{"as_of":"2026-08-16T12:11:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:f3fe4350e730090c45e9c32a2f496ac641a42da77cb0c1fdba592821f662d9d5","coverage":[{"denominator":57,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":57,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-16T01:10:23.967947Z","state":"measured"},{"denominator":60,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":60,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-16T06:30:59.297886+00:00","state":"measured"},{"denominator":3,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":3,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-15T18:52:52.228456Z","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":"2026-05-25T07:50:28.831913Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2505.02125","last_updated":"2025-05-04T14:15:03Z","snapshot_observed_at":"2026-08-16T00:58:25.913254Z","submitted_at":"2025-05-04T14:15:03Z","title":"R\\'{e}nyi Markov length in one-dimensional non-trivial mixed state phases and mixed state phase transitions","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2505.02125","snapshot_observed_at":"2026-08-15T18:52:52.228456Z","title":null,"venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2506.18475","last_updated":"2025-06-23T10:18:53Z","snapshot_observed_at":"2026-08-15T18:45:50.129614Z","submitted_at":"2025-06-23T10:18:53Z","title":"R\\'{e}nyi and Shannon mutual information in critical and decohered critical system","version":1},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-08-15T18:52:52.228456Z"},"links":{"cited_paper":"/paper/2505.02125","citing_paper":"/paper/2506.18475"},"observation_digest":"sha256:f543cc75380acb28d671531273e5f121c8d70414625c0a9cdd569a02ba66bb0d","observation_id":"9f2c3ba5-52ca-44f7-bdfe-d08b3166285b","resolution":{"observed_at":"2026-08-15T18:52:52.228456Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2505.02125","last_updated":"2025-05-04T14:15:03Z","snapshot_observed_at":"2026-08-16T00:58:25.913254Z","submitted_at":"2025-05-04T14:15:03Z","title":"R\\'{e}nyi Markov length in one-dimensional non-trivial mixed state phases and mixed state phase transitions","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2505.02125","snapshot_observed_at":"2026-08-15T17:07:04.534171Z","title":null,"venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2508.17871","last_updated":"2025-08-25T10:26:13Z","snapshot_observed_at":"2026-08-16T07:49:16.138604Z","submitted_at":"2025-08-25T10:26:13Z","title":"Succession of Ising criticality and its threshold in critical quantum Ising model subject to symmetric decoherence","version":1},"reference_index":48,"source":"pdf_text","source_observed_at":"2026-08-15T17:07:04.534171Z"},"links":{"cited_paper":"/paper/2505.02125","citing_paper":"/paper/2508.17871"},"observation_digest":"sha256:0d31bd07be13422e2e43c718c9e0455f2446650be1410fd30e4ff21a6df58bf9","observation_id":"ecab2227-b7cf-4d29-b386-09c5d500d511","resolution":{"observed_at":"2026-08-15T17:07:04.534171Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2505.02125","last_updated":"2025-05-04T14:15:03Z","snapshot_observed_at":"2026-08-16T00:58:25.913254Z","submitted_at":"2025-05-04T14:15:03Z","title":"R\\'{e}nyi Markov length in one-dimensional non-trivial mixed state phases and mixed state phase transitions","version":1},"cited_work":{"arxiv_id":"2505.02125","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2505.02125","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"a93e683f-fe3c-4ab1-8403-0deee56a5ad7","year":2025},"citing_paper":{"arxiv_id":"2510.22542","last_updated":"2026-05-22T01:39:25Z","snapshot_observed_at":"2026-08-16T12:07:55.212228Z","submitted_at":"2025-10-26T05:46:34Z","title":"Krylov Complexity and Mixed-State Phase Transition","version":4},"reference_index":70,"source":"pdf_text","source_observed_at":"2026-05-25T07:50:05.277937Z"},"links":{"cited_paper":"/paper/2505.02125","citing_paper":"/paper/2510.22542"},"observation_digest":"sha256:de27a961d9ccc9ff69e888f094f9ebc156045606190bc65f30c6bf586a6346f7","observation_id":"7963df86-75ba-4061-835e-379d27734e33","resolution":{"observed_at":"2026-05-25T07:50:28.835245Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}}],"links":{"evidence":"/evidence","html":"/paper/2505.02125/citation-record","integrity":"/paper/2505.02125/integrity","json":"/paper/2505.02125/citation-record.json","paper":"/paper/2505.02125"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T01:10:24.749964Z","title":"Thus, as discussed in Sec","venue":null,"work_id":"ee2addac-8a59-42e9-b4b7-d5734a072f80","year":null},"citing_paper":{"arxiv_id":"2505.02125","last_updated":"2025-05-04T14:15:03Z","snapshot_observed_at":"2026-08-16T00:58:25.913254Z","submitted_at":"2025-05-04T14:15:03Z","title":"R\\'{e}nyi Markov length in one-dimensional non-trivial mixed state phases and mixed state phase transitions","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-16T01:10:23.750995Z"},"links":{"citing_paper":"/paper/2505.02125"},"observation_digest":"sha256:7dacc87404af922484276df46db0965a4706cc4521a6c45af578db4b8c4807f5","observation_id":"8317e498-dcd3-48cf-b57e-dabef6930a8c","resolution":{"observed_at":"2026-08-16T01:10:24.754244Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-16T01:10:23.756453Z","title":null,"venue":null,"work_id":null,"year":2000},"citing_paper":{"arxiv_id":"2505.02125","last_updated":"2025-05-04T14:15:03Z","snapshot_observed_at":"2026-08-16T00:58:25.913254Z","submitted_at":"2025-05-04T14:15:03Z","title":"R\\'{e}nyi Markov length in one-dimensional non-trivial mixed state phases and mixed state phase transitions","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-16T01:10:23.756453Z"},"links":{"citing_paper":"/paper/2505.02125"},"observation_digest":"sha256:e31be140647e3a8957cee7221b090711048b433a042c043bad608331b8090f65","observation_id":"a2f09d57-4298-4572-873e-086ae14ca129","resolution":{"observed_at":"2026-08-16T01:10:23.756453Z","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":"2026-08-16T01:10:23.760983Z","title":null,"venue":null,"work_id":null,"year":2003},"citing_paper":{"arxiv_id":"2505.02125","last_updated":"2025-05-04T14:15:03Z","snapshot_observed_at":"2026-08-16T00:58:25.913254Z","submitted_at":"2025-05-04T14:15:03Z","title":"R\\'{e}nyi Markov length in one-dimensional non-trivial mixed state phases and mixed state phase