.348169Z"},"links":{"citing_paper":"/paper/2507.05107"},"observation_digest":"sha256:6b516d2e7fb094d9a2c02549673fb02d5aec42f5e67cb1671ea1305eae182d41","observation_id":"55e1d6b6-8a87-4963-9081-0cc025c07f53","resolution":{"observed_at":"2026-08-06T19:42:19.103449Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:42:19.082634Z","title":"Optimal transport–inspired deep learning framework for slow-decaying K olmogorov n -width problems: E xploiting S inkhorn loss and W asserstein kernel","venue":null,"work_id":"c6d93aef-35aa-4fef-b239-a18c405efc17","year":2025},"citing_paper":{"arxiv_id":"2507.05107","last_updated":"2025-07-07T15:25:54Z","snapshot_observed_at":"2026-08-06T19:29:56.334273Z","submitted_at":"2025-07-07T15:25:54Z","title":"DICE: Discrete inverse continuity equation for learning population dynamics","version":1},"reference_index":22,"source":"arxiv_source","source_observed_at":"2026-08-06T19:42:18.352856Z"},"links":{"citing_paper":"/paper/2507.05107"},"observation_digest":"sha256:2792c316fc9329070490bc8209abf1e0e3d88af1789c61ed809e79659aeae683","observation_id":"e698bc90-b3df-4960-b71b-eef2d6bcfb7a","resolution":{"observed_at":"2026-08-06T19:42:19.087624Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:42:19.066008Z","title":null,"venue":null,"work_id":"20cf6995-b9ad-4c60-9d61-0310dc02fc4b","year":2024},"citing_paper":{"arxiv_id":"2507.05107","last_updated":"2025-07-07T15:25:54Z","snapshot_observed_at":"2026-08-06T19:29:56.334273Z","submitted_at":"2025-07-07T15:25:54Z","title":"DICE: Discrete inverse continuity equation for learning population dynamics","version":1},"reference_index":23,"source":"arxiv_source","source_observed_at":"2026-08-06T19:42:18.357713Z"},"links":{"citing_paper":"/paper/2507.05107"},"observation_digest":"sha256:87f1d3c7a887d3e44f1576df7aa44889f4d6d36180ea87a448811cd38504cb97","observation_id":"a9129e3d-0a5e-49f5-a7ef-055244ca94eb","resolution":{"observed_at":"2026-08-06T19:42:19.071762Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:42:19.047283Z","title":"Toward a mathematical theory of trajectory inference","venue":null,"work_id":"6100176d-5942-42f9-98aa-6a551f1f13b9","year":2024},"citing_paper":{"arxiv_id":"2507.05107","last_updated":"2025-07-07T15:25:54Z","snapshot_observed_at":"2026-08-06T19:29:56.334273Z","submitted_at":"2025-07-07T15:25:54Z","title":"DICE: Discrete inverse continuity equation for learning population dynamics","version":1},"reference_index":24,"source":"arxiv_source","source_observed_at":"2026-08-06T19:42:18.362688Z"},"links":{"citing_paper":"/paper/2507.05107"},"observation_digest":"sha256:01ac2cc314c93a0f043a5900c2bba59c3b3aad1e27af2db79688c84596f82b35","observation_id":"fe798559-ea8b-40c4-a192-29250e84168c","resolution":{"observed_at":"2026-08-06T19:42:19.052639Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:42:19.027614Z","title":"Deep JKO : Time -implicit particle methods for general nonlinear gradient flows","venue":null,"work_id":"5e866ce3-d392-468b-94d3-f263dfccabe1","year":2024},"citing_paper":{"arxiv_id":"2507.05107","last_updated":"2025-07-07T15:25:54Z","snapshot_observed_at":"2026-08-06T19:29:56.334273Z","submitted_at":"2025-07-07T15:25:54Z","title":"DICE: Discrete inverse continuity equation for learning population