{"as_of":"2026-08-13T02:51:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:c4c34163028c0d4fa948b1d096ff7846934663ded3118d2647ad9b8de0c2c129","coverage":[{"denominator":32,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":32,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-11T19:30:50.541977Z","state":"measured"},{"denominator":32,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":32,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-12T06:34:41.77262+00:00","state":"measured"},{"denominator":0,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":0,"source":"paper_references, paper_reference_links","source_observed_at":null,"state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"cited_works","source_observed_at":null,"state":"measured"}],"external_citation_measurements":[],"inbound":[],"links":{"evidence":"/evidence","html":"/paper/2412.06723/citation-record","integrity":"/paper/2412.06723/integrity","json":"/paper/2412.06723/citation-record.json","paper":"/paper/2412.06723"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T19:30:50.356084Z","title":"write newline","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2412.06723","last_updated":"2024-12-09T18:10:28Z","snapshot_observed_at":"2026-08-11T19:16:48.053797Z","submitted_at":"2024-12-09T18:10:28Z","title":"Universal chain rules from entropic triangle inequalities","version":1},"reference_index":1,"source":"arxiv_source","source_observed_at":"2026-08-11T19:30:50.356084Z"},"links":{"citing_paper":"/paper/2412.06723"},"observation_digest":"sha256:efcb1ef080259a09e53bc605d3b374ac3567b00d918af1adf7fdab53b39de68c","observation_id":"ac175618-26f9-443e-8ce8-4f4765a64515","resolution":{"observed_at":"2026-08-11T19:30:50.356084Z","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":"2020.29815","doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T19:30:51.513094Z","title":"Partially smoothed information measures","venue":null,"work_id":"a4055077-72eb-4da5-8d45-99fbffe5da6c","year":2020},"citing_paper":{"arxiv_id":"2412.06723","last_updated":"2024-12-09T18:10:28Z","snapshot_observed_at":"2026-08-11T19:16:48.053797Z","submitted_at":"2024-12-09T18:10:28Z","title":"Universal chain rules from entropic triangle inequalities","version":1},"reference_index":2,"source":"arxiv_source","source_observed_at":"2026-08-11T19:30:50.362409Z"},"links":{"citing_paper":"/paper/2412.06723"},"observation_digest":"sha256:1d4b47f3c6e320ee0820b95c7b11ab85ab3ca1f566d229b21f44d714a848f20a","observation_id":"07973a76-3cf9-424c-8ed8-3bd41bddd595","resolution":{"observed_at":"2026-08-11T19:30:51.519774Z","resolver_source":"raw_fallback","status":"metadata_mismatch"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1088/0305-4470/37/5/l01","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T19:30:50.795702Z","title":"Continuity of quantum conditional information","venue":null,"work_id":"961864a4-ac7e-4c4f-9f5e-54b0dfcd1e42","year":2004},"citing_paper":{"arxiv_id":"2412.06723","last_updated":"2024-12-09T18:10:28Z","snapshot_observed_at":"2026-08-11T19:16:48.053797Z","submitted_at":"2024-12-09T18:10:28Z","title":"Universal chain rules from entropic triangle inequalities","version":1},"reference_index":3,"source":"arxiv_source","source_observed_at":"2026-08-11T19:30:50.367663Z"},"links":{"citing_paper":"/paper/2412.06723"},"observation_digest":"sha256:ec2d237ece7f0a4a69b23484a9bf3044d94f9f017f394cf9664cea97393d0a2b","observation_id":"42b89eea-b651-430d-8e68-1ed0fcb43afd","resolution":{"observed_at":"2026-08-11T19:30:50.800953Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T19:30:50.377385Z","title":"Practical device-independent quantum cryptography via entropy