transitions","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-16T01:10:23.760983Z"},"links":{"citing_paper":"/paper/2505.02125"},"observation_digest":"sha256:8c64587a0322fe24801d10a99ca3056bf196dd6661a722d19ee31be937e2a20a","observation_id":"a4b37d02-7923-4304-86a1-79b562aae7f1","resolution":{"observed_at":"2026-08-16T01:10:23.760983Z","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":"2026-08-16T01:10:23.765137Z","title":"Dennis, A","venue":null,"work_id":null,"year":2002},"citing_paper":{"arxiv_id":"2505.02125","last_updated":"2025-05-04T14:15:03Z","snapshot_observed_at":"2026-08-16T00:58:25.913254Z","submitted_at":"2025-05-04T14:15:03Z","title":"R\\'{e}nyi Markov length in one-dimensional non-trivial mixed state phases and mixed state phase transitions","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-16T01:10:23.765137Z"},"links":{"citing_paper":"/paper/2505.02125"},"observation_digest":"sha256:b9e894643cc0b96edceae8b8b1ef46c5aab2214e590c6a5fe1909043e339ad16","observation_id":"396d7a9a-65d9-4e7f-86e1-efe49d0d502f","resolution":{"observed_at":"2026-08-16T01:10:23.765137Z","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":"2026-08-16T01:10:23.769210Z","title":null,"venue":null,"work_id":null,"year":2003},"citing_paper":{"arxiv_id":"2505.02125","last_updated":"2025-05-04T14:15:03Z","snapshot_observed_at":"2026-08-16T00:58:25.913254Z","submitted_at":"2025-05-04T14:15:03Z","title":"R\\'{e}nyi Markov length in one-dimensional non-trivial mixed state phases and mixed state phase transitions","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-16T01:10:23.769210Z"},"links":{"citing_paper":"/paper/2505.02125"},"observation_digest":"sha256:01d13c903eef37e0982ac39c167698c1d7d98dc841321e43e028134d5a5c3104","observation_id":"8bb1681b-a03e-4244-bb63-3c2d06ad2c32","resolution":{"observed_at":"2026-08-16T01:10:23.769210Z","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":"2026-08-16T01:10:23.772970Z","title":null,"venue":null,"work_id":null,"year":2004},"citing_paper":{"arxiv_id":"2505.02125","last_updated":"2025-05-04T14:15:03Z","snapshot_observed_at":"2026-08-16T00:58:25.913254Z","submitted_at":"2025-05-04T14:15:03Z","title":"R\\'{e}nyi Markov length in one-dimensional non-trivial mixed state phases and mixed state phase transitions","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-16T01:10:23.772970Z"},"links":{"citing_paper":"/paper/2505.02125"},"observation_digest":"sha256:299e8dc4e1f4973938b99a983a1e8716d34bf5046c7ba2a771b5509d820c2b3b","observation_id":"0061a09b-a80c-4341-a5b8-de1b924acc64","resolution":{"observed_at":"2026-08-16T01:10:23.772970Z","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":"2026-08-16T01:10:23.777382Z","title":"Ebadi, T","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2505.02125","last_updated":"2025-05-04T14:15:03Z","snapshot_observed_at":"2026-08-16T00:58:25.913254Z","submitted_at":"2025-05-04T14:15:03Z","title":"R\\'{e}nyi Markov length in one-dimensional non-trivial mixed state phases and mixed state phase transitions","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-16T01:10:23.777382Z"},"links":{"citing_paper":"/paper/2505.02125"},"observation_digest":"sha256:510c3a9451fc2e7cb612fa837139b89f0b0e97bb5a9e6b899be20d6c15256fa5","observation_id":"8bd7ccc5-d04d-4eea-9629-a12fa41047c1","resolution":{"observed_at":"2026-08-16T01:10:23.777382Z","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":"2026-08-16T01:10:23.781465Z","title":"Bluvstein, S","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2505.02125","last_updated":"2025-05-04T14:15:03Z","snapshot_observed_at":"2026-08-16T00:58:25.913254Z","submitted_at":"2025-05-04T14:15:03Z","title":"R\\'{e}nyi Markov length in one-dimensional non-trivial mixed state phases and mixed state phase transitions","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-16T01:10:23.781465Z"},"links":{"citing_paper":"/paper/2505.02125"},"observation_digest":"sha256:0e9808a71ac846c81a5be4eddf8362d89a339babff1ddc471af9beee3f60491e","observation_id":"db6055aa-cb30-46fc-88ad-45b4e36deedd","resolution":{"observed_at":"2026-08-16T01:10:23.781465Z","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":"2026-08-16T01:10:23.785693Z","title":"Bharti, A","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2505.02125","last_updated":"2025-05-04T14:15:03Z","snapshot_observed_at":"2026-08-16T00:58:25.913254Z","submitted_at":"2025-05-04T14:15:03Z","title":"R\\'{e}nyi Markov length in one-dimensional non-trivial mixed state phases and mixed state phase transitions","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-16T01:10:23.785693Z"},"links":{"citing_paper":"/paper/2505.02125"},"observation_digest":"sha256:e32d7db33d5bbc3cfaf6f45d3512f5ec038299a69ac36d67e7e47821923fe419","observation_id":"8c5ffca6-d515-4b75-9fcd-594fdfad228d","resolution":{"observed_at":"2026-08-16T01:10:23.785693Z","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":"2026-08-16T01:10:23.789982Z","title":"Preskill, Quantum computing in the nisq era and beyond, Quantum 2, 79 (2018)","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2505.02125","last_updated":"2025-05-04T14:15:03Z","snapshot_observed_at":"2026-08-16T00:58:25.913254Z","submitted_at":"2025-05-04T14:15:03Z","title":"R\\'{e}nyi Markov length in one-dimensional non-trivial mixed state phases and mixed state phase transitions","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-16T01:10:23.789982Z"},"links":{"citing_paper":"/paper/2505.02125"},"observation_digest":"sha256:2c5319ecc6cde7e379783d106f6b51e6a7ab1dae7a3d615b765f00cf929d4fd4","observation_id":"cfb465c0-ba46-4026-ad26-77f1aea5923f","resolution":{"observed_at":"2026-08-16T01:10:23.789982Z","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":"2026-08-16T01:10:23.793676Z","title":"Bu ˇca and T","venue":null,"work_id":null,"year":2012},"citing_paper":{"arxiv_id":"2505.02125","last_updated":"2025-05-04T14:15:03Z","snapshot_observed_at":"2026-08-16T00:58:25.913254Z","submitted_at":"2025-05-04T14:15:03Z","title":"R\\'{e}nyi Markov length in one-dimensional non-trivial mixed state phases and mixed state phase transitions","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-16T01:10:23.793676Z"},"links":{"citing_paper":"/paper/2505.02125"},"observation_digest":"sha256:d04cebb282bcb2c32040cca4bbff1781c6e1f96727902ee50dbd7eb1ba4c788f","observation_id":"79da2d2e-c99c-4857-bfe4-7d1ef6098bd2","resolution":{"observed_at":"2026-08-16T01:10:23.793676Z","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":"2026-08-16T01:10:23.797499Z","title":"de Groot, A","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2505.02125","last_updated":"2025-05-04T14:15:03Z","snapshot_observed_at":"2026-08-16T00:58:25.913254Z","submitted_at":"2025-05-04T14:15:03Z","title":"R\\'{e}nyi Markov length in one-dimensional non-trivial mixed state phases and mixed state phase