dynamics","version":1},"reference_index":25,"source":"arxiv_source","source_observed_at":"2026-08-06T19:42:18.367969Z"},"links":{"citing_paper":"/paper/2507.05107"},"observation_digest":"sha256:8679e752503380cfc878a92cef153ad1c5aa55b3621e4f3eaf9971e8303812e8","observation_id":"37e32cea-6de6-42e1-8ad3-e2b35b62c94d","resolution":{"observed_at":"2026-08-06T19:42:19.032304Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:42:19.012344Z","title":null,"venue":null,"work_id":"b08a92b6-005c-47d5-be99-04e0f06ebc85","year":2023},"citing_paper":{"arxiv_id":"2507.05107","last_updated":"2025-07-07T15:25:54Z","snapshot_observed_at":"2026-08-06T19:29:56.334273Z","submitted_at":"2025-07-07T15:25:54Z","title":"DICE: Discrete inverse continuity equation for learning population dynamics","version":1},"reference_index":26,"source":"arxiv_source","source_observed_at":"2026-08-06T19:42:18.372352Z"},"links":{"citing_paper":"/paper/2507.05107"},"observation_digest":"sha256:72009f123fd5663189819c51d2a494ffe2ed3e5efbb7eb1dae82adee37603c6c","observation_id":"810e070e-5ba4-4d42-b66e-57571804bd61","resolution":{"observed_at":"2026-08-06T19:42:19.016873Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:42:18.994845Z","title":"Flow Straight and Fast : Learning to generate and transfer data with rectified flow","venue":null,"work_id":"8015bcfd-cc2e-4d8c-86bc-952b1351b99b","year":2023},"citing_paper":{"arxiv_id":"2507.05107","last_updated":"2025-07-07T15:25:54Z","snapshot_observed_at":"2026-08-06T19:29:56.334273Z","submitted_at":"2025-07-07T15:25:54Z","title":"DICE: Discrete inverse continuity equation for learning population dynamics","version":1},"reference_index":27,"source":"arxiv_source","source_observed_at":"2026-08-06T19:42:18.376779Z"},"links":{"citing_paper":"/paper/2507.05107"},"observation_digest":"sha256:a8aa9956782f3d5e7bf3d4e208523c4446b8fe4c282843e75f55fe21eddabda8","observation_id":"e2d463fc-48dd-4b1e-a685-7938145e0752","resolution":{"observed_at":"2026-08-06T19:42:18.999813Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:42:18.979569Z","title":null,"venue":null,"work_id":"fcf60910-b50c-4599-a4e7-b670307ab79a","year":1963},"citing_paper":{"arxiv_id":"2507.05107","last_updated":"2025-07-07T15:25:54Z","snapshot_observed_at":"2026-08-06T19:29:56.334273Z","submitted_at":"2025-07-07T15:25:54Z","title":"DICE: Discrete inverse continuity equation for learning population dynamics","version":1},"reference_index":28,"source":"arxiv_source","source_observed_at":"2026-08-06T19:42:18.381420Z"},"links":{"citing_paper":"/paper/2507.05107"},"observation_digest":"sha256:167bb5d42e3e5274fbfe3be96df4fe030124169aff73ec10376dbde12ee76fe7","observation_id":"462f15ef-6d09-45f0-9cb1-b683db2a062f","resolution":{"observed_at":"2026-08-06T19:42:18.984190Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:42:18.963591Z","title":"A survey of the Schrödinger problem and some of its connections with optimal transport","venue":null,"work_id":"246518b0-2aca-4951-a86c-46e9570a73b5","year":2014},"citing_paper":{"arxiv_id":"2507.05107","last_updated":"2025-07-07T15:25:54Z","snapshot_observed_at":"2026-08-06T19:29:56.334273Z","submitted_at":"2025-07-07T15:25:54Z","title":"DICE: Discrete inverse continuity equation for learning population dynamics","version":1},"reference_index":29,"source":"arxiv_source","source_observed_at":"2026-08-06T19:42:18.385685Z"},"links":{"citing_paper":"/paper/2507.05107"},"observation_digest":"sha256:a0af32c2ae5d573c8cd92e6933baa2300945cf348d1c30c101ae73fcfce03d68","observation_id":"4c23dbf5-a697-4a26-9fb6-9480dcc24f25","resolution":{"observed_at":"2026-08-06T19:42:18.968233Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:42:18.946707Z","title":"Ergodicity