accumulation","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2412.06723","last_updated":"2024-12-09T18:10:28Z","snapshot_observed_at":"2026-08-11T19:16:48.053797Z","submitted_at":"2024-12-09T18:10:28Z","title":"Universal chain rules from entropic triangle inequalities","version":1},"reference_index":4,"source":"arxiv_source","source_observed_at":"2026-08-11T19:30:50.377385Z"},"links":{"citing_paper":"/paper/2412.06723"},"observation_digest":"sha256:fa98a2397e758bcb806f65cd5a2e5bfb3eaef749d06dfe7d8ec03241977c8f82","observation_id":"e6293dcb-3784-4cbc-9db6-2958d278f258","resolution":{"observed_at":"2026-08-11T19:30:50.377385Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T19:30:50.383586Z","title":"Simple and tight device-independent security proofs","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2412.06723","last_updated":"2024-12-09T18:10:28Z","snapshot_observed_at":"2026-08-11T19:16:48.053797Z","submitted_at":"2024-12-09T18:10:28Z","title":"Universal chain rules from entropic triangle inequalities","version":1},"reference_index":5,"source":"arxiv_source","source_observed_at":"2026-08-11T19:30:50.383586Z"},"links":{"citing_paper":"/paper/2412.06723"},"observation_digest":"sha256:5bfae561f187f154181d7f947f89feb3af23dee90d6fbc557eba562febf39f41","observation_id":"ea9f5b16-79db-4729-adad-0b480bd8a036","resolution":{"observed_at":"2026-08-11T19:30:50.383586Z","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":"2026-08-11T19:30:51.612757Z","title":null,"venue":null,"work_id":"40738a36-039f-4dc5-9f6d-005f12bcb256","year":2014},"citing_paper":{"arxiv_id":"2412.06723","last_updated":"2024-12-09T18:10:28Z","snapshot_observed_at":"2026-08-11T19:16:48.053797Z","submitted_at":"2024-12-09T18:10:28Z","title":"Universal chain rules from entropic triangle inequalities","version":1},"reference_index":6,"source":"arxiv_source","source_observed_at":"2026-08-11T19:30:50.388364Z"},"links":{"citing_paper":"/paper/2412.06723"},"observation_digest":"sha256:2b3f106039067efc28d6eb656d4dbcb799b795a2cbb1ed7d9d687b8c84801acc","observation_id":"332c32a4-58ec-4e31-8446-bf2e146c36e4","resolution":{"observed_at":"2026-08-11T19:30:51.617586Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T19:30:50.399589Z","title":"On variational expressions for quantum relative entropies","venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2412.06723","last_updated":"2024-12-09T18:10:28Z","snapshot_observed_at":"2026-08-11T19:16:48.053797Z","submitted_at":"2024-12-09T18:10:28Z","title":"Universal chain rules from entropic triangle inequalities","version":1},"reference_index":7,"source":"arxiv_source","source_observed_at":"2026-08-11T19:30:50.399589Z"},"links":{"citing_paper":"/paper/2412.06723"},"observation_digest":"sha256:39d26a35960ee988303d7e9ce954b2125274c160d878c0a5645ec0bdec8f75c8","observation_id":"94ca9b72-e573-40ee-a53f-dac1deb57282","resolution":{"observed_at":"2026-08-11T19:30:50.399589Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T19:30:50.405935Z","title":"Positive Definite Matrices","venue":null,"work_id":null,"year":2007},"citing_paper":{"arxiv_id":"2412.06723","last_updated":"2024-12-09T18:10:28Z","snapshot_observed_at":"2026-08-11T19:16:48.053797Z","submitted_at":"2024-12-09T18:10:28Z","title":"Universal chain rules from entropic triangle inequalities","version":1},"reference_index":8,"source":"arxiv_source","source_observed_at":"2026-08-11T19:30:50.405935Z"},"links":{"citing_paper":"/paper/2412.06723"},"observation_digest":"sha256:2b710b9c213e53a5013c266a9168e2baa6f78d174eddd18c637a04699e3c676e","observation_id":"173cc377-914f-42c4-b90f-6b6f38c0b903","resolution":{"observed_at":"2026-08-11T19:30:50.405935Z","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":"10.1007/s00220-014-1990-4","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T19:30:50.742286Z","title":"One-shot