{"as_of":"2026-08-10T11:54:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:524767419655d504aee2b06ddf893fd161899d80e5793d332dc777e9c6990e85","coverage":[{"denominator":39,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":39,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-07T10:54:50.904769Z","state":"measured"},{"denominator":40,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":40,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-10T06:31:04.303077+00:00","state":"measured"},{"denominator":1,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":1,"source":"paper_references, paper_reference_links","source_observed_at":"2026-05-16T23:00:20.852667Z","state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"arxiv_reference","source_observed_at":"2026-05-16T23:01:20.531590Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2506.04197","last_updated":"2025-06-04T17:42:33Z","snapshot_observed_at":"2026-08-09T08:24:48.141790Z","submitted_at":"2025-06-04T17:42:33Z","title":"Transportation cost and contraction coefficient for channels on von Neumann algebras","version":1},"cited_work":{"arxiv_id":"2506.04197","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2506.04197","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Quantum metrics on crossed products with groups of polynomial growth","venue":null,"work_id":"c22c45e6-7e9b-4a24-9f1c-e728abd3da50","year":2025},"citing_paper":{"arxiv_id":"2512.10842","last_updated":"2026-05-13T11:18:35Z","snapshot_observed_at":"2026-08-06T03:12:13.486506Z","submitted_at":"2025-12-11T17:31:18Z","title":"Metrics on completely positive maps via noncommutative geometry","version":3},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-05-16T23:00:20.852667Z"},"links":{"cited_paper":"/paper/2506.04197","citing_paper":"/paper/2512.10842"},"observation_digest":"sha256:e3805807eeb8d56a190e7c023966c7d129cbbc8b44fe374eb034941052498ecb","observation_id":"5c417e86-6abb-4f0a-959f-9b0feeaf05d3","resolution":{"observed_at":"2026-05-16T23:01:20.533955Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}}],"links":{"evidence":"/evidence","html":"/paper/2506.04197/citation-record","integrity":"/paper/2506.04197/integrity","json":"/paper/2506.04197/citation-record.json","paper":"/paper/2506.04197"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T10:54:51.804864Z","title":"A Wasserstein-type Distance to Measure Deviation from Equilibrium of Quantum Markov Semi- groups","venue":null,"work_id":"2f10e9c2-0712-4819-a046-ecc6ec3719be","year":2013},"citing_paper":{"arxiv_id":"2506.04197","last_updated":"2025-06-04T17:42:33Z","snapshot_observed_at":"2026-08-09T08:24:48.141790Z","submitted_at":"2025-06-04T17:42:33Z","title":"Transportation cost and contraction coefficient for channels on von Neumann algebras","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-07T10:54:50.718275Z"},"links":{"citing_paper":"/paper/2506.04197"},"observation_digest":"sha256:a88bf15ca140727285dc6a437ba077f7802378a3e7ad550ee04d1cda1a76d03b","observation_id":"c89acf79-a03e-400a-a152-549e155fd675","resolution":{"observed_at":"2026-08-07T10:54:51.809604Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2505.19269","last_updated":"2025-09-03T11:54:33Z","snapshot_observed_at":"2026-08-10T03:54:06.610274Z","submitted_at":"2025-05-25T18:59:33Z","title":"Quantum Wasserstein distances for quantum permutation groups","version":2},"cited_work":{"arxiv_id":"2505.19269","doi":null,"metadata_source":"pith","pith_arxiv_id":"2505.19269","snapshot_observed_at":"2026-08-07T10:54:51.334513Z","title":"Quantum Wasserstein distances for quantum permutation groups","venue":"math.OA","work_id":"ef743633-2911-4e15-9960-ce381bce9e09","year":2025},"citing_paper":{"arxiv_id":"2506.04197","last_updated":"2025-06-04T17:42:33Z","snapshot_observed_at":"2026-08-09T08:24:48.141790Z","submitted_at":"2025-06-04T17:42:33Z","title":"Transportation cost and contraction coefficient for channels on von Neumann algebras","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-07T10:54:50.724653Z"},"links":{"cited_paper":"/paper/2505.19269","citing_paper":"/paper/2506.04197"},"observation_digest":"sha256:12986cad10c7382630e434ee9ce276fc2529cd6bfefec4080b3ff75c6b9c8d38","observation_id":"256b1c5f-5921-4195-bbe1-80458aa87c21","resolution":{"observed_at":"2026-08-07T10:54:51.341436Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-07T10:54:50.730196Z","title":"Resource-Dependent Complexity of Quantum