transitions","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-16T01:10:23.797499Z"},"links":{"citing_paper":"/paper/2505.02125"},"observation_digest":"sha256:5e78358775f2898ece9e3d85795d83530a435dc5342aa8ce393dbcb70acd72be","observation_id":"95731d1c-7a57-4838-829b-35a1ef065cb5","resolution":{"observed_at":"2026-08-16T01:10:23.797499Z","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":"2026-08-16T01:10:23.801025Z","title":"Ma and C","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2505.02125","last_updated":"2025-05-04T14:15:03Z","snapshot_observed_at":"2026-08-16T00:58:25.913254Z","submitted_at":"2025-05-04T14:15:03Z","title":"R\\'{e}nyi Markov length in one-dimensional non-trivial mixed state phases and mixed state phase transitions","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-16T01:10:23.801025Z"},"links":{"citing_paper":"/paper/2505.02125"},"observation_digest":"sha256:f7222f4be7925a0532f21b88eb1b2d729e05d8b09fa2784a90269e3f4fc9ced0","observation_id":"da929132-1363-44ff-a4d9-d4ad26a8d8c1","resolution":{"observed_at":"2026-08-16T01:10:23.801025Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2305.16399","last_updated":"2025-01-23T03:52:44Z","snapshot_observed_at":"2026-08-14T12:51:21.111258Z","submitted_at":"2023-05-25T18:04:22Z","title":"Topological Phases with Average Symmetries: the Decohered, the Disordered, and the Intrinsic","version":4},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2305.16399","snapshot_observed_at":"2026-08-16T01:10:23.804573Z","title":"Ma, J.-H","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2505.02125","last_updated":"2025-05-04T14:15:03Z","snapshot_observed_at":"2026-08-16T00:58:25.913254Z","submitted_at":"2025-05-04T14:15:03Z","title":"R\\'{e}nyi Markov length in one-dimensional non-trivial mixed state phases and mixed state phase transitions","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-16T01:10:23.804573Z"},"links":{"cited_paper":"/paper/2305.16399","citing_paper":"/paper/2505.02125"},"observation_digest":"sha256:ed0eb09c30c5ae4928b2827edfe3f818cb3f2e79d7d260e0146c38c8acfa1a30","observation_id":"4ee5725c-d18f-4682-aeff-f248cfa98673","resolution":{"observed_at":"2026-08-16T01:10:23.804573Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2403.13280","last_updated":"2024-06-02T23:59:08Z","snapshot_observed_at":"2026-08-13T00:49:50.782637Z","submitted_at":"2024-03-20T03:40:28Z","title":"Symmetry Protected Topological Phases of Mixed States in the Doubled Space","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2403.13280","snapshot_observed_at":"2026-08-16T01:10:23.809116Z","title":"Ma and A","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2505.02125","last_updated":"2025-05-04T14:15:03Z","snapshot_observed_at":"2026-08-16T00:58:25.913254Z","submitted_at":"2025-05-04T14:15:03Z","title":"R\\'{e}nyi Markov length in one-dimensional non-trivial mixed state phases and mixed state phase transitions","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-16T01:10:23.809116Z"},"links":{"cited_paper":"/paper/2403.13280","citing_paper":"/paper/2505.02125"},"observation_digest":"sha256:1c3dd1ed57812e70abe255cd6f71f93c6701c85b535b7f699b76723c9bd9e4bb","observation_id":"0eb9839f-9172-4405-ba9a-8e5b01d40543","resolution":{"observed_at":"2026-08-16T01:10:23.809116Z","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":"2026-08-16T01:10:23.813013Z","title":null,"venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2505.02125","last_updated":"2025-05-04T14:15:03Z","snapshot_observed_at":"2026-08-16T00:58:25.913254Z","submitted_at":"2025-05-04T14:15:03Z","title":"R\\'{e}nyi Markov length in one-dimensional non-trivial mixed state phases and mixed state phase transitions","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-16T01:10:23.813013Z"},"links":{"citing_paper":"/paper/2505.02125"},"observation_digest":"sha256:851eba0c1d1bc20e5a290665ae2ddde8df94bc737ae9b38849ac0d486e9c46b3","observation_id":"39e09319-1749-4b5a-b759-0fd1cca0a861","resolution":{"observed_at":"2026-08-16T01:10:23.813013Z","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":"2026-08-16T01:10:23.817090Z","title":null,"venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2505.02125","last_updated":"2025-05-04T14:15:03Z","snapshot_observed_at":"2026-08-16T00:58:25.913254Z","submitted_at":"2025-05-04T14:15:03Z","title":"R\\'{e}nyi Markov length in one-dimensional non-trivial mixed state phases and mixed state phase transitions","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-16T01:10:23.817090Z"},"links":{"citing_paper":"/paper/2505.02125"},"observation_digest":"sha256:32af571044ce1bd3be88b1f629013b32ba60cc521ce6afc4ce76620cbf984dae","observation_id":"516a3921-4d0f-461c-ae04-cb6e049402e9","resolution":{"observed_at":"2026-08-16T01:10:23.817090Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2410.09327","last_updated":"2024-10-12T02:04:40Z","snapshot_observed_at":"2026-08-12T22:25:00.165765Z","submitted_at":"2024-10-12T02:04:40Z","title":"Diagnosing Strong-to-Weak Symmetry Breaking via Wightman Correlators","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2410.09327","snapshot_observed_at":"2026-08-16T01:10:23.820864Z","title":null,"venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2505.02125","last_updated":"2025-05-04T14:15:03Z","snapshot_observed_at":"2026-08-16T00:58:25.913254Z","submitted_at":"2025-05-04T14:15:03Z","title":"R\\'{e}nyi Markov length in one-dimensional non-trivial mixed state phases and mixed state phase transitions","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-16T01:10:23.820864Z"},"links":{"cited_paper":"/paper/2410.09327","citing_paper":"/paper/2505.02125"},"observation_digest":"sha256:abc737c9ed3b2181a8e0821d62476952b42349e43a86950095e718ce38410500","observation_id":"5fe33f51-088a-4cc2-a724-eb3c4fa6e811","resolution":{"observed_at":"2026-08-16T01:10:23.820864Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2410.13734","last_updated":"2025-04-30T05:17:41Z","snapshot_observed_at":"2026-08-14T13:27:07.280864Z","submitted_at":"2024-10-17T16:36:53Z","title":"Strong-to-weak spontaneous symmetry breaking meets average symmetry-protected topological order","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2410.13734","snapshot_observed_at":"2026-08-16T01:10:23.824792Z","title":"Guo and S","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2505.02125","last_updated":"2025-05-04T14:15:03Z","snapshot_observed_at":"2026-08-16T00:58:25.913254Z","submitted_at":"2025-05-04T14:15:03Z","title":"R\\'{e}nyi Markov length in one-dimensional non-trivial mixed state phases and mixed state phase