for SDEs and approximations: locally Lipschitz vector fields and degenerate noise","venue":null,"work_id":"2d21e005-8d57-4b31-b9c8-819a132655fb","year":2002},"citing_paper":{"arxiv_id":"2507.05107","last_updated":"2025-07-07T15:25:54Z","snapshot_observed_at":"2026-08-06T19:29:56.334273Z","submitted_at":"2025-07-07T15:25:54Z","title":"DICE: Discrete inverse continuity equation for learning population dynamics","version":1},"reference_index":30,"source":"arxiv_source","source_observed_at":"2026-08-06T19:42:18.390097Z"},"links":{"citing_paper":"/paper/2507.05107"},"observation_digest":"sha256:cafb287e9dc63d041afbe1dfaf005633285ebcb81e51ad120b71141fbadde9e9","observation_id":"54db64c5-b423-40a5-9b79-5511af8f5c1a","resolution":{"observed_at":"2026-08-06T19:42:18.951700Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:42:18.931622Z","title":"Sampling in unit time with kernel F isher-rao flow","venue":null,"work_id":"3b8d2a5d-0828-437b-a968-221a08e49e55","year":2024},"citing_paper":{"arxiv_id":"2507.05107","last_updated":"2025-07-07T15:25:54Z","snapshot_observed_at":"2026-08-06T19:29:56.334273Z","submitted_at":"2025-07-07T15:25:54Z","title":"DICE: Discrete inverse continuity equation for learning population dynamics","version":1},"reference_index":31,"source":"arxiv_source","source_observed_at":"2026-08-06T19:42:18.394538Z"},"links":{"citing_paper":"/paper/2507.05107"},"observation_digest":"sha256:8e6fb1e1984a76b2c6552ef387c22284fb7f360115ccf67a99884b4aa79e07d8","observation_id":"bcfa98d1-42c9-4df2-b91b-409515e8f7f1","resolution":{"observed_at":"2026-08-06T19:42:18.936127Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:42:18.916205Z","title":"Almost sure invariance principle for nonuniformly hyperbolic systems","venue":null,"work_id":"971f31ac-f24b-46ce-a35e-69dba99d84b2","year":2005},"citing_paper":{"arxiv_id":"2507.05107","last_updated":"2025-07-07T15:25:54Z","snapshot_observed_at":"2026-08-06T19:29:56.334273Z","submitted_at":"2025-07-07T15:25:54Z","title":"DICE: Discrete inverse continuity equation for learning population dynamics","version":1},"reference_index":32,"source":"arxiv_source","source_observed_at":"2026-08-06T19:42:18.398966Z"},"links":{"citing_paper":"/paper/2507.05107"},"observation_digest":"sha256:5b1c6c1071db9c8bf9263635646c6210cdf9e3be83b6588b4ea4f5e1659f4535","observation_id":"6213a6af-c4f9-45d3-bdcd-29236618916b","resolution":{"observed_at":"2026-08-06T19:42:18.921035Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:42:18.900829Z","title":"Large deviations for nonuniformly hyperbolic systems","venue":null,"work_id":"74b5ba40-631a-43a9-a535-2d8284b8f233","year":2008},"citing_paper":{"arxiv_id":"2507.05107","last_updated":"2025-07-07T15:25:54Z","snapshot_observed_at":"2026-08-06T19:29:56.334273Z","submitted_at":"2025-07-07T15:25:54Z","title":"DICE: Discrete inverse continuity equation for learning population dynamics","version":1},"reference_index":33,"source":"arxiv_source","source_observed_at":"2026-08-06T19:42:18.403679Z"},"links":{"citing_paper":"/paper/2507.05107"},"observation_digest":"sha256:8f3454cc9047d3e667bc1987e9dad9afea22410016b177c99616b7ac83baf9bb","observation_id":"8ba6c147-92d2-4181-870d-ac88c8796306","resolution":{"observed_at":"2026-08-06T19:42:18.905863Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:42:18.885285Z","title":"Thiéry, Kainan