decoupling","venue":null,"work_id":"e63b30ed-8079-4a76-8d02-dbaf90bd44df","year":2014},"citing_paper":{"arxiv_id":"2412.06723","last_updated":"2024-12-09T18:10:28Z","snapshot_observed_at":"2026-08-11T19:16:48.053797Z","submitted_at":"2024-12-09T18:10:28Z","title":"Universal chain rules from entropic triangle inequalities","version":1},"reference_index":9,"source":"arxiv_source","source_observed_at":"2026-08-11T19:30:50.411566Z"},"links":{"citing_paper":"/paper/2412.06723"},"observation_digest":"sha256:ecd4f6d1c8b8c08e1eb29564687e31dca852e00735a6df77d74d34302f1dcdce","observation_id":"b12ee34f-bffa-44f7-979c-b0011d50fff1","resolution":{"observed_at":"2026-08-11T19:30:50.746353Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":"2019.29295","doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T19:30:51.370531Z","title":"Entropy accumulation with improved second-order term","venue":null,"work_id":"c7272a8c-96f8-49da-9442-e4dfcc568693","year":2019},"citing_paper":{"arxiv_id":"2412.06723","last_updated":"2024-12-09T18:10:28Z","snapshot_observed_at":"2026-08-11T19:16:48.053797Z","submitted_at":"2024-12-09T18:10:28Z","title":"Universal chain rules from entropic triangle inequalities","version":1},"reference_index":10,"source":"arxiv_source","source_observed_at":"2026-08-11T19:30:50.417651Z"},"links":{"citing_paper":"/paper/2412.06723"},"observation_digest":"sha256:86c2e3efc622d9840108eaa16a8df736184035517eb7d0dc0d43fa70b5f234e7","observation_id":"15b18461-cc75-4d2c-b709-9a31838c9796","resolution":{"observed_at":"2026-08-11T19:30:51.382912Z","resolver_source":"raw_fallback","status":"metadata_mismatch"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T19:30:50.424158Z","title":"Entropy accumulation","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2412.06723","last_updated":"2024-12-09T18:10:28Z","snapshot_observed_at":"2026-08-11T19:16:48.053797Z","submitted_at":"2024-12-09T18:10:28Z","title":"Universal chain rules from entropic triangle inequalities","version":1},"reference_index":11,"source":"arxiv_source","source_observed_at":"2026-08-11T19:30:50.424158Z"},"links":{"citing_paper":"/paper/2412.06723"},"observation_digest":"sha256:e6fc547998df4f71b75d6071465f5e3a9432838ad3ab435287e5ddbabafc0ddf","observation_id":"058e668c-3ba7-4532-94eb-9b287d584ee8","resolution":{"observed_at":"2026-08-11T19:30:50.424158Z","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":"2026-08-11T19:30:51.592182Z","title":"Does approximate equality of quantum states imply operator inequality in a large subspace? MathOverflow https://mathoverflow.net/q/451757, 2023","venue":null,"work_id":"949c1c2c-90d4-4c5a-bb4e-f117ded5d41c","year":2023},"citing_paper":{"arxiv_id":"2412.06723","last_updated":"2024-12-09T18:10:28Z","snapshot_observed_at":"2026-08-11T19:16:48.053797Z","submitted_at":"2024-12-09T18:10:28Z","title":"Universal chain rules from entropic triangle inequalities","version":1},"reference_index":12,"source":"arxiv_source","source_observed_at":"2026-08-11T19:30:50.430648Z"},"links":{"citing_paper":"/paper/2412.06723"},"observation_digest":"sha256:4ed2a0d447085d0f238e862641e7f3aec2c146da7c1a9fadc74f79691072d05c","observation_id":"8c4ca5e2-5bf1-4cf1-8d94-d24275527c0e","resolution":{"observed_at":"2026-08-11T19:30:51.598606Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T19:30:50.436247Z","title":"Renes, and David Sutter","venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2412.06723","last_updated":"2024-12-09T18:10:28Z","snapshot_observed_at":"2026-08-11T19:16:48.053797Z","submitted_at":"2024-12-09T18:10:28Z","title":"Universal