Channels","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2506.04197","last_updated":"2025-06-04T17:42:33Z","snapshot_observed_at":"2026-08-09T08:24:48.141790Z","submitted_at":"2025-06-04T17:42:33Z","title":"Transportation cost and contraction coefficient for channels on von Neumann algebras","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-07T10:54:50.730196Z"},"links":{"citing_paper":"/paper/2506.04197"},"observation_digest":"sha256:96a5d6c89e6f73f4e0d961fb87f5357dffc896365ddc1633a27b46bd78e5c517","observation_id":"aa507c49-1db3-4618-ae83-919a3d388f0b","resolution":{"observed_at":"2026-08-07T10:54:50.730196Z","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":"2026-08-07T10:54:51.789623Z","title":"Order p Quantum Wasserstein Distances from Couplings","venue":null,"work_id":"2531b333-8192-4208-890b-034bf09dd081","year":2025},"citing_paper":{"arxiv_id":"2506.04197","last_updated":"2025-06-04T17:42:33Z","snapshot_observed_at":"2026-08-09T08:24:48.141790Z","submitted_at":"2025-06-04T17:42:33Z","title":"Transportation cost and contraction coefficient for channels on von Neumann algebras","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-07T10:54:50.735727Z"},"links":{"citing_paper":"/paper/2506.04197"},"observation_digest":"sha256:1a9e29813d15216372922fada31bf4b0f43a0d57dc1ee252f9980b6aae3d1b6e","observation_id":"242e210a-e152-4bef-9b07-2a6885636f43","resolution":{"observed_at":"2026-08-07T10:54:51.794676Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":"2411.19890","doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T10:54:51.242710Z","title":"Reverse-type Data Processing Inequality","venue":null,"work_id":"22af82f4-e1d7-4d8d-9bd2-d9d575032199","year":2024},"citing_paper":{"arxiv_id":"2506.04197","last_updated":"2025-06-04T17:42:33Z","snapshot_observed_at":"2026-08-09T08:24:48.141790Z","submitted_at":"2025-06-04T17:42:33Z","title":"Transportation cost and contraction coefficient for channels on von Neumann algebras","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-07T10:54:50.741181Z"},"links":{"citing_paper":"/paper/2506.04197"},"observation_digest":"sha256:6d4dabf037a811b9c02db8179394316e7a9446ae9db741d72e578ef80d053cd1","observation_id":"05de4232-0bed-4724-b488-f8214ba7bac5","resolution":{"observed_at":"2026-08-07T10:54:51.251425Z","resolver_source":"raw_fallback","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-07T10:54:51.774755Z","title":"A free probability analogue of the Wasserstein metric on the trace-state space","venue":null,"work_id":"64f1162e-21af-4bb8-8235-a5adb3401e14","year":2001},"citing_paper":{"arxiv_id":"2506.04197","last_updated":"2025-06-04T17:42:33Z","snapshot_observed_at":"2026-08-09T08:24:48.141790Z","submitted_at":"2025-06-04T17:42:33Z","title":"Transportation cost and contraction coefficient for channels on von Neumann algebras","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-07T10:54:50.746418Z"},"links":{"citing_paper":"/paper/2506.04197"},"observation_digest":"sha256:abce6339b9ef979930068c3e0a6af432a846b65cc22cce410cd5daf810e70009","observation_id":"88203d6e-2f8c-463c-8ef5-17d243b76e85","resolution":{"observed_at":"2026-08-07T10:54:51.779597Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2101.03256","last_updated":"2021-02-08T19:32:02Z","snapshot_observed_at":"2026-08-10T03:58:37.373804Z","submitted_at":"2021-01-08T23:34:26Z","title":"Towards Optimal Transport for Quantum Densities","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2101.03256","snapshot_observed_at":"2026-08-07T10:54:50.753395Z","title":"Towards Optimal Transport for Quantum Densities","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2506.04197","last_updated":"2025-06-04T17:42:33Z","snapshot_observed_at":"2026-08-09T08:24:48.141790Z","submitted_at":"2025-06-04T17:42:33Z","title":"Transportation cost and contraction coefficient for channels on von Neumann algebras","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-07T10:54:50.753395Z"},"links":{"cited_paper":"/paper/2101.03256","citing_paper":"/paper/2506.04197"},"observation_digest":"sha256:5b658aa66e39a1c4e4c7ecd3a582474fffd91a1bf020219708e5e27160b8e197","observation_id":"8cf1c7a1-d178-4a63-b4f8-2913f71b0f36","resolution":{"observed_at":"2026-08-07T10:54:50.753395Z","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":"2026-08-07T10:54:51.759979Z","title":"Entropy and curvature: beyond the Peres-Tetali conjecture","venue":null,"work_id":"38a04249-939a-4d14-af94-f09a8b6bdcc1","year":2025},"citing_paper":{"arxiv_id":"2506.04197","last_updated":"2025-06-04T17:42:33Z","snapshot_observed_at":"2026-08-09T08:24:48.141790Z","submitted_at":"2025-06-04T17:42:33Z","title":"Transportation