transitions","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-16T01:10:23.824792Z"},"links":{"cited_paper":"/paper/2410.13734","citing_paper":"/paper/2505.02125"},"observation_digest":"sha256:2f5d12f12ff6e15064b21755d0110efe203f25540f32a723e13757c904fa96c9","observation_id":"ca2a290a-de6d-414a-a9dd-64bb31f8a598","resolution":{"observed_at":"2026-08-16T01:10:23.824792Z","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":"2026-08-16T01:10:23.828930Z","title":null,"venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2505.02125","last_updated":"2025-05-04T14:15:03Z","snapshot_observed_at":"2026-08-16T00:58:25.913254Z","submitted_at":"2025-05-04T14:15:03Z","title":"R\\'{e}nyi Markov length in one-dimensional non-trivial mixed state phases and mixed state phase transitions","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-16T01:10:23.828930Z"},"links":{"citing_paper":"/paper/2505.02125"},"observation_digest":"sha256:c2fdc995f56499f04a86e344c31725f5115ef53d54dbe7355e579d1b6003120d","observation_id":"e54accea-3229-40b2-afed-c78edb1c9335","resolution":{"observed_at":"2026-08-16T01:10:23.828930Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2410.23512","last_updated":"2025-05-14T00:51:37Z","snapshot_observed_at":"2026-08-12T22:11:18.672600Z","submitted_at":"2024-10-30T23:44:23Z","title":"Efficient Detection of Strong-To-Weak Spontaneous Symmetry Breaking via the R\\'enyi-1 Correlator","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2410.23512","snapshot_observed_at":"2026-08-16T01:10:23.833311Z","title":"Weinstein, Efficient detection of strong-to-weak sponta- neous symmetry breaking via the r ´enyi-1 correlator (2024), arXiv:2410.23512 [quant-ph]","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2505.02125","last_updated":"2025-05-04T14:15:03Z","snapshot_observed_at":"2026-08-16T00:58:25.913254Z","submitted_at":"2025-05-04T14:15:03Z","title":"R\\'{e}nyi Markov length in one-dimensional non-trivial mixed state phases and mixed state phase transitions","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-16T01:10:23.833311Z"},"links":{"cited_paper":"/paper/2410.23512","citing_paper":"/paper/2505.02125"},"observation_digest":"sha256:ed17f242e2834ebcdcdd5a71e16e93d60279f8a6927ea44c7012603571258da0","observation_id":"547a9a35-81a2-480c-881b-1f7d02b05b20","resolution":{"observed_at":"2026-08-16T01:10:23.833311Z","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":"2026-08-16T01:10:23.838282Z","title":null,"venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2505.02125","last_updated":"2025-05-04T14:15:03Z","snapshot_observed_at":"2026-08-16T00:58:25.913254Z","submitted_at":"2025-05-04T14:15:03Z","title":"R\\'{e}nyi Markov length in one-dimensional non-trivial mixed state phases and mixed state phase transitions","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-16T01:10:23.838282Z"},"links":{"citing_paper":"/paper/2505.02125"},"observation_digest":"sha256:abbe2b3d2c095b569e21b44811e4cfa3ed5c94fe57ddc7e52c515f66f212adbc","observation_id":"cd860556-91cf-4c67-a10f-2b4344cd9344","resolution":{"observed_at":"2026-08-16T01:10:23.838282Z","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":"2026-08-16T01:10:23.842702Z","title":"Orito, Y","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2505.02125","last_updated":"2025-05-04T14:15:03Z","snapshot_observed_at":"2026-08-16T00:58:25.913254Z","submitted_at":"2025-05-04T14:15:03Z","title":"R\\'{e}nyi Markov length in one-dimensional non-trivial mixed state phases and mixed state phase transitions","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-16T01:10:23.842702Z"},"links":{"citing_paper":"/paper/2505.02125"},"observation_digest":"sha256:0b908d9faf80dbc76a8615ef00b735dee015a266f9da24fe434addf9a2cf255c","observation_id":"0ece46dd-f277-4f63-8744-b6b31dc66060","resolution":{"observed_at":"2026-08-16T01:10:23.842702Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2501.17481","last_updated":"2025-09-05T15:08:10Z","snapshot_observed_at":"2026-08-16T09:41:28.833061Z","submitted_at":"2025-01-29T08:45:46Z","title":"System-environmental entanglement in critical spin systems under $ZZ$-decoherence and its relation to strong and weak symmetries","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2501.17481","snapshot_observed_at":"2026-08-16T01:10:23.846402Z","title":null,"venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2505.02125","last_updated":"2025-05-04T14:15:03Z","snapshot_observed_at":"2026-08-16T00:58:25.913254Z","submitted_at":"2025-05-04T14:15:03Z","title":"R\\'{e}nyi Markov length in one-dimensional non-trivial mixed state phases and mixed state phase transitions","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-16T01:10:23.846402Z"},"links":{"cited_paper":"/paper/2501.17481","citing_paper":"/paper/2505.02125"},"observation_digest":"sha256:3d422cd94903d1544ad0b09cc3e9c99af19a1fd9ad31249745196f3438eb1c2f","observation_id":"b041635f-8837-460e-b354-cce76a0c0249","resolution":{"observed_at":"2026-08-16T01:10:23.846402Z","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":"2026-08-16T01:10:23.850353Z","title":null,"venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2505.02125","last_updated":"2025-05-04T14:15:03Z","snapshot_observed_at":"2026-08-16T00:58:25.913254Z","submitted_at":"2025-05-04T14:15:03Z","title":"R\\'{e}nyi Markov length in one-dimensional non-trivial mixed state phases and mixed state phase transitions","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-16T01:10:23.850353Z"},"links":{"citing_paper":"/paper/2505.02125"},"observation_digest":"sha256:d9560a9893422b5f78f61d8ed5688af5aec22c17cce6ed5aa3cbeaba5da85353","observation_id":"cc92dc72-08d0-4fac-9006-5500f13340f3","resolution":{"observed_at":"2026-08-16T01:10:23.850353Z","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":"2026-08-16T01:10:23.854536Z","title":null,"venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2505.02125","last_updated":"2025-05-04T14:15:03Z","snapshot_observed_at":"2026-08-16T00:58:25.913254Z","submitted_at":"2025-05-04T14:15:03Z","title":"R\\'{e}nyi Markov length in one-dimensional non-trivial mixed state phases and mixed state phase transitions","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-16T01:10:23.854536Z"},"links":{"citing_paper":"/paper/2505.02125"},"observation_digest":"sha256:7b8c415a89b585b8732fd8cae3b7e9b999117b091e987540a1251595756a8ceb","observation_id":"4164d6f1-df22-4fad-9537-4de42e1315af","resolution":{"observed_at":"2026-08-16T01:10:23.854536Z","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":"2026-08-16T01:10:23.858587Z","title":null,"venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2505.02125","last_updated":"2025-05-04T14:15:03Z","snapshot_observed_at":"2026-08-16T00:58:25.913254Z","submitted_at":"2025-05-04T14:15:03Z","title":"R\\'{e}nyi