Wang, and Tan Bui-Thanh","venue":null,"work_id":"4a613ec6-a07e-4d9a-8473-2474f293ac19","year":2021},"citing_paper":{"arxiv_id":"2507.05107","last_updated":"2025-07-07T15:25:54Z","snapshot_observed_at":"2026-08-06T19:29:56.334273Z","submitted_at":"2025-07-07T15:25:54Z","title":"DICE: Discrete inverse continuity equation for learning population dynamics","version":1},"reference_index":34,"source":"arxiv_source","source_observed_at":"2026-08-06T19:42:18.408238Z"},"links":{"citing_paper":"/paper/2507.05107"},"observation_digest":"sha256:94153c97232680c1ff9ae45fe8b1fe6fa64bb619f8646f567d82ca2c70801568","observation_id":"c9844a73-d166-44d8-8054-7a80fbef728f","resolution":{"observed_at":"2026-08-06T19:42:18.889833Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:42:18.868566Z","title":"Action Matching : Learning stochastic dynamics from samples","venue":null,"work_id":"a3360285-8086-44c9-ae18-3d0dca4c0139","year":2023},"citing_paper":{"arxiv_id":"2507.05107","last_updated":"2025-07-07T15:25:54Z","snapshot_observed_at":"2026-08-06T19:29:56.334273Z","submitted_at":"2025-07-07T15:25:54Z","title":"DICE: Discrete inverse continuity equation for learning population dynamics","version":1},"reference_index":35,"source":"arxiv_source","source_observed_at":"2026-08-06T19:42:18.412900Z"},"links":{"citing_paper":"/paper/2507.05107"},"observation_digest":"sha256:573cee5f5fcb6e7b2c1ae550f8944c9edf0bf05f20fef5f0793cc25e2b7ce589","observation_id":"2f730f01-855c-48e7-a330-906c8599ca60","resolution":{"observed_at":"2026-08-06T19:42:18.873504Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:42:18.853194Z","title":"OT-Flow : Fast and accurate continuous normalizing flows via optimal transport","venue":null,"work_id":"f8b4350a-9578-402f-834d-d5fc7b565e53","year":2021},"citing_paper":{"arxiv_id":"2507.05107","last_updated":"2025-07-07T15:25:54Z","snapshot_observed_at":"2026-08-06T19:29:56.334273Z","submitted_at":"2025-07-07T15:25:54Z","title":"DICE: Discrete inverse continuity equation for learning population dynamics","version":1},"reference_index":36,"source":"arxiv_source","source_observed_at":"2026-08-06T19:42:18.417928Z"},"links":{"citing_paper":"/paper/2507.05107"},"observation_digest":"sha256:396b0372bb00fbcf853ac8767c8a73d65a45c84747a8a8fa844d5bd5f948274e","observation_id":"86d2bd1f-a5ef-4453-893f-9cc06e1a88ea","resolution":{"observed_at":"2026-08-06T19:42:18.857852Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:42:18.835740Z","title":"The geometry of dissipative evolution equations: the porous medium equation","venue":null,"work_id":"43e010da-a75a-4c61-9f06-4110a5ecc926","year":2001},"citing_paper":{"arxiv_id":"2507.05107","last_updated":"2025-07-07T15:25:54Z","snapshot_observed_at":"2026-08-06T19:29:56.334273Z","submitted_at":"2025-07-07T15:25:54Z","title":"DICE: Discrete inverse continuity equation for learning population dynamics","version":1},"reference_index":37,"source":"arxiv_source","source_observed_at":"2026-08-06T19:42:18.422127Z"},"links":{"citing_paper":"/paper/2507.05107"},"observation_digest":"sha256:1fc6e8124d5af1c26a9980c0809fcc235559871d4135c369acafeac91a03dc38","observation_id":"4bbc1c8d-f544-41f9-85b4-aea8e59e55fd","resolution":{"observed_at":"2026-08-06T19:42:18.841535Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:42:18.818614Z","title":"Peherstorfer","venue":null,"work_id":"2abb2864-8b50-41a0-a199-be157b236f26","year":2022},"citing_paper":{"arxiv_id":"2507.05107","last_updated":"2025-07-07T15:25:54Z","snapshot_observed_at":"2026-08-06T19:29:56.334273Z","submitted_at":"2025-07-07T15:25:54Z","title":"DICE: Discrete inverse continuity equation for learning population dynamics","version":1},"reference_index":38,"source":"arxiv_source","source_observed_at":"2026-08-06T19:42:18.426591Z"},"links":{"citing_paper":"/paper/2507.05107"},"observation_digest":"sha256:2c4a4e13291b3d198ae69b13dc6913b67229b12c65a3bed5d3fb452477c418a7","observation_id":"4ab60154-235f-4288-9037-62b9301822df","resolution":{"observed_at":"2026-08-06T19:42:18.823425Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:42:18.799762Z","title":"High- Order structure-preserving algorithms for plasma hybrid models","venue":null,"work_id":"bbe2b23a-1ce7-4031-b675-ab816e81634f","year":2023},"citing_paper":{"arxiv_id":"2507.05107","last_updated":"2025-07-07T15:25:54Z","snapshot_observed_at":"2026-08-06T19:29:56.334273Z","submitted_at":"2025-07-07T15:25:54Z","title":"DICE: Discrete inverse continuity equation for learning population dynamics","version":1},"reference_index":39,"source":"arxiv_source","source_observed_at":"2026-08-06T19:42:18.431482Z"},"links":{"citing_paper":"/paper/2507.05107"},"observation_digest":"sha256:277fe35c90cd8d28f14afe1094c2bd75d43367365ed70b13f8d072a8d28cba9c","observation_id":"5f678268-2cac-47d1-86d2-328b7a995808","resolution":{"observed_at":"2026-08-06T19:42:18.806892Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:42:18.782265Z","title":"A nonparametric ensemble transform method for Bayesian inference","venue":null,"work_id":"911be85c-a7be-4c41-9e52-70ede276986a","year":2013},"citing_paper":{"arxiv_id":"2507.05107","last_updated":"2025-07-07T15:25:54Z","snapshot_observed_at":"2026-08-06T19:29:56.334273Z","submitted_at":"2025-07-07T15:25:54Z","title":"DICE: Discrete inverse continuity equation for learning population dynamics","version":1},"reference_index":40,"source":"arxiv_source","source_observed_at":"2026-08-06T19:42:18.436324Z"},"links":{"citing_paper":"/paper/2507.05107"},"observation_digest":"sha256:bef042956619e54fcd54ad9bf87855e83f472e3dcfe7a83da2e675be70679715","observation_id":"deada3ae-5d68-460a-b8f9-a0654e688d8d","resolution":{"observed_at":"2026-08-06T19:42:18.787451Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:42:18.766056Z","title":"A nine-dimensional Lorenz system to study high-dimensional chaos","venue":null,"work_id":"133aed3e-350d-49a1-9e09-38d76a31ce94","year":1998},"citing_paper":{"arxiv_id":"2507.05107","last_updated":"2025-07-07T15:25:54Z","snapshot_observed_at":"2026-08-06T19:29:56.334273Z","submitted_at":"2025-07-07T15:25:54Z","title":"DICE: Discrete inverse continuity equation for learning population dynamics","version":1},"reference_index":41,"source":"arxiv_source","source_observed_at":"2026-08-06T19:42:18.441612Z"},"links":{"citing_paper":"/paper/2507.05107"},"observation_digest":"sha256:4d7be2af4e25ad5af3d109599ad83012241728d09b3b3fe401998941c845d8ba","observation_id":"85e2c77e-cd14-4f7e-97d8-bbe34662c47e","resolution":{"observed_at":"2026-08-06T19:42:18.770851Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:42:18.750026Z","title":null,"venue":null,"work_id":"2456c444-9cd2-48bd-893f-ee7ed9108740","year":2023},"citing_paper":{"arxiv_id":"2507.05107","last_updated":"2025-07-07T15:25:54Z","snapshot_observed_at":"2026-08-06T19:29:56.334273Z","submitted_at":"2025-07-07T15:25:54Z","title":"DICE: Discrete inverse continuity equation for learning population dynamics","version":1},"reference_index":42,"source":"arxiv_source","source_observed_at":"2026-08-06T19:42:18.447194Z"},"links":{"citing_paper":"/paper/2507.05107"},"observation_digest":"sha256:60cb540540db3685f31842bfd352d358e9a109afaf2ef08cde8c82b035fe2ba1","observation_id":"5da8877b-85a1-42f3-82b6-3f911a652fd4","resolution":{"observed_at":"2026-08-06T19:42:18.754593Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-06T19:42:18.454378Z","title":"High-resolution image synthesis with latent diffusion models","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2507.05107","last_updated":"2025-07-07T15:25:54Z","snapshot_observed_at":"2026-08-06T19:29:56.334273Z","submitted_at":"2025-07-07T15:25:54Z","title":"DICE: Discrete inverse continuity equation for learning population dynamics","version":1},"reference_index":43,"source":"arxiv_source","source_observed_at":"2026-08-06T19:42:18.454378Z"},"links":{"citing_paper":"/paper/2507.05107"},"observation_digest":"sha256:90a58b53c7230f4b4325e23ab91d2758a968935b426314f3681c5b3249f14d69","observation_id":"dbbb23aa-216a-40a0-b8ae-1fe7e8703a1e","resolution":{"observed_at":"2026-08-06T19:42:18.454378Z","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":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:42:18.723297Z","title":"Rozza, D","venue":null,"work_id":"ad026c02-f367-4da1-b4f1-bd23fd38814a","year":2008},"citing_paper":{"arxiv_id":"2507.05107","last_updated":"2025-07-07T15:25:54Z","snapshot_observed_at":"2026-08-06T19:29:56.334273Z","submitted_at":"2025-07-07T15:25:54Z","title":"DICE: Discrete inverse continuity equation for learning population dynamics","version":1},"reference_index":44,"source":"arxiv_source","source_observed_at":"2026-08-06T19:42:18.459634Z"},"links":{"citing_paper":"/paper/2507.05107"},"observation_digest":"sha256:0848ff3e72b052d1f2c78285ede891efed8d6a0d26ef1ccf7fbd59999b163445","observation_id":"b9699c69-9913-4b27-a77e-a031bdd551ea","resolution":{"observed_at":"2026-08-06T19:42:18.728199Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:42:18.706922Z","title":"Fast hybrid tempered ensemble transform filter formulation for Bayesian elliptical problems via Sinkhorn approximation","venue":null,"work_id":"241829b2-a162-4c88-8d92-85b245538300","year":2021},"citing_paper":{"arxiv_id":"2507.05107","last_updated":"2025-07-07T15:25:54Z","snapshot_observed_at":"2026-08-06T19:29:56.334273Z","submitted_at":"2025-07-07T15:25:54Z","title":"DICE: Discrete inverse continuity equation for learning population dynamics","version":1},"reference_index":45,"source":"arxiv_source","source_observed_at":"2026-08-06T19:42:18.464336Z"},"links":{"citing_paper":"/paper/2507.05107"},"observation_digest":"sha256:e7b70baf6762d5528a6277558159a10afa0d00c020891e9b9d4e68e0fc47b40e","observation_id":"f8dab3c7-e831-4065-ba2f-901b36b8efa8","resolution":{"observed_at":"2026-08-06T19:42:18.711923Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:42:18.690449Z","title":"Optimal Transport for Applied Mathematicians, volume 87 of Progress in Nonlinear Differential Equations and Their Applications","venue":null,"work_id":"ed6d007c-e21d-47cf-9588-ae1e4f628fc5","year":2015},"citing_paper":{"arxiv_id":"2507.05107","last_updated":"2025-07-07T15:25:54Z","snapshot_observed_at":"2026-08-06T19:29:56.334273Z","submitted_at":"2025-07-07T15:25:54Z","title":"DICE: Discrete inverse continuity