cost and contraction coefficient for channels on von Neumann algebras","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-07T10:54:50.758555Z"},"links":{"citing_paper":"/paper/2506.04197"},"observation_digest":"sha256:286d835cc245ecd88e51b255b250b8287196095e6ecd50aefaf01f6936275057","observation_id":"6cb9d48f-ad21-4821-a553-14b3a0a606fc","resolution":{"observed_at":"2026-08-07T10:54:51.764672Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-07T10:54:51.744865Z","title":"BMO-estimates for non-commutative vector valued Lipschitz functions","venue":null,"work_id":"8cfe40a6-37cb-4bda-807e-063d646bad74","year":2020},"citing_paper":{"arxiv_id":"2506.04197","last_updated":"2025-06-04T17:42:33Z","snapshot_observed_at":"2026-08-09T08:24:48.141790Z","submitted_at":"2025-06-04T17:42:33Z","title":"Transportation cost and contraction coefficient for channels on von Neumann algebras","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-07T10:54:50.764258Z"},"links":{"citing_paper":"/paper/2506.04197"},"observation_digest":"sha256:756b3e1be892bb3b26e2388cd583090cb10c172234911cb9239ced059566ecfa","observation_id":"04fddb12-310d-406d-bdcc-0857f341129f","resolution":{"observed_at":"2026-08-07T10:54:51.749729Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-07T10:54:51.730352Z","title":"The metric aspect of noncommutative geometry","venue":null,"work_id":"a02d9790-9db5-476a-8a91-61ab90beccd4","year":1992},"citing_paper":{"arxiv_id":"2506.04197","last_updated":"2025-06-04T17:42:33Z","snapshot_observed_at":"2026-08-09T08:24:48.141790Z","submitted_at":"2025-06-04T17:42:33Z","title":"Transportation cost and contraction coefficient for channels on von Neumann algebras","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-07T10:54:50.768903Z"},"links":{"citing_paper":"/paper/2506.04197"},"observation_digest":"sha256:0f47a3e2e28d1d6af975c03a7c72df80a4cca875e9f7976863f321de14ea765d","observation_id":"04582347-ff1f-4d18-a244-5a47fd0e787c","resolution":{"observed_at":"2026-08-07T10:54:51.734916Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-07T10:54:51.715445Z","title":"The Quantum Wasserstein Distance of Order 1","venue":null,"work_id":"e4eafc26-e77d-4580-b7c3-a8c31e23475a","year":2021},"citing_paper":{"arxiv_id":"2506.04197","last_updated":"2025-06-04T17:42:33Z","snapshot_observed_at":"2026-08-09T08:24:48.141790Z","submitted_at":"2025-06-04T17:42:33Z","title":"Transportation cost and contraction coefficient for channels on von Neumann algebras","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-07T10:54:50.773853Z"},"links":{"citing_paper":"/paper/2506.04197"},"observation_digest":"sha256:11fb5ba3bdd48d98f149bc36158afef85e2ac695ac6e72c50397ad0b4106d60d","observation_id":"6d63c44e-6218-4fd1-9410-e5fd16c3c198","resolution":{"observed_at":"2026-08-07T10:54:51.720080Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-07T10:54:51.700492Z","title":"Quantum Optimal Transport with Quantum Channels","venue":null,"work_id":"db922278-6694-46a2-a010-6805c0cfa8d3","year":2021},"citing_paper":{"arxiv_id":"2506.04197","last_updated":"2025-06-04T17:42:33Z","snapshot_observed_at":"2026-08-09T08:24:48.141790Z","submitted_at":"2025-06-04T17:42:33Z","title":"Transportation cost and contraction coefficient for channels on von Neumann algebras","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-07T10:54:50.778425Z"},"links":{"citing_paper":"/paper/2506.04197"},"observation_digest":"sha256:b098586786a691d5c1dca8ddcefdb951b9f423621ee6a0ae4cae230552110cd6","observation_id":"14105f47-240b-49fa-9aa9-10d0aa624818","resolution":{"observed_at":"2026-08-07T10:54:51.705296Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-07T10:54:51.685440Z","title":"Lower Bound for Simulation Cost of Open Quantum Systems: Lipschitz Continuity Approach","venue":null,"work_id":"5b1d7bb9-5056-4577-a781-beac6e3d8470","year":2025},"citing_paper":{"arxiv_id":"2506.04197","last_updated":"2025-06-04T17:42:33Z","snapshot_observed_at":"2026-08-09T08:24:48.141790Z","submitted_at":"2025-06-04T17:42:33Z","title":"Transportation cost and contraction coefficient for channels on von Neumann algebras","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-07T10:54:50.783411Z"},"links":{"citing_paper":"/paper/2506.04197"},"observation_digest":"sha256:2ae0eba181fbbf8c7543b9d71370867b51f0727a3ef4b32839dfa14e5f01e38f","observation_id":"9f783c8e-6b24-46dd-b58a-20769657b96f","resolution":{"observed_at":"2026-08-07T10:54:51.690338Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-07T10:54:51.670544Z","title":"Dixmier.von