chain rules from entropic triangle inequalities","version":1},"reference_index":13,"source":"arxiv_source","source_observed_at":"2026-08-11T19:30:50.436247Z"},"links":{"citing_paper":"/paper/2412.06723"},"observation_digest":"sha256:91a5081f6de6aa0edea23acb379d1550c502470761cf1083428cc3f128774876","observation_id":"e8171f00-86b0-4e9d-b7cb-72f47932c403","resolution":{"observed_at":"2026-08-11T19:30:50.436247Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1103.6067","last_updated":"2012-01-12T05:12:45Z","snapshot_observed_at":"2026-07-06T02:25:37.478069Z","submitted_at":"2011-03-31T00:22:40Z","title":"Short proofs of the Quantum Substate Theorem","version":2},"cited_work":{"arxiv_id":"1103.6067","doi":"10.48550/arxiv.1103.6067","metadata_source":"pith","pith_arxiv_id":"1103.6067","snapshot_observed_at":"2026-08-12T00:16:22.474752Z","title":"Short proofs of the Quantum Substate Theorem","venue":"quant-ph","work_id":"afbb74bf-4b63-4768-9b12-fd89b0723fda","year":2011},"citing_paper":{"arxiv_id":"2412.06723","last_updated":"2024-12-09T18:10:28Z","snapshot_observed_at":"2026-08-11T19:16:48.053797Z","submitted_at":"2024-12-09T18:10:28Z","title":"Universal chain rules from entropic triangle inequalities","version":1},"reference_index":14,"source":"arxiv_source","source_observed_at":"2026-08-11T19:30:50.440134Z"},"links":{"cited_paper":"/paper/1103.6067","citing_paper":"/paper/2412.06723"},"observation_digest":"sha256:e23cfc331d047a08942ddfabc566aa3ca5347536018ce8247d094cce00357d67","observation_id":"2ffec80d-2940-4397-902f-fb40e818f50e","resolution":{"observed_at":"2026-08-11T19:30:50.721449Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2002.11819","last_updated":"2020-02-26T22:06:15Z","snapshot_observed_at":"2026-08-12T23:24:35.047310Z","submitted_at":"2020-02-26T22:06:15Z","title":"The Trigger Mechanism of Recurrent Solar Active Region Jets Revealed by the Magnetic Properties of a Coronal Geyser Site","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2002.11819","snapshot_observed_at":"2026-08-11T19:30:50.445063Z","title":null,"venue":null,"work_id":null,"year":2002},"citing_paper":{"arxiv_id":"2412.06723","last_updated":"2024-12-09T18:10:28Z","snapshot_observed_at":"2026-08-11T19:16:48.053797Z","submitted_at":"2024-12-09T18:10:28Z","title":"Universal chain rules from entropic triangle inequalities","version":1},"reference_index":15,"source":"arxiv_source","source_observed_at":"2026-08-11T19:30:50.445063Z"},"links":{"cited_paper":"/paper/2002.11819","citing_paper":"/paper/2412.06723"},"observation_digest":"sha256:a1813bffd1faac2cd7d95f6b9c69a352c8c823541325703e6c020b5d70ad840b","observation_id":"57303516-6b12-4226-990b-9b229e11aedc","resolution":{"observed_at":"2026-08-11T19:30:50.445063Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T19:30:50.450417Z","title":"The operational meaning of min- and max-entropy","venue":null,"work_id":null,"year":2009},"citing_paper":{"arxiv_id":"2412.06723","last_updated":"2024-12-09T18:10:28Z","snapshot_observed_at":"2026-08-11T19:16:48.053797Z","submitted_at":"2024-12-09T18:10:28Z","title":"Universal chain rules from entropic triangle inequalities","version":1},"reference_index":16,"source":"arxiv_source","source_observed_at":"2026-08-11T19:30:50.450417Z"},"links":{"citing_paper":"/paper/2412.06723"},"observation_digest":"sha256:082ca7b73e090455079abcd715f266d32f0779999f39d5e77d9165d14438cd2d","observation_id":"22a489cd-ab8d-45ae-84c3-9fdc4053263a","resolution":{"observed_at":"2026-08-11T19:30:50.450417Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T19:30:50.454990Z","title":"Brown, Jun Zhang, Roger Colbeck, Jingyun Fan, Qiang Zhang, and Jian-Wei