equation for learning population dynamics","version":1},"reference_index":46,"source":"arxiv_source","source_observed_at":"2026-08-06T19:42:18.468957Z"},"links":{"citing_paper":"/paper/2507.05107"},"observation_digest":"sha256:0c9a9f86d127e7aec03fa0558bd26107fee63771fb9e326fd02b10f883d014df","observation_id":"f07fd2a6-7753-444b-af81-e70a9b8b293a","resolution":{"observed_at":"2026-08-06T19:42:18.695934Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-06T19:42:18.475624Z","title":"Generative modeling by estimating gradients of the data distribution","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2507.05107","last_updated":"2025-07-07T15:25:54Z","snapshot_observed_at":"2026-08-06T19:29:56.334273Z","submitted_at":"2025-07-07T15:25:54Z","title":"DICE: Discrete inverse continuity equation for learning population dynamics","version":1},"reference_index":47,"source":"arxiv_source","source_observed_at":"2026-08-06T19:42:18.475624Z"},"links":{"citing_paper":"/paper/2507.05107"},"observation_digest":"sha256:792549defda8b471cc7ad782f81f6b4b5d338787dd96ec119d6ac88c28e63d72","observation_id":"ba2cb2ba-af12-41be-b6cb-b36af39581c9","resolution":{"observed_at":"2026-08-06T19:42:18.475624Z","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":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:42:18.662483Z","title":"Learning diffusion at lightspeed","venue":null,"work_id":"9dd12953-7d09-4ab3-8f11-a794754f7693","year":2024},"citing_paper":{"arxiv_id":"2507.05107","last_updated":"2025-07-07T15:25:54Z","snapshot_observed_at":"2026-08-06T19:29:56.334273Z","submitted_at":"2025-07-07T15:25:54Z","title":"DICE: Discrete inverse continuity equation for learning population dynamics","version":1},"reference_index":48,"source":"arxiv_source","source_observed_at":"2026-08-06T19:42:18.480169Z"},"links":{"citing_paper":"/paper/2507.05107"},"observation_digest":"sha256:afc85c6067e36671afe8b253560beccde475189c107b853b0febb7a16a520964","observation_id":"ef57e4eb-aa4f-4616-a0dc-02f1471c0e85","resolution":{"observed_at":"2026-08-06T19:42:18.667410Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:42:18.645919Z","title":"Liouville flow importance sampler","venue":null,"work_id":"9e384432-19bb-4caf-af18-c1c508552fa7","year":2024},"citing_paper":{"arxiv_id":"2507.05107","last_updated":"2025-07-07T15:25:54Z","snapshot_observed_at":"2026-08-06T19:29:56.334273Z","submitted_at":"2025-07-07T15:25:54Z","title":"DICE: Discrete inverse continuity equation for learning population dynamics","version":1},"reference_index":49,"source":"arxiv_source","source_observed_at":"2026-08-06T19:42:18.484957Z"},"links":{"citing_paper":"/paper/2507.05107"},"observation_digest":"sha256:ca3891ac00fffdb2df6a85555b80bf2bc0df392050b2828b328331f20e4f04fa","observation_id":"c0b3da4c-509f-4516-9988-bce315d172db","resolution":{"observed_at":"2026-08-06T19:42:18.650717Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:42:18.628810Z","title":"T rajectory N et: A dynamic optimal transport network for modeling cellular dynamics","venue":null,"work_id":"4eb2e20b-d92a-4b00-b5dc-a5f2b249ead8","year":2020},"citing_paper":{"arxiv_id":"2507.05107","last_updated":"2025-07-07T15:25:54Z","snapshot_observed_at":"2026-08-06T19:29:56.334273Z","submitted_at":"2025-07-07T15:25:54Z","title":"DICE: Discrete inverse continuity equation for learning population