Neumann algebras","venue":null,"work_id":"b0a3fc57-2883-44ba-8055-5274bec7f2b0","year":2011},"citing_paper":{"arxiv_id":"2506.04197","last_updated":"2025-06-04T17:42:33Z","snapshot_observed_at":"2026-08-09T08:24:48.141790Z","submitted_at":"2025-06-04T17:42:33Z","title":"Transportation cost and contraction coefficient for channels on von Neumann algebras","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-07T10:54:50.788141Z"},"links":{"citing_paper":"/paper/2506.04197"},"observation_digest":"sha256:7a29b621d90519d2852727ed1b3ca615c5d02ffa978fe545bef110cdf07f2cdc","observation_id":"6c0a43ea-e690-458f-bc3c-695a034977a6","resolution":{"observed_at":"2026-08-07T10:54:51.675401Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-07T10:54:51.654613Z","title":"A View on Optimal Transport from Noncommutative Geometry","venue":null,"work_id":"605b1367-b42f-4f85-b479-fe7afb4023f0","year":2010},"citing_paper":{"arxiv_id":"2506.04197","last_updated":"2025-06-04T17:42:33Z","snapshot_observed_at":"2026-08-09T08:24:48.141790Z","submitted_at":"2025-06-04T17:42:33Z","title":"Transportation cost and contraction coefficient for channels on von Neumann algebras","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-07T10:54:50.792824Z"},"links":{"citing_paper":"/paper/2506.04197"},"observation_digest":"sha256:eb15e60d1d784f08782390983e579e3439a00db22361b52574817b59a8b92422","observation_id":"4a25865b-e8e1-4e0a-adc7-2848db565d69","resolution":{"observed_at":"2026-08-07T10:54:51.659589Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-07T10:54:51.638995Z","title":"Fisher information and logarithmic Sobolev inequality for matrix-valued functions","venue":null,"work_id":"4a6c3387-2128-426c-8660-694499bc10b2","year":2020},"citing_paper":{"arxiv_id":"2506.04197","last_updated":"2025-06-04T17:42:33Z","snapshot_observed_at":"2026-08-09T08:24:48.141790Z","submitted_at":"2025-06-04T17:42:33Z","title":"Transportation cost and contraction coefficient for channels on von Neumann algebras","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-07T10:54:50.797923Z"},"links":{"citing_paper":"/paper/2506.04197"},"observation_digest":"sha256:92b6cab6c40c2c1aeb0dba0b62ffd57755a0d39b45bf94817f79b1831e1680e3","observation_id":"8ce2cdd2-20d5-4fbc-befc-1539ade2561c","resolution":{"observed_at":"2026-08-07T10:54:51.644142Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-07T10:54:51.622705Z","title":"Relative entropy for von Neumann subalgebras","venue":null,"work_id":"83942fe5-d531-47c9-bcc8-0580cee05e25","year":2020},"citing_paper":{"arxiv_id":"2506.04197","last_updated":"2025-06-04T17:42:33Z","snapshot_observed_at":"2026-08-09T08:24:48.141790Z","submitted_at":"2025-06-04T17:42:33Z","title":"Transportation cost and contraction coefficient for channels on von Neumann algebras","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-07T10:54:50.802763Z"},"links":{"citing_paper":"/paper/2506.04197"},"observation_digest":"sha256:c1764173d8862bb91968f622e2bf442d04968ead47703152ac5b9ce4fa2b316e","observation_id":"b98f36b4-dadd-40cc-9b3c-2f21e93ec974","resolution":{"observed_at":"2026-08-07T10:54:51.627743Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2209.11684","last_updated":"2023-10-16T12:08:18Z","snapshot_observed_at":"2026-08-01T21:19:13.880094Z","submitted_at":"2022-09-22T17:40:22Z","title":"Relative entropy decay and complete positivity mixing time","version":2},"cited_work":{"arxiv_id":"2209.11684","doi":null,"metadata_source":"pith","pith_arxiv_id":"2209.11684","snapshot_observed_at":"2026-08-07T10:54:51.128901Z","title":"Relative entropy decay and complete positivity mixing time","venue":"quant-ph","work_id":"4ebf40fd-a3af-4bb7-bd95-856efbe4b027","year":2022},"citing_paper":{"arxiv_id":"2506.04197","last_updated":"2025-06-04T17:42:33Z","snapshot_observed_at":"2026-08-09T08:24:48.141790Z","submitted_at":"2025-06-04T17:42:33Z","title":"Transportation cost and contraction coefficient for channels on von Neumann algebras","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-07T10:54:50.807621Z"},"links":{"cited_paper":"/paper/2209.11684","citing_paper":"/paper/2506.04197"},"observation_digest":"sha256:5729594c47b3376cbe0d93ac1e093d9ddcf1ff846a0162b4f85af4064567018a","observation_id":"ce00cdda-cfe0-4f94-bdf3-184dfe432418","resolution":{"observed_at":"2026-08-07T10:54:51.137688Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-07T10:54:51.607301Z","title":"Complete Entropic Inequalities for Quantum Markov