Pan","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2412.06723","last_updated":"2024-12-09T18:10:28Z","snapshot_observed_at":"2026-08-11T19:16:48.053797Z","submitted_at":"2024-12-09T18:10:28Z","title":"Universal chain rules from entropic triangle inequalities","version":1},"reference_index":17,"source":"arxiv_source","source_observed_at":"2026-08-11T19:30:50.454990Z"},"links":{"citing_paper":"/paper/2412.06723"},"observation_digest":"sha256:a3750271010f42fb3392fce41314648659136fa0e5f5b88a73e6fd51d3462f80","observation_id":"6524dc68-1796-4725-a046-e0371e379927","resolution":{"observed_at":"2026-08-11T19:30:50.454990Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2308.11736","last_updated":"2024-02-08T20:01:38Z","snapshot_observed_at":"2026-08-09T14:21:12.089258Z","submitted_at":"2023-08-22T18:55:16Z","title":"Smooth min-entropy lower bounds for approximation chains","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2308.11736","snapshot_observed_at":"2026-08-11T19:30:50.459698Z","title":"Smooth min-entropy lower bounds for approximation chains, 2023, 2308.11736 http://arxiv.org/abs/2308.11736","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2412.06723","last_updated":"2024-12-09T18:10:28Z","snapshot_observed_at":"2026-08-11T19:16:48.053797Z","submitted_at":"2024-12-09T18:10:28Z","title":"Universal chain rules from entropic triangle inequalities","version":1},"reference_index":18,"source":"arxiv_source","source_observed_at":"2026-08-11T19:30:50.459698Z"},"links":{"cited_paper":"/paper/2308.11736","citing_paper":"/paper/2412.06723"},"observation_digest":"sha256:ad6bbadcd003607b65129c0a9b82c580ae9c7a5ca6f61e10a8d95c27c915cad6","observation_id":"0707f7c4-9b28-4e82-8df9-371e0d165945","resolution":{"observed_at":"2026-08-11T19:30:50.459698Z","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":"2026-08-11T19:30:51.575080Z","title":"Proving security of parallel device independent QKD using approximate entropy accumulation","venue":null,"work_id":"f1f7ead7-1286-44d6-9727-c1471a1a7779","year":2024},"citing_paper":{"arxiv_id":"2412.06723","last_updated":"2024-12-09T18:10:28Z","snapshot_observed_at":"2026-08-11T19:16:48.053797Z","submitted_at":"2024-12-09T18:10:28Z","title":"Universal chain rules from entropic triangle inequalities","version":1},"reference_index":19,"source":"arxiv_source","source_observed_at":"2026-08-11T19:30:50.465154Z"},"links":{"citing_paper":"/paper/2412.06723"},"observation_digest":"sha256:a483a7caae2ad1908b449e5af11ec989258475b778530f98a5102c09ce361035","observation_id":"7ee438be-4897-4ca7-83bd-d732d61c2173","resolution":{"observed_at":"2026-08-11T19:30:51.580770Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2402.12346","last_updated":"2025-08-02T14:59:00Z","snapshot_observed_at":"2026-07-06T17:32:24.161667Z","submitted_at":"2024-02-12T18:14:02Z","title":"Proving security of BB84 under source correlations","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2402.12346","snapshot_observed_at":"2026-08-11T19:30:50.469574Z","title":"Proving security of BB84 under source correlations, 2024, 2402.12346 http://arxiv.org/abs/2402.12346","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2412.06723","last_updated":"2024-12-09T18:10:28Z","snapshot_observed_at":"2026-08-11T19:16:48.053797Z","submitted_at":"2024-12-09T18:10:28Z","title":"Universal chain rules from entropic triangle inequalities","version":1},"reference_index":20,"source":"arxiv_source","source_observed_at":"2026-08-11T19:30:50.469574Z"},"links":{"cited_paper":"/paper/2402.12346","citing_paper":"/paper/2412.06723"},"observation_digest":"sha256:6d0cc4f6c5d6c77ba102ae61bbafa075005deaa4984aca902b5172e743ea604b","observation_id":"c4090546-04e5-4cb5-93fc-30aabdefde65","resolution":{"observed_at":"2026-08-11T19:30:50.469574Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2203.04989","last_updated":"2022-10-28T14:04:52Z","snapshot_observed_at":"2026-08-10T11:15:12.260556Z","submitted_at":"2022-03-09T19:00:05Z","title":"Generalised