Markov length in one-dimensional non-trivial mixed state phases and mixed state phase transitions","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-16T01:10:23.858587Z"},"links":{"citing_paper":"/paper/2505.02125"},"observation_digest":"sha256:a4af60ec85865051a229f4a9c38b075139d4db9bca557e97ed109d4a5695c849","observation_id":"abba03c3-452f-49a6-bf0f-a5f0be568be2","resolution":{"observed_at":"2026-08-16T01:10:23.858587Z","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":"2026-08-16T01:10:24.608523Z","title":null,"venue":null,"work_id":"1221d6bb-1191-4e28-93a8-370344b829fc","year":2024},"citing_paper":{"arxiv_id":"2505.02125","last_updated":"2025-05-04T14:15:03Z","snapshot_observed_at":"2026-08-16T00:58:25.913254Z","submitted_at":"2025-05-04T14:15:03Z","title":"R\\'{e}nyi Markov length in one-dimensional non-trivial mixed state phases and mixed state phase transitions","version":1},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-16T01:10:23.863241Z"},"links":{"citing_paper":"/paper/2505.02125"},"observation_digest":"sha256:8d84a4a00bdf69e2a83c8f6d76be310b73f2b397cf91c02ca8c1f3ad94a7ec62","observation_id":"c9500144-a2b2-44dd-a855-fdc6487410bb","resolution":{"observed_at":"2026-08-16T01:10:24.613265Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-16T01:10:23.866783Z","title":null,"venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2505.02125","last_updated":"2025-05-04T14:15:03Z","snapshot_observed_at":"2026-08-16T00:58:25.913254Z","submitted_at":"2025-05-04T14:15:03Z","title":"R\\'{e}nyi Markov length in one-dimensional non-trivial mixed state phases and mixed state phase transitions","version":1},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-16T01:10:23.866783Z"},"links":{"citing_paper":"/paper/2505.02125"},"observation_digest":"sha256:e805423f8802394a291d0852e5ab603de4c6512a9aaccd26522f8bf1ea2c3076","observation_id":"05c937ed-10bf-4a3b-b612-81df1dc3e8b7","resolution":{"observed_at":"2026-08-16T01:10:23.866783Z","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":"2026-08-16T01:10:23.870371Z","title":"Chen and T","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2505.02125","last_updated":"2025-05-04T14:15:03Z","snapshot_observed_at":"2026-08-16T00:58:25.913254Z","submitted_at":"2025-05-04T14:15:03Z","title":"R\\'{e}nyi Markov length in one-dimensional non-trivial mixed state phases and mixed state phase transitions","version":1},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-16T01:10:23.870371Z"},"links":{"citing_paper":"/paper/2505.02125"},"observation_digest":"sha256:9ae1992f91adda54a0e845f8528b720a194328e3f7ab77487e6a63c599a8b608","observation_id":"f7b72907-43ab-4905-a553-8b5da85b4a25","resolution":{"observed_at":"2026-08-16T01:10:23.870371Z","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":"2026-08-16T01:10:23.873756Z","title":"Sohal and A","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2505.02125","last_updated":"2025-05-04T14:15:03Z","snapshot_observed_at":"2026-08-16T00:58:25.913254Z","submitted_at":"2025-05-04T14:15:03Z","title":"R\\'{e}nyi Markov length in one-dimensional non-trivial mixed state phases and mixed state phase transitions","version":1},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-16T01:10:23.873756Z"},"links":{"citing_paper":"/paper/2505.02125"},"observation_digest":"sha256:300016b431e081e8b4922ae9cab1df566d9c70d48aa38901ab09d25c483a0f3c","observation_id":"7b1cbd0b-8f7d-4cc4-89c7-5850a8090f98","resolution":{"observed_at":"2026-08-16T01:10:23.873756Z","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":"2026-08-16T01:10:23.877142Z","title":"Zhang, Y","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2505.02125","last_updated":"2025-05-04T14:15:03Z","snapshot_observed_at":"2026-08-16T00:58:25.913254Z","submitted_at":"2025-05-04T14:15:03Z","title":"R\\'{e}nyi Markov length in one-dimensional non-trivial mixed state phases and mixed state phase transitions","version":1},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-16T01:10:23.877142Z"},"links":{"citing_paper":"/paper/2505.02125"},"observation_digest":"sha256:fd71681366118f4f4a079aaa57cd13238a9e788106c9cef2bc3ec4b3f9625ef8","observation_id":"a8c12db7-3405-465f-8e55-e7acda08aecf","resolution":{"observed_at":"2026-08-16T01:10:23.877142Z","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":"2026-08-16T01:10:23.880598Z","title":null,"venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2505.02125","last_updated":"2025-05-04T14:15:03Z","snapshot_observed_at":"2026-08-16T00:58:25.913254Z","submitted_at":"2025-05-04T14:15:03Z","title":"R\\'{e}nyi Markov length in one-dimensional non-trivial mixed state phases and mixed state phase transitions","version":1},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-16T01:10:23.880598Z"},"links":{"citing_paper":"/paper/2505.02125"},"observation_digest":"sha256:a115955a90db2da64c27b8b372cd195d5208574a70f9a32cd6cb7426857c15bf","observation_id":"ae0b3c04-1b45-45ef-a065-e545be1084c4","resolution":{"observed_at":"2026-08-16T01:10:23.880598Z","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":"2026-08-16T01:10:23.884053Z","title":"Sang and T","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2505.02125","last_updated":"2025-05-04T14:15:03Z","snapshot_observed_at":"2026-08-16T00:58:25.913254Z","submitted_at":"2025-05-04T14:15:03Z","title":"R\\'{e}nyi Markov length in one-dimensional non-trivial mixed state phases and mixed state phase transitions","version":1},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-16T01:10:23.884053Z"},"links":{"citing_paper":"/paper/2505.02125"},"observation_digest":"sha256:2352faa9075f86678fb2d89d7c6fefa8d1d6414ac9a30df8fc6837e76b8cf83d","observation_id":"279e6526-101a-4017-93ca-df30feffb2ee","resolution":{"observed_at":"2026-08-16T01:10:23.884053Z","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":"2026-08-16T01:10:24.560017Z","title":"Petz, Sufficiency of channels over von neumann algebras, The Quarterly Journal of Mathematics 39, 97 (1988)","venue":null,"work_id":"37d5caed-3385-4218-b0be-5a72d824574d","year":1988},"citing_paper":{"arxiv_id":"2505.02125","last_updated":"2025-05-04T14:15:03Z","snapshot_observed_at":"2026-08-16T00:58:25.913254Z","submitted_at":"2025-05-04T14:15:03Z","title":"R\\'{e}nyi Markov length in one-dimensional non-trivial mixed state phases and mixed state phase