dynamics","version":1},"reference_index":50,"source":"arxiv_source","source_observed_at":"2026-08-06T19:42:18.489575Z"},"links":{"citing_paper":"/paper/2507.05107"},"observation_digest":"sha256:12f194360cd3a022b263f5215d5e6b9aa46e32c11f7d6313407332caf507f62f","observation_id":"f0e1a922-566b-49a2-853d-237dbee02c8e","resolution":{"observed_at":"2026-08-06T19:42:18.634501Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:42:18.613139Z","title":"The Lorenz attractor exists","venue":null,"work_id":"7d0d323a-5091-4284-9dd1-e76ba715ae4b","year":1999},"citing_paper":{"arxiv_id":"2507.05107","last_updated":"2025-07-07T15:25:54Z","snapshot_observed_at":"2026-08-06T19:29:56.334273Z","submitted_at":"2025-07-07T15:25:54Z","title":"DICE: Discrete inverse continuity equation for learning population dynamics","version":1},"reference_index":51,"source":"arxiv_source","source_observed_at":"2026-08-06T19:42:18.495009Z"},"links":{"citing_paper":"/paper/2507.05107"},"observation_digest":"sha256:9d059acd4e4f0cd4e9f66150835c48c4f6f7c83557ba7a0fd5254aede93bb947","observation_id":"183b977a-750f-4064-85c6-274452df43b8","resolution":{"observed_at":"2026-08-06T19:42:18.617990Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:42:18.597759Z","title":"Optimal transport: old and new","venue":null,"work_id":"67abe7cf-dc4f-4675-a609-e2d232a28548","year":2009},"citing_paper":{"arxiv_id":"2507.05107","last_updated":"2025-07-07T15:25:54Z","snapshot_observed_at":"2026-08-06T19:29:56.334273Z","submitted_at":"2025-07-07T15:25:54Z","title":"DICE: Discrete inverse continuity equation for learning population dynamics","version":1},"reference_index":52,"source":"arxiv_source","source_observed_at":"2026-08-06T19:42:18.500297Z"},"links":{"citing_paper":"/paper/2507.05107"},"observation_digest":"sha256:f6a677448004fef2c52205bca9a067f8117331e9598c2d7cd8b6fb9f036f06dd","observation_id":"55d7813f-555b-4296-93ac-918ba6e39a88","resolution":{"observed_at":"2026-08-06T19:42:18.602442Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:42:18.580072Z","title":"Topics in optimal transportation","venue":null,"work_id":"76d04528-889f-4714-95a1-6166a02de065","year":2016},"citing_paper":{"arxiv_id":"2507.05107","last_updated":"2025-07-07T15:25:54Z","snapshot_observed_at":"2026-08-06T19:29:56.334273Z","submitted_at":"2025-07-07T15:25:54Z","title":"DICE: Discrete inverse continuity equation for learning population dynamics","version":1},"reference_index":53,"source":"arxiv_source","source_observed_at":"2026-08-06T19:42:18.505376Z"},"links":{"citing_paper":"/paper/2507.05107"},"observation_digest":"sha256:a5e99d7079c1bfa4bfc064e655eb23acf215b472f67ab462d272c801bccd49b7","observation_id":"4adf0ef3-2dc7-40fd-ae04-790d86c0f318","resolution":{"observed_at":"2026-08-06T19:42:18.586004Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2507.05107","last_updated":"2025-07-07T15:25:54Z","latest_version":1,"primary_category":"cs.LG","snapshot_observed_at":"2026-08-06T19:29:56.334273Z","submitted_at":"2025-07-07T15:25:54Z","title":"DICE: Discrete inverse continuity equation for learning population dynamics"},"reference_resolution":{"displayed":53,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":9,"verified_exact":0,"verified_fuzzy":44},"total_outbound_references":53},"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":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"thesis":"As of 9 August 2026, this Paper Citation Record lists 53 of 53 outbound references and 5 inbound Pith citation observations for arXiv:2507.05107."}