entropy accumulation","version":2},"cited_work":{"arxiv_id":"2203.04989","doi":"10.48550/arxiv.2203.04989","metadata_source":"pith","pith_arxiv_id":"2203.04989","snapshot_observed_at":"2026-08-12T00:16:22.474752Z","title":"Generalised entropy accumulation","venue":"quant-ph","work_id":"d9bc981d-0962-4791-878f-8e887b4a3453","year":2022},"citing_paper":{"arxiv_id":"2412.06723","last_updated":"2024-12-09T18:10:28Z","snapshot_observed_at":"2026-08-11T19:16:48.053797Z","submitted_at":"2024-12-09T18:10:28Z","title":"Universal chain rules from entropic triangle inequalities","version":1},"reference_index":21,"source":"arxiv_source","source_observed_at":"2026-08-11T19:30:50.474323Z"},"links":{"cited_paper":"/paper/2203.04989","citing_paper":"/paper/2412.06723"},"observation_digest":"sha256:07f54cc7490334f19e48e8b8e5dde4c0a947ad6788a0ca2681fa952f28d41e33","observation_id":"20053d15-5346-4d4c-ac50-2d717b522e14","resolution":{"observed_at":"2026-08-11T19:30:50.684122Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T19:30:50.479393Z","title":"A variational expression for the relative entropy","venue":null,"work_id":null,"year":1988},"citing_paper":{"arxiv_id":"2412.06723","last_updated":"2024-12-09T18:10:28Z","snapshot_observed_at":"2026-08-11T19:16:48.053797Z","submitted_at":"2024-12-09T18:10:28Z","title":"Universal chain rules from entropic triangle inequalities","version":1},"reference_index":22,"source":"arxiv_source","source_observed_at":"2026-08-11T19:30:50.479393Z"},"links":{"citing_paper":"/paper/2412.06723"},"observation_digest":"sha256:bb96483b1c01d35e5eaebfb03541a6e5cfa3d528c9bb697f29bcc3a9a8cbb228","observation_id":"e31b5e64-351d-4b31-ac31-4bd8c4745385","resolution":{"observed_at":"2026-08-11T19:30:50.479393Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"quant-ph/0512258","last_updated":"2006-01-11T15:33:56Z","snapshot_observed_at":"2026-07-07T07:21:27.186046Z","submitted_at":"2005-12-30T15:13:42Z","title":"Security of Quantum Key Distribution","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"quant-ph/0512258","snapshot_observed_at":"2026-08-11T19:30:50.485807Z","title":"Security of Quantum Key Distribution","venue":null,"work_id":null,"year":2006},"citing_paper":{"arxiv_id":"2412.06723","last_updated":"2024-12-09T18:10:28Z","snapshot_observed_at":"2026-08-11T19:16:48.053797Z","submitted_at":"2024-12-09T18:10:28Z","title":"Universal chain rules from entropic triangle inequalities","version":1},"reference_index":23,"source":"arxiv_source","source_observed_at":"2026-08-11T19:30:50.485807Z"},"links":{"cited_paper":"/paper/quant-ph/0512258","citing_paper":"/paper/2412.06723"},"observation_digest":"sha256:fe34cb26b4459ef8391d59c4263a253f924af5ab553e278022376fc7fcccf27d","observation_id":"96acf7c2-a731-4dbf-ae42-6b3ef15b7539","resolution":{"observed_at":"2026-08-11T19:30:50.485807Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T19:30:50.490913Z","title":"Universally composable privacy amplification against quantum adversaries","venue":null,"work_id":null,"year":2005},"citing_paper":{"arxiv_id":"2412.06723","last_updated":"2024-12-09T18:10:28Z","snapshot_observed_at":"2026-08-11T19:16:48.053797Z","submitted_at":"2024-12-09T18:10:28Z","title":"Universal chain rules from entropic triangle