transitions","version":1},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-08-16T01:10:23.887421Z"},"links":{"citing_paper":"/paper/2505.02125"},"observation_digest":"sha256:da7bbdd93b69e436b03f972f5ff5b00eddcc373b09e37413004ae7292c288801","observation_id":"daf6e4c8-885b-48cc-a201-a0b900a91bf0","resolution":{"observed_at":"2026-08-16T01:10:24.564909Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-16T01:10:24.547909Z","title":"Junge, R","venue":null,"work_id":"b5f6491f-2a8f-4dcb-b100-17ff62b7c307","year":2018},"citing_paper":{"arxiv_id":"2505.02125","last_updated":"2025-05-04T14:15:03Z","snapshot_observed_at":"2026-08-16T00:58:25.913254Z","submitted_at":"2025-05-04T14:15:03Z","title":"R\\'{e}nyi Markov length in one-dimensional non-trivial mixed state phases and mixed state phase transitions","version":1},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-08-16T01:10:23.891068Z"},"links":{"citing_paper":"/paper/2505.02125"},"observation_digest":"sha256:15af6f7f1d234d6f1ad54079ca45d427e1a114f8ab354f04f4f4314d2e9687e8","observation_id":"b58d10f6-c754-4dda-bc99-8a621bc37647","resolution":{"observed_at":"2026-08-16T01:10:24.552004Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2412.00193","last_updated":"2025-06-05T14:50:47Z","snapshot_observed_at":"2026-08-15T11:04:55.070415Z","submitted_at":"2024-11-29T19:00:03Z","title":"Spacetime Markov length: a diagnostic for fault tolerance via mixed-state phases","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2412.00193","snapshot_observed_at":"2026-08-16T01:10:23.894616Z","title":"Negari, T","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2505.02125","last_updated":"2025-05-04T14:15:03Z","snapshot_observed_at":"2026-08-16T00:58:25.913254Z","submitted_at":"2025-05-04T14:15:03Z","title":"R\\'{e}nyi Markov length in one-dimensional non-trivial mixed state phases and mixed state phase transitions","version":1},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-08-16T01:10:23.894616Z"},"links":{"cited_paper":"/paper/2412.00193","citing_paper":"/paper/2505.02125"},"observation_digest":"sha256:35552e396161e4c3543407357fdeb8ebd6df774d58277f06a2166ada5fb6de80","observation_id":"f839dd5e-e49b-4f42-bb87-a0387483f513","resolution":{"observed_at":"2026-08-16T01:10:23.894616Z","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":"2026-08-16T01:10:23.898020Z","title":"Hauschild and F","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2505.02125","last_updated":"2025-05-04T14:15:03Z","snapshot_observed_at":"2026-08-16T00:58:25.913254Z","submitted_at":"2025-05-04T14:15:03Z","title":"R\\'{e}nyi Markov length in one-dimensional non-trivial mixed state phases and mixed state phase transitions","version":1},"reference_index":38,"source":"pdf_text","source_observed_at":"2026-08-16T01:10:23.898020Z"},"links":{"citing_paper":"/paper/2505.02125"},"observation_digest":"sha256:a667e5b8fff517f131180fdb6329b32bad719a1267fb1ab28829f2d9bb17b5d4","observation_id":"85228ac3-ef98-43fb-b624-f158cabdfbc2","resolution":{"observed_at":"2026-08-16T01:10:23.898020Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2408.02010","last_updated":"2024-11-26T14:56:05Z","snapshot_observed_at":"2026-08-12T23:08:56.736775Z","submitted_at":"2024-08-04T12:27:10Z","title":"Tensor Network Python (TeNPy) version 1","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2408.02010","snapshot_observed_at":"2026-08-16T01:10:23.901202Z","title":"Hauschild, J","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2505.02125","last_updated":"2025-05-04T14:15:03Z","snapshot_observed_at":"2026-08-16T00:58:25.913254Z","submitted_at":"2025-05-04T14:15:03Z","title":"R\\'{e}nyi Markov length in one-dimensional non-trivial mixed state phases and mixed state phase transitions","version":1},"reference_index":39,"source":"pdf_text","source_observed_at":"2026-08-16T01:10:23.901202Z"},"links":{"cited_paper":"/paper/2408.02010","citing_paper":"/paper/2505.02125"},"observation_digest":"sha256:c4fb1c1c2f351c148cbbd934b55f07f8d41e609391046e578d1f97feae543f67","observation_id":"5305f0ae-ecfc-484e-bbde-d8bbf37d28cd","resolution":{"observed_at":"2026-08-16T01:10:23.901202Z","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":"2026-08-16T01:10:23.904615Z","title":null,"venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2505.02125","last_updated":"2025-05-04T14:15:03Z","snapshot_observed_at":"2026-08-16T00:58:25.913254Z","submitted_at":"2025-05-04T14:15:03Z","title":"R\\'{e}nyi Markov length in one-dimensional non-trivial mixed state phases and mixed state phase transitions","version":1},"reference_index":40,"source":"pdf_text","source_observed_at":"2026-08-16T01:10:23.904615Z"},"links":{"citing_paper":"/paper/2505.02125"},"observation_digest":"sha256:485c5d7377c00e81c910aa6809d0b047e202c5b267dca6c8a27bc2ad62995f6b","observation_id":"a8a08c91-abc8-4944-93c0-40a63744813b","resolution":{"observed_at":"2026-08-16T01:10:23.904615Z","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":"2026-08-16T01:10:23.907997Z","title":"Zabalo, M","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2505.02125","last_updated":"2025-05-04T14:15:03Z","snapshot_observed_at":"2026-08-16T00:58:25.913254Z","submitted_at":"2025-05-04T14:15:03Z","title":"R\\'{e}nyi Markov length in one-dimensional non-trivial mixed state phases and mixed state phase transitions","version":1},"reference_index":41,"source":"pdf_text","source_observed_at":"2026-08-16T01:10:23.907997Z"},"links":{"citing_paper":"/paper/2505.02125"},"observation_digest":"sha256:826f09bb6092467bc4b2b894142433ababf55549b3d642dc324d67266e77aa97","observation_id":"6e199050-3ef8-4656-b697-f4dd69547573","resolution":{"observed_at":"2026-08-16T01:10:23.907997Z","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":"2026-08-16T01:10:23.911677Z","title":"Micallo, V","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2505.02125","last_updated":"2025-05-04T14:15:03Z","snapshot_observed_at":"2026-08-16T00:58:25.913254Z","submitted_at":"2025-05-04T14:15:03Z","title":"R\\'{e}nyi Markov length in one-dimensional non-trivial mixed state phases and mixed state phase transitions","version":1},"reference_index":42,"source":"pdf_text","source_observed_at":"2026-08-16T01:10:23.911677Z"},"links":{"citing_paper":"/paper/2505.02125"},"observation_digest":"sha256:66c41d765dac618b15165376362a1ba2a1a126a3ba80639c99c4df48b815af92","observation_id":"64d68765-9373-4ebf-aa6f-7d2144091cd0","resolution":{"observed_at":"2026-08-16T01:10:23.911677Z","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":"2026-08-16T01:10:23.915506Z","title":"Choi, Completely positive linear maps on complex ma- trices, Lin","venue":null,"work_id":null,"year":1975},"citing_paper":{"arxiv_id":"2505.02125","last_updated":"2025-05-04T14:15:03Z","snapshot_observed_at":"2026-08-16T00:58:25.913254Z","submitted_at":"2025-05-04T14:15:03Z","title":"R\\'{e}nyi Markov length in one-dimensional non-trivial mixed state phases and mixed state phase