Chains","venue":null,"work_id":"4395e539-16c8-486f-8233-5f683db95871","year":2022},"citing_paper":{"arxiv_id":"2506.04197","last_updated":"2025-06-04T17:42:33Z","snapshot_observed_at":"2026-08-09T08:24:48.141790Z","submitted_at":"2025-06-04T17:42:33Z","title":"Transportation cost and contraction coefficient for channels on von Neumann algebras","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-07T10:54:50.812779Z"},"links":{"citing_paper":"/paper/2506.04197"},"observation_digest":"sha256:7e6b5b22bf09a6f7c40ab7e12c83fe302fce339b87c4ab7cfd96fb4838c6a9b7","observation_id":"8ba1e9e2-9fe7-497c-9a88-0d5418414a15","resolution":{"observed_at":"2026-08-07T10:54:51.612251Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-07T10:54:51.592226Z","title":"Coarse Ricci curvature of quantum channels","venue":null,"work_id":"18296b2b-bea6-4cf0-81bf-b6571017b04a","year":2024},"citing_paper":{"arxiv_id":"2506.04197","last_updated":"2025-06-04T17:42:33Z","snapshot_observed_at":"2026-08-09T08:24:48.141790Z","submitted_at":"2025-06-04T17:42:33Z","title":"Transportation cost and contraction coefficient for channels on von Neumann algebras","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-07T10:54:50.817478Z"},"links":{"citing_paper":"/paper/2506.04197"},"observation_digest":"sha256:4e71aa5c1d8c2db3ec144ac6dacb37d0251c3d9a6b912b2674b54afba01aa31a","observation_id":"e19b0b0c-432d-46be-b0c2-bbe678ae239b","resolution":{"observed_at":"2026-08-07T10:54:51.597201Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-07T10:54:50.821900Z","title":"A Unified Approach to Quantum Contraction and Correlation Coefficients","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2506.04197","last_updated":"2025-06-04T17:42:33Z","snapshot_observed_at":"2026-08-09T08:24:48.141790Z","submitted_at":"2025-06-04T17:42:33Z","title":"Transportation cost and contraction coefficient for channels on von Neumann algebras","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-07T10:54:50.821900Z"},"links":{"citing_paper":"/paper/2506.04197"},"observation_digest":"sha256:351265a23eda03eb54922651fc862ac02bf38141f7e484e2ffd04d4f568aa25a","observation_id":"7fe67219-6616-49c7-8cab-e400f9d33c42","resolution":{"observed_at":"2026-08-07T10:54:50.821900Z","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":"2026-08-07T10:54:51.577164Z","title":"Carnot–Carath´ eodory Spaces Seen from Within","venue":null,"work_id":"5d2fadf0-02c3-43ab-bbe6-39368b4efc9c","year":1996},"citing_paper":{"arxiv_id":"2506.04197","last_updated":"2025-06-04T17:42:33Z","snapshot_observed_at":"2026-08-09T08:24:48.141790Z","submitted_at":"2025-06-04T17:42:33Z","title":"Transportation cost and contraction coefficient for channels on von Neumann algebras","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-07T10:54:50.826539Z"},"links":{"citing_paper":"/paper/2506.04197"},"observation_digest":"sha256:cb307dbfa11acf8d09bf0e640cdba9acf21ea970387c737a0f3a4d54d20afe93","observation_id":"3d35e122-4269-46bb-add5-ca8fa5587229","resolution":{"observed_at":"2026-08-07T10:54:51.581996Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-07T10:54:51.561654Z","title":"Contraction coefficients for noisy quantum channels","venue":null,"work_id":"7af844c5-c332-44ea-a6b0-bfcc745588da","year":2016},"citing_paper":{"arxiv_id":"2506.04197","last_updated":"2025-06-04T17:42:33Z","snapshot_observed_at":"2026-08-09T08:24:48.141790Z","submitted_at":"2025-06-04T17:42:33Z","title":"Transportation cost and contraction coefficient for channels on von Neumann algebras","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-07T10:54:50.831811Z"},"links":{"citing_paper":"/paper/2506.04197"},"observation_digest":"sha256:4f8355bec6eb1182ada53f7602c1bc5982578f98988fa5e9990bc79e245de9b5","observation_id":"445d5383-8924-46ca-ae9b-85e71761e0b1","resolution":{"observed_at":"2026-08-07T10:54:51.566713Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-07T10:54:51.545303Z","title":"BMO spaces associated with semigroups of operators","venue":null,"work_id":"738b4ed2-ebd5-49f0-a7e9-c581907c8587","year":2012},"citing_paper":{"arxiv_id":"2506.04197","last_updated":"2025-06-04T17:42:33Z","snapshot_observed_at":"2026-08-09T08:24:48.141790Z","submitted_at":"2025-06-04T17:42:33Z","title":"Transportation cost and contraction coefficient for channels on von Neumann algebras","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-07T10:54:50.836309Z"},"links":{"citing_paper":"/paper/2506.04197"},"observation_digest":"sha256:d0758ec6b10fc25cfce2939a13808dc5b5c532c434325061002dd0a957fd53af","observation_id":"81658807-a02d-4437-aa73-159ac4ef1e4a","resolution":{"observed_at":"2026-08-07T10:54:51.550882Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-07T10:54:51.530105Z","title":"A