inequalities","version":1},"reference_index":24,"source":"arxiv_source","source_observed_at":"2026-08-11T19:30:50.490913Z"},"links":{"citing_paper":"/paper/2412.06723"},"observation_digest":"sha256:28c709785bbd739f18a5e1c6aa651ab4ea946dedf75aa6c659ad02e7167ae952","observation_id":"2a0f8ee1-2e13-4d94-8f1e-901d31bc9d37","resolution":{"observed_at":"2026-08-11T19:30:50.490913Z","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":"2026-08-11T19:30:51.534867Z","title":"Multivariate trace inequalities","venue":null,"work_id":"d66fdaf5-98d8-42fa-bdb3-0d6cb5dedb0d","year":2017},"citing_paper":{"arxiv_id":"2412.06723","last_updated":"2024-12-09T18:10:28Z","snapshot_observed_at":"2026-08-11T19:16:48.053797Z","submitted_at":"2024-12-09T18:10:28Z","title":"Universal chain rules from entropic triangle inequalities","version":1},"reference_index":25,"source":"arxiv_source","source_observed_at":"2026-08-11T19:30:50.498028Z"},"links":{"citing_paper":"/paper/2412.06723"},"observation_digest":"sha256:c99ef213243f626838c1f468c8aac97509b7fb47cd861f241d8fceb0231b669a","observation_id":"51fae792-1e28-47ed-af9b-e2d7cfbf4e4a","resolution":{"observed_at":"2026-08-11T19:30:51.540356Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T19:30:50.502397Z","title":"Quantum coding","venue":null,"work_id":null,"year":1995},"citing_paper":{"arxiv_id":"2412.06723","last_updated":"2024-12-09T18:10:28Z","snapshot_observed_at":"2026-08-11T19:16:48.053797Z","submitted_at":"2024-12-09T18:10:28Z","title":"Universal chain rules from entropic triangle inequalities","version":1},"reference_index":26,"source":"arxiv_source","source_observed_at":"2026-08-11T19:30:50.502397Z"},"links":{"citing_paper":"/paper/2412.06723"},"observation_digest":"sha256:138323773ee574152346fbc444d90919602705c72d65dd05538eb4bfb1fd6711","observation_id":"3344f0eb-3ce8-4033-87e6-3279d9b45bb7","resolution":{"observed_at":"2026-08-11T19:30:50.502397Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T19:30:50.508207Z","title":"Quantum Information Processing with Finite Resources","venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2412.06723","last_updated":"2024-12-09T18:10:28Z","snapshot_observed_at":"2026-08-11T19:16:48.053797Z","submitted_at":"2024-12-09T18:10:28Z","title":"Universal chain rules from entropic triangle inequalities","version":1},"reference_index":27,"source":"arxiv_source","source_observed_at":"2026-08-11T19:30:50.508207Z"},"links":{"citing_paper":"/paper/2412.06723"},"observation_digest":"sha256:d4da206a7870336c1cf60ebfeb1ba3e346ffc4284817f6a4c146fb6730bcd873","observation_id":"447e75d7-96cc-46bf-b942-3439b4f60a4b","resolution":{"observed_at":"2026-08-11T19:30:50.508207Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T19:30:50.517020Z","title":"Leftover hashing against quantum side information","venue":null,"work_id":null,"year":2010},"citing_paper":{"arxiv_id":"2412.06723","last_updated":"2024-12-09T18:10:28Z","snapshot_observed_at":"2026-08-11T19:16:48.053797Z","submitted_at":"2024-12-09T18:10:28Z","title":"Universal chain rules from entropic triangle inequalities","version":1},"reference_index":28,"source":"arxiv_source","source_observed_at":"2026-08-11T19:30:50.517020Z"},"links":{"citing_paper":"/paper/2412.06723"},"observation_digest":"sha256:d07b1c2aec8cf4e38bf5975c8f878cec61af1c94ed1b4c4da41a00e6356dea18","observation_id":"7a9f8c75-f243-4959-8ebe-cddbf788afb7","resolution":{"observed_at":"2026-08-11T19:30:50.517020Z","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":"2013.22386","doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T19:30:50.923265Z","title":"Chain rules for smooth min- and max-entropies","venue":null,"work_id":"2a21a34e-0282-4930-b9a1-8b4869ce3038","year":2013},"citing_paper":{"arxiv_id":"2412.06723","last_updated":"2024-12-09T18:10:28Z","snapshot_observed_at":"2026-08-11T19:16:48.053797Z","submitted_at":"2024-12-09T18:10:28Z","title":"Universal