transitions","version":1},"reference_index":43,"source":"pdf_text","source_observed_at":"2026-08-16T01:10:23.915506Z"},"links":{"citing_paper":"/paper/2505.02125"},"observation_digest":"sha256:fd58ea91a1f1391979d9fe72720d326987f5de0ab7b4c8d163b7a1517c85b422","observation_id":"a2ab2eb7-0f50-4835-8923-da0e9183a442","resolution":{"observed_at":"2026-08-16T01:10:23.915506Z","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":"2026-08-16T01:10:23.919766Z","title":"Jamiołkowski, Linear transformations which preserve trace and positive semidefiniteness of operators, Rep","venue":null,"work_id":null,"year":1972},"citing_paper":{"arxiv_id":"2505.02125","last_updated":"2025-05-04T14:15:03Z","snapshot_observed_at":"2026-08-16T00:58:25.913254Z","submitted_at":"2025-05-04T14:15:03Z","title":"R\\'{e}nyi Markov length in one-dimensional non-trivial mixed state phases and mixed state phase transitions","version":1},"reference_index":44,"source":"pdf_text","source_observed_at":"2026-08-16T01:10:23.919766Z"},"links":{"citing_paper":"/paper/2505.02125"},"observation_digest":"sha256:4c7c759a701fa543b9c6136ea6f372d04fd99193748260fa918d67f2610ae7ec","observation_id":"fe93ceac-9b66-4b11-971f-406293d2046a","resolution":{"observed_at":"2026-08-16T01:10:23.919766Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2503.09597","last_updated":"2025-03-12T17:58:55Z","snapshot_observed_at":"2026-08-07T17:09:24.488020Z","submitted_at":"2025-03-12T17:58:55Z","title":"Universal Properties of Critical Mixed States from Measurement and Feedback","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2503.09597","snapshot_observed_at":"2026-08-16T01:10:23.923117Z","title":"Zhang, Y","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2505.02125","last_updated":"2025-05-04T14:15:03Z","snapshot_observed_at":"2026-08-16T00:58:25.913254Z","submitted_at":"2025-05-04T14:15:03Z","title":"R\\'{e}nyi Markov length in one-dimensional non-trivial mixed state phases and mixed state phase transitions","version":1},"reference_index":45,"source":"pdf_text","source_observed_at":"2026-08-16T01:10:23.923117Z"},"links":{"cited_paper":"/paper/2503.09597","citing_paper":"/paper/2505.02125"},"observation_digest":"sha256:87a0834a7b8ebae7892f3ed435cf5b7c52dec70a356c6f7ad990559756b2baa8","observation_id":"0e6d41ad-8371-4471-8e31-081358f0a756","resolution":{"observed_at":"2026-08-16T01:10:23.923117Z","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":"2026-08-16T01:10:23.926746Z","title":null,"venue":null,"work_id":null,"year":2011},"citing_paper":{"arxiv_id":"2505.02125","last_updated":"2025-05-04T14:15:03Z","snapshot_observed_at":"2026-08-16T00:58:25.913254Z","submitted_at":"2025-05-04T14:15:03Z","title":"R\\'{e}nyi Markov length in one-dimensional non-trivial mixed state phases and mixed state phase transitions","version":1},"reference_index":46,"source":"pdf_text","source_observed_at":"2026-08-16T01:10:23.926746Z"},"links":{"citing_paper":"/paper/2505.02125"},"observation_digest":"sha256:c8a96f916f32a44b0955db2a4cff341698b15f04c219483fb11d0abe29ccf3c3","observation_id":"7a2fd220-4e3b-4b16-a2a1-fbd47e5eb9eb","resolution":{"observed_at":"2026-08-16T01:10:23.926746Z","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":"2026-08-16T01:10:23.930113Z","title":"Raussendorf and H","venue":null,"work_id":null,"year":2001},"citing_paper":{"arxiv_id":"2505.02125","last_updated":"2025-05-04T14:15:03Z","snapshot_observed_at":"2026-08-16T00:58:25.913254Z","submitted_at":"2025-05-04T14:15:03Z","title":"R\\'{e}nyi Markov length in one-dimensional non-trivial mixed state phases and mixed state phase transitions","version":1},"reference_index":47,"source":"pdf_text","source_observed_at":"2026-08-16T01:10:23.930113Z"},"links":{"citing_paper":"/paper/2505.02125"},"observation_digest":"sha256:bcd8490aabdc24169d2ca970005227b17c152fed37bf3aa8acf49b1191a77ef2","observation_id":"e1c1f2bd-c919-4bbe-a071-d16e730c72ee","resolution":{"observed_at":"2026-08-16T01:10:23.930113Z","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":"2026-08-16T01:10:24.481309Z","title":null,"venue":null,"work_id":"a25f057c-41eb-4c46-a6fd-bf9b888f3282","year":2012},"citing_paper":{"arxiv_id":"2505.02125","last_updated":"2025-05-04T14:15:03Z","snapshot_observed_at":"2026-08-16T00:58:25.913254Z","submitted_at":"2025-05-04T14:15:03Z","title":"R\\'{e}nyi Markov length in one-dimensional non-trivial mixed state phases and mixed state phase transitions","version":1},"reference_index":48,"source":"pdf_text","source_observed_at":"2026-08-16T01:10:23.933387Z"},"links":{"citing_paper":"/paper/2505.02125"},"observation_digest":"sha256:19957cd4a6923f717e8c14b839c950cb37fa7e03a4f06305581aceac69679baa","observation_id":"826f84e9-02ac-4433-aa27-d98bd7e3443f","resolution":{"observed_at":"2026-08-16T01:10:24.485675Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-16T01:10:24.468040Z","title":null,"venue":null,"work_id":"1933b598-4397-4591-b4de-8f92e2a85399","year":null},"citing_paper":{"arxiv_id":"2505.02125","last_updated":"2025-05-04T14:15:03Z","snapshot_observed_at":"2026-08-16T00:58:25.913254Z","submitted_at":"2025-05-04T14:15:03Z","title":"R\\'{e}nyi Markov length in one-dimensional non-trivial mixed state phases and mixed state phase transitions","version":1},"reference_index":49,"source":"pdf_text","source_observed_at":"2026-08-16T01:10:23.937074Z"},"links":{"citing_paper":"/paper/2505.02125"},"observation_digest":"sha256:ad4f640f144653c2a337dde4a73c6dec294988691e8d6659d62e86289ed2ba78","observation_id":"b29ea184-0b5e-47d6-958e-d5036897d052","resolution":{"observed_at":"2026-08-16T01:10:24.472616Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-16T01:10:24.453468Z","title":null,"venue":null,"work_id":"50fbad2e-8aad-4135-8264-d9ce0f83a3c2","year":null},"citing_paper":{"arxiv_id":"2505.02125","last_updated":"2025-05-04T14:15:03Z","snapshot_observed_at":"2026-08-16T00:58:25.913254Z","submitted_at":"2025-05-04T14:15:03Z","title":"R\\'{e}nyi Markov length in one-dimensional non-trivial mixed state phases and mixed state phase transitions","version":1},"reference_index":50,"source":"pdf_text","source_observed_at":"2026-08-16T01:10:23.940527Z"},"links":{"citing_paper":"/paper/2505.02125"},"observation_digest":"sha256:ff6914671cf0e0ec79a807ad7609add8465c8097d59dc0a34173d6685d5b2bf6","observation_id":"a2cb1afb-1259-4400-80d6-2048bde80a7d","resolution":{"observed_at":"2026-08-16T01:10:24.457638Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-16T01:10:23.944428Z","title":null,"venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2505.02125","last_updated":"2025-05-04T14:15:03Z","snapshot_observed_at":"2026-08-16T00:58:25.913254Z","submitted_at":"2025-05-04T14:15:03Z","title":"R\\'{e}nyi