noncommutative version of the John-Nirenberg theorem","venue":null,"work_id":"00779ac7-8989-42c5-909d-04fd34bfb9c5","year":2007},"citing_paper":{"arxiv_id":"2506.04197","last_updated":"2025-06-04T17:42:33Z","snapshot_observed_at":"2026-08-09T08:24:48.141790Z","submitted_at":"2025-06-04T17:42:33Z","title":"Transportation cost and contraction coefficient for channels on von Neumann algebras","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-07T10:54:50.841096Z"},"links":{"citing_paper":"/paper/2506.04197"},"observation_digest":"sha256:b5ad60eb88ac655b8a5541b1bdd705cd82f53170ef77fe0df3754c293470ad8d","observation_id":"74600a50-3cb5-4b47-9eea-e7bcafdea36c","resolution":{"observed_at":"2026-08-07T10:54:51.534919Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-07T10:54:51.514786Z","title":"On the translocation of masses","venue":null,"work_id":"28d9b905-79a5-4f4f-a448-629e0f6550a1","year":1942},"citing_paper":{"arxiv_id":"2506.04197","last_updated":"2025-06-04T17:42:33Z","snapshot_observed_at":"2026-08-09T08:24:48.141790Z","submitted_at":"2025-06-04T17:42:33Z","title":"Transportation cost and contraction coefficient for channels on von Neumann algebras","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-07T10:54:50.845532Z"},"links":{"citing_paper":"/paper/2506.04197"},"observation_digest":"sha256:6af3ecf2fc5b5ca4d9527f7a74bcc2eb76ebef0ca734271e489074ac2e2dd25e","observation_id":"80049205-76b0-4c35-b085-718e0c45e3c2","resolution":{"observed_at":"2026-08-07T10:54:51.519574Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2208.06306","last_updated":"2022-08-12T14:44:13Z","snapshot_observed_at":"2026-08-10T07:04:35.196509Z","submitted_at":"2022-08-12T14:44:13Z","title":"Wasserstein Complexity of Quantum Circuits","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2208.06306","snapshot_observed_at":"2026-08-07T10:54:50.850418Z","title":"Wasserstein Complexity of Quantum Circuits","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2506.04197","last_updated":"2025-06-04T17:42:33Z","snapshot_observed_at":"2026-08-09T08:24:48.141790Z","submitted_at":"2025-06-04T17:42:33Z","title":"Transportation cost and contraction coefficient for channels on von Neumann algebras","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-07T10:54:50.850418Z"},"links":{"cited_paper":"/paper/2208.06306","citing_paper":"/paper/2506.04197"},"observation_digest":"sha256:89311153275ce1b914952395a794f8cfcb85196c46ecd7a0f1cf8ec62bfb6a49","observation_id":"c3f6d2eb-694c-4dc4-8e01-7c777edfa322","resolution":{"observed_at":"2026-08-07T10:54:50.850418Z","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":"2026-08-07T10:54:51.497407Z","title":"Monge.M´ emoire sur la th´ eorie des d´ eblais et des remblais","venue":null,"work_id":"8a1fbada-c7b1-4b7e-a8e5-a79d632e3e29","year":null},"citing_paper":{"arxiv_id":"2506.04197","last_updated":"2025-06-04T17:42:33Z","snapshot_observed_at":"2026-08-09T08:24:48.141790Z","submitted_at":"2025-06-04T17:42:33Z","title":"Transportation cost and contraction coefficient for channels on von Neumann algebras","version":1},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-07T10:54:50.855500Z"},"links":{"citing_paper":"/paper/2506.04197"},"observation_digest":"sha256:828f56db4559d31dfdc4180529f9fc531daacc943f805a2e6bb41e5d9d61d68f","observation_id":"1c889650-9e1f-45df-87e1-2d5d1a1367bf","resolution":{"observed_at":"2026-08-07T10:54:51.503476Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-07T10:54:51.481412Z","title":"A Geometric Approach to Quantum Circuit Lower Bounds","venue":null,"work_id":"9c182d0e-d73b-44a8-8011-3749d2c2866b","year":2006},"citing_paper":{"arxiv_id":"2506.04197","last_updated":"2025-06-04T17:42:33Z","snapshot_observed_at":"2026-08-09T08:24:48.141790Z","submitted_at":"2025-06-04T17:42:33Z","title":"Transportation cost and contraction coefficient for channels on von Neumann algebras","version":1},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-07T10:54:50.860176Z"},"links":{"citing_paper":"/paper/2506.04197"},"observation_digest":"sha256:ead8ee56cb00ddf53d80c94dc12df02888acc22ad03c4379ea1fccf17d6eaf52","observation_id":"0c4a2868-806f-4122-8a7e-447604bae5e0","resolution":{"observed_at":"2026-08-07T10:54:51.486479Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-07T10:54:51.465134Z","title":"Optimal control, geometry, and quantum