chain rules from entropic triangle inequalities","version":1},"reference_index":29,"source":"arxiv_source","source_observed_at":"2026-08-11T19:30:50.524053Z"},"links":{"citing_paper":"/paper/2412.06723"},"observation_digest":"sha256:72288a7f1fe4794421e09bae26b97bff4cc9f697ec42b434e58f5e8052e76c7f","observation_id":"713aa7a0-1154-4e2a-b010-ff201f455ebb","resolution":{"observed_at":"2026-08-11T19:30:50.931610Z","resolver_source":"raw_fallback","status":"metadata_mismatch"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T19:30:50.529357Z","title":"The Theory of Quantum Information","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2412.06723","last_updated":"2024-12-09T18:10:28Z","snapshot_observed_at":"2026-08-11T19:16:48.053797Z","submitted_at":"2024-12-09T18:10:28Z","title":"Universal chain rules from entropic triangle inequalities","version":1},"reference_index":30,"source":"arxiv_source","source_observed_at":"2026-08-11T19:30:50.529357Z"},"links":{"citing_paper":"/paper/2412.06723"},"observation_digest":"sha256:23a81d9e2f36de5944e22c08376f004c422d47da82c18090f5862c730ed91ac6","observation_id":"1c98370a-2f99-4cc0-bacd-de6e9e9bfb44","resolution":{"observed_at":"2026-08-11T19:30:50.529357Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T19:30:50.535999Z","title":null,"venue":null,"work_id":null,"year":2013},"citing_paper":{"arxiv_id":"2412.06723","last_updated":"2024-12-09T18:10:28Z","snapshot_observed_at":"2026-08-11T19:16:48.053797Z","submitted_at":"2024-12-09T18:10:28Z","title":"Universal chain rules from entropic triangle inequalities","version":1},"reference_index":31,"source":"arxiv_source","source_observed_at":"2026-08-11T19:30:50.535999Z"},"links":{"citing_paper":"/paper/2412.06723"},"observation_digest":"sha256:f6f2e99eff3b8495b86895846fbe4e9b3e3a89990426791b22e6f54d2880fb78","observation_id":"c07f4ee3-35e4-4a28-a28a-e3f568e59316","resolution":{"observed_at":"2026-08-11T19:30:50.535999Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T19:30:50.541977Z","title":"Tight uniform continuity bounds for quantum entropies: Conditional entropy, relative entropy distance and energy constraints","venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2412.06723","last_updated":"2024-12-09T18:10:28Z","snapshot_observed_at":"2026-08-11T19:16:48.053797Z","submitted_at":"2024-12-09T18:10:28Z","title":"Universal chain rules from entropic triangle inequalities","version":1},"reference_index":32,"source":"arxiv_source","source_observed_at":"2026-08-11T19:30:50.541977Z"},"links":{"citing_paper":"/paper/2412.06723"},"observation_digest":"sha256:92fd1094451979ee3b251049aed2bb164967eea28de7dd3a49aea9adda33ddf5","observation_id":"f07b73ec-fc89-4ac5-a209-bb47c527e9cd","resolution":{"observed_at":"2026-08-11T19:30:50.541977Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2412.06723","last_updated":"2024-12-09T18:10:28Z","latest_version":1,"primary_category":"quant-ph","snapshot_observed_at":"2026-08-11T19:16:48.053797Z","submitted_at":"2024-12-09T18:10:28Z","title":"Universal chain rules from entropic triangle inequalities"},"reference_resolution":{"displayed":32,"state_counts":{"malformed_identifier":0,"metadata_mismatch":3,"parse_uncertain":0,"unresolved":22,"verified_exact":4,"verified_fuzzy":3},"total_outbound_references":32},"refusal":"A citation records a reference. It does not transfer a finding from one paper to another.","schema":"pith.paper-citation-record.v1","standing_sources":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"thesis":"As of 13 August 2026, this Paper Citation Record lists 32 of 32 outbound references and 0 inbound Pith citation observations for arXiv:2412.06723."}