Markov length in one-dimensional non-trivial mixed state phases and mixed state phase transitions","version":1},"reference_index":51,"source":"pdf_text","source_observed_at":"2026-08-16T01:10:23.944428Z"},"links":{"citing_paper":"/paper/2505.02125"},"observation_digest":"sha256:30be9ab735e460fc4af1b5786a6e948fde98bb8032d2a27e1362aa9c78192d33","observation_id":"458379ad-ea08-42be-9ce4-da10d78c0ced","resolution":{"observed_at":"2026-08-16T01:10:23.944428Z","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":"2026-08-16T01:10:24.434199Z","title":null,"venue":null,"work_id":"2f66a68e-3cdd-47f2-a58c-f16eb66b0068","year":null},"citing_paper":{"arxiv_id":"2505.02125","last_updated":"2025-05-04T14:15:03Z","snapshot_observed_at":"2026-08-16T00:58:25.913254Z","submitted_at":"2025-05-04T14:15:03Z","title":"R\\'{e}nyi Markov length in one-dimensional non-trivial mixed state phases and mixed state phase transitions","version":1},"reference_index":52,"source":"pdf_text","source_observed_at":"2026-08-16T01:10:23.948520Z"},"links":{"citing_paper":"/paper/2505.02125"},"observation_digest":"sha256:01f913d0471d852ae28c2a7f71591812223b8bf964a8ae9ceef049b1b013e613","observation_id":"b49ca052-97cd-4d84-9db3-ee51c23b76ca","resolution":{"observed_at":"2026-08-16T01:10:24.438809Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-16T01:10:23.952491Z","title":null,"venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2505.02125","last_updated":"2025-05-04T14:15:03Z","snapshot_observed_at":"2026-08-16T00:58:25.913254Z","submitted_at":"2025-05-04T14:15:03Z","title":"R\\'{e}nyi Markov length in one-dimensional non-trivial mixed state phases and mixed state phase transitions","version":1},"reference_index":53,"source":"pdf_text","source_observed_at":"2026-08-16T01:10:23.952491Z"},"links":{"citing_paper":"/paper/2505.02125"},"observation_digest":"sha256:0f2fc821f9e00d0554d829be7e025aeebecbbfbb4007a13dd9098579d378bf66","observation_id":"187f232f-67c3-41a2-90e6-ffd0117c09e3","resolution":{"observed_at":"2026-08-16T01:10:23.952491Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1902.00967","last_updated":"2020-02-21T02:02:30Z","snapshot_observed_at":"2026-08-16T03:35:27.718250Z","submitted_at":"2019-02-03T21:09:32Z","title":"Lecture Notes on the Theory of Open Quantum Systems","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1902.00967","snapshot_observed_at":"2026-08-16T01:10:23.956160Z","title":null,"venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2505.02125","last_updated":"2025-05-04T14:15:03Z","snapshot_observed_at":"2026-08-16T00:58:25.913254Z","submitted_at":"2025-05-04T14:15:03Z","title":"R\\'{e}nyi Markov length in one-dimensional non-trivial mixed state phases and mixed state phase transitions","version":1},"reference_index":54,"source":"pdf_text","source_observed_at":"2026-08-16T01:10:23.956160Z"},"links":{"cited_paper":"/paper/1902.00967","citing_paper":"/paper/2505.02125"},"observation_digest":"sha256:d4f1974c0b72e5730a84bfbb0650d359b747c3b34218a717485368449b8a63f4","observation_id":"30ba0e21-57d5-484d-b80e-b76a08170f3e","resolution":{"observed_at":"2026-08-16T01:10:23.956160Z","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":"2026-08-16T01:10:23.960106Z","title":"Ashida, S","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2505.02125","last_updated":"2025-05-04T14:15:03Z","snapshot_observed_at":"2026-08-16T00:58:25.913254Z","submitted_at":"2025-05-04T14:15:03Z","title":"R\\'{e}nyi Markov length in one-dimensional non-trivial mixed state phases and mixed state phase transitions","version":1},"reference_index":55,"source":"pdf_text","source_observed_at":"2026-08-16T01:10:23.960106Z"},"links":{"citing_paper":"/paper/2505.02125"},"observation_digest":"sha256:39532a422afbc4eb490bd141a714bba5f3029616618ca38affb46847470ef84f","observation_id":"e0146948-983e-4978-b946-80c6af5727f1","resolution":{"observed_at":"2026-08-16T01:10:23.960106Z","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":"2026-08-16T01:10:24.404559Z","title":"Weinstein, Y","venue":null,"work_id":"e9faa174-76ad-45cd-b8ce-f5cdd8bde4a6","year":2022},"citing_paper":{"arxiv_id":"2505.02125","last_updated":"2025-05-04T14:15:03Z","snapshot_observed_at":"2026-08-16T00:58:25.913254Z","submitted_at":"2025-05-04T14:15:03Z","title":"R\\'{e}nyi Markov length in one-dimensional non-trivial mixed state phases and mixed state phase transitions","version":1},"reference_index":56,"source":"pdf_text","source_observed_at":"2026-08-16T01:10:23.963603Z"},"links":{"citing_paper":"/paper/2505.02125"},"observation_digest":"sha256:384c2095c85875b6fea11155b7b9fefc8878b801b5100688b170a2674ffd4754","observation_id":"895df6f7-3c1f-4e62-9bf0-57d6e3806f0f","resolution":{"observed_at":"2026-08-16T01:10:24.412157Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2012.00040","last_updated":"2021-08-30T08:49:47Z","snapshot_observed_at":"2026-08-15T17:56:18.136098Z","submitted_at":"2020-11-30T19:00:18Z","title":"Entanglement negativity at the critical point of measurement-driven transition","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2012.00040","snapshot_observed_at":"2026-08-16T01:10:23.967947Z","title":null,"venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2505.02125","last_updated":"2025-05-04T14:15:03Z","snapshot_observed_at":"2026-08-16T00:58:25.913254Z","submitted_at":"2025-05-04T14:15:03Z","title":"R\\'{e}nyi Markov length in one-dimensional non-trivial mixed state phases and mixed state phase transitions","version":1},"reference_index":57,"source":"pdf_text","source_observed_at":"2026-08-16T01:10:23.967947Z"},"links":{"cited_paper":"/paper/2012.00040","citing_paper":"/paper/2505.02125"},"observation_digest":"sha256:5ee8ce40831282e2e6997a2f7cd0da6407dca7bca18cd012c5001a8362a5cfc2","observation_id":"e1d017e5-f817-4591-917c-91a9251ca042","resolution":{"observed_at":"2026-08-16T01:10:23.967947Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2505.02125","last_updated":"2025-05-04T14:15:03Z","latest_version":1,"primary_category":"quant-ph","snapshot_observed_at":"2026-08-16T00:58:25.913254Z","submitted_at":"2025-05-04T14:15:03Z","title":"R\\'{e}nyi Markov length in one-dimensional non-trivial mixed state phases and mixed state phase transitions"},"reference_resolution":{"displayed":57,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":53,"verified_exact":0,"verified_fuzzy":4},"total_outbound_references":57},"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":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"thesis":"As of 16 August 2026, this Paper Citation Record lists 57 of 57 outbound references and 3 inbound Pith citation observations for arXiv:2505.02125."}