computing","venue":null,"work_id":"d9bf8472-7aa9-4956-94d5-81346d848396","year":2006},"citing_paper":{"arxiv_id":"2506.04197","last_updated":"2025-06-04T17:42:33Z","snapshot_observed_at":"2026-08-09T08:24:48.141790Z","submitted_at":"2025-06-04T17:42:33Z","title":"Transportation cost and contraction coefficient for channels on von Neumann algebras","version":1},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-07T10:54:50.864438Z"},"links":{"citing_paper":"/paper/2506.04197"},"observation_digest":"sha256:a99493f9dab13d5f02a51126ec27ec8adb4cd983a3eff848dba6dd74ad920650","observation_id":"ff6b0593-8a44-4130-8aa6-532195a75c13","resolution":{"observed_at":"2026-08-07T10:54:51.470438Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-07T10:54:51.448120Z","title":"Quantum Computation as Geometry","venue":null,"work_id":"e32a741d-34a0-458c-a17d-8cd692e2bd7e","year":2006},"citing_paper":{"arxiv_id":"2506.04197","last_updated":"2025-06-04T17:42:33Z","snapshot_observed_at":"2026-08-09T08:24:48.141790Z","submitted_at":"2025-06-04T17:42:33Z","title":"Transportation cost and contraction coefficient for channels on von Neumann algebras","version":1},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-07T10:54:50.868923Z"},"links":{"citing_paper":"/paper/2506.04197"},"observation_digest":"sha256:ef941dd8945aba32ca146705227ba05f01eac1ca86edf7092946dccc61ee0e06","observation_id":"735a2a3d-5577-4ee5-84a6-e30eaf83cea6","resolution":{"observed_at":"2026-08-07T10:54:51.453673Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-07T10:54:51.432749Z","title":"Paulsen.Completely Bounded Maps and Operator Algebras","venue":null,"work_id":"baf17adf-2b52-40a4-afd9-4bf0a93c28f1","year":2003},"citing_paper":{"arxiv_id":"2506.04197","last_updated":"2025-06-04T17:42:33Z","snapshot_observed_at":"2026-08-09T08:24:48.141790Z","submitted_at":"2025-06-04T17:42:33Z","title":"Transportation cost and contraction coefficient for channels on von Neumann algebras","version":1},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-07T10:54:50.873333Z"},"links":{"citing_paper":"/paper/2506.04197"},"observation_digest":"sha256:cce9c76f361ce099affcb9f72677a4915a370fa422162e6261db946de56d9626","observation_id":"484576f5-4c82-46d4-b210-67a9cded38cd","resolution":{"observed_at":"2026-08-07T10:54:51.437483Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-07T10:54:51.415662Z","title":"Metrics on state spaces","venue":null,"work_id":"49fd1d1b-dfd3-4e9f-a025-9b5f72ca821d","year":1999},"citing_paper":{"arxiv_id":"2506.04197","last_updated":"2025-06-04T17:42:33Z","snapshot_observed_at":"2026-08-09T08:24:48.141790Z","submitted_at":"2025-06-04T17:42:33Z","title":"Transportation cost and contraction coefficient for channels on von Neumann algebras","version":1},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-07T10:54:50.877816Z"},"links":{"citing_paper":"/paper/2506.04197"},"observation_digest":"sha256:06e90a5f0845487b129b169924c62b731aff8e55f4f6494fb973f89688d45b50","observation_id":"36d4cfd4-5451-4a13-92ef-1a1ec982c2e3","resolution":{"observed_at":"2026-08-07T10:54:51.421105Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-07T10:54:51.400486Z","title":"Compact quantum metric spaces","venue":null,"work_id":"61f5823b-48db-4689-8701-f271afee2031","year":2004},"citing_paper":{"arxiv_id":"2506.04197","last_updated":"2025-06-04T17:42:33Z","snapshot_observed_at":"2026-08-09T08:24:48.141790Z","submitted_at":"2025-06-04T17:42:33Z","title":"Transportation cost and contraction coefficient for channels on von Neumann algebras","version":1},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-07T10:54:50.882272Z"},"links":{"citing_paper":"/paper/2506.04197"},"observation_digest":"sha256:48cdc313b482e32b1e6c8dd713147e67c92a7a51a1f4f33039eb591bfb6aab06","observation_id":"e483fbfa-acdb-487a-b943-ddc55ab3298e","resolution":{"observed_at":"2026-08-07T10:54:51.405168Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-07T10:54:50.886968Z","title":"Optimal quantum algorithm for Gibbs state preparation","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2506.04197","last_updated":"2025-06-04T17:42:33Z","snapshot_observed_at":"2026-08-09T08:24:48.141790Z","submitted_at":"2025-06-04T17:42:33Z","title":"Transportation cost and contraction coefficient for channels on von Neumann algebras","version":1},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-08-07T10:54:50.886968Z"},"links":{"citing_paper":"/paper/2506.04197"},"observation_digest":"sha256:d97c07d0944024af62dc689ab54b93838619b7ff81a3e5f6da1aa9ceb105cffe","observation_id":"3c661739-c6ea-45e1-8008-38fbb3e01f01","resolution":{"observed_at":"2026-08-07T10:54:50.886968Z","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":"2026-08-07T10:54:51.384523Z","title":"Sakai.C*-algebras and W*-algebras","venue":null,"work_id":"282c1e0e-a08d-4432-898d-41574eab5f08","year":2012},"citing_paper":{"arxiv_id":"2506.04197","last_updated":"2025-06-04T17:42:33Z","snapshot_observed_at":"2026-08-09T08:24:48.141790Z","submitted_at":"2025-06-04T17:42:33Z","title":"Transportation cost and contraction coefficient for channels on von Neumann algebras","version":1},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-08-07T10:54:50.891460Z"},"links":{"citing_paper":"/paper/2506.04197"},"observation_digest":"sha256:ccd33e3778efdfb7bf1d4a0bb7871abe06143d77ca788c348fc55a20c01aad03","observation_id":"ded037c9-8561-454a-a2d5-1e1b702ff693","resolution":{"observed_at":"2026-08-07T10:54:51.389505Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-07T10:54:51.368459Z","title":"Quasi-relative entropy: the closest separable state and reversed Pinsker inequality","venue":null,"work_id":"4d5132d9-506d-4acf-973b-c057eb23ee75","year":2021},"citing_paper":{"arxiv_id":"2506.04197","last_updated":"2025-06-04T17:42:33Z","snapshot_observed_at":"2026-08-09T08:24:48.141790Z","submitted_at":"2025-06-04T17:42:33Z","title":"Transportation cost and contraction coefficient for channels on von Neumann algebras","version":1},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-08-07T10:54:50.895695Z"},"links":{"citing_paper":"/paper/2506.04197"},"observation_digest":"sha256:2e66781ead2a9ef9f428032f74cf655d2c9b87c79c30b2cc29b14d712d01d6a5","observation_id":"de94c81b-ea63-4397-a2fd-ed024674cbc6","resolution":{"observed_at":"2026-08-07T10:54:51.373196Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2505.07549","last_updated":"2025-06-26T14:00:49Z","snapshot_observed_at":"2026-08-08T03:03:19.009077Z","submitted_at":"2025-05-12T13:29:34Z","title":"Exponential Relative Entropy Decay Along Quantum Markov Semigroups","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2505.07549","snapshot_observed_at":"2026-08-07T10:54:50.900153Z","title":"Exponential Relative Entropy Decay Along Quantum Markov Semigroups","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2506.04197","last_updated":"2025-06-04T17:42:33Z","snapshot_observed_at":"2026-08-09T08:24:48.141790Z","submitted_at":"2025-06-04T17:42:33Z","title":"Transportation cost and contraction coefficient for channels on von Neumann algebras","version":1},"reference_index":38,"source":"pdf_text","source_observed_at":"2026-08-07T10:54:50.900153Z"},"links":{"cited_paper":"/paper/2505.07549","citing_paper":"/paper/2506.04197"},"observation_digest":"sha256:dadcb476da8f48a5debae728e3571ec090cefc292102d7fc6b5d59e7826a024e","observation_id":"76483b28-de09-4295-9f98-e0c2d255113e","resolution":{"observed_at":"2026-08-07T10:54:50.900153Z","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":"2026-08-07T10:54:51.352464Z","title":"Non-commutative metric topology on matrix state space","venue":null,"work_id":"a7141e55-19bc-4a14-878c-3f000253a2e7","year":2006},"citing_paper":{"arxiv_id":"2506.04197","last_updated":"2025-06-04T17:42:33Z","snapshot_observed_at":"2026-08-09T08:24:48.141790Z","submitted_at":"2025-06-04T17:42:33Z","title":"Transportation cost and contraction coefficient for channels on von Neumann algebras","version":1},"reference_index":39,"source":"pdf_text","source_observed_at":"2026-08-07T10:54:50.904769Z"},"links":{"citing_paper":"/paper/2506.04197"},"observation_digest":"sha256:96e00a2ec5266b00fb9cd1df5613e6d2fe79577de6fdf7c0cc7866df24114d3a","observation_id":"1b6de95a-f116-407c-b00e-89076f6cdc8b","resolution":{"observed_at":"2026-08-07T10:54:51.357463Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2506.04197","last_updated":"2025-06-04T17:42:33Z","latest_version":1,"primary_category":"math.OA","snapshot_observed_at":"2026-08-09T08:24:48.141790Z","submitted_at":"2025-06-04T17:42:33Z","title":"Transportation cost and contraction coefficient for channels on von Neumann algebras"},"reference_resolution":{"displayed":39,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":6,"verified_exact":3,"verified_fuzzy":30},"total_outbound_references":39},"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":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"thesis":"As of 10 August 2026, this Paper Citation Record lists 39 of 39 outbound references and 1 inbound Pith citation observation for arXiv:2506.04197."}