{"as_of":"2026-08-10T12:16:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:c71a26ec0380c1ab9414d5e181101833b9746b2117bf1930a178977119c60aab","coverage":[{"denominator":71,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":71,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-06T20:44:23.341206Z","state":"measured"},{"denominator":88,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":88,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-10T06:31:04.303077+00:00","state":"measured"},{"denominator":17,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":17,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-08T19:23:26.275182Z","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":"2026-07-03T13:18:12.883835Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2507.02292","last_updated":"2025-07-25T18:39:08Z","snapshot_observed_at":"2026-08-08T00:49:34.815340Z","submitted_at":"2025-07-03T03:59:07Z","title":"Mixed-state phases from local reversibility","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2507.02292","snapshot_observed_at":"2026-08-06T20:44:23.007884Z","title":"INTRODUCTION Quantum information insights have led to substantial progress in understanding quantum many-body phenom- ena","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2507.02292","last_updated":"2025-07-25T18:39:08Z","snapshot_observed_at":"2026-08-08T00:49:34.815340Z","submitted_at":"2025-07-03T03:59:07Z","title":"Mixed-state phases from local reversibility","version":2},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-06T20:44:23.007884Z"},"links":{"cited_paper":"/paper/2507.02292","citing_paper":"/paper/2507.02292"},"observation_digest":"sha256:0664033e8909f8c8eabec0293a6f0d07f1a80dd0c2b8a0a8ff37142dbca364f7","observation_id":"5be803aa-4e6a-4b78-a7dd-9c37b22389c4","resolution":{"observed_at":"2026-08-06T20:44:23.007884Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2507.02292","last_updated":"2025-07-25T18:39:08Z","snapshot_observed_at":"2026-08-08T00:49:34.815340Z","submitted_at":"2025-07-03T03:59:07Z","title":"Mixed-state phases from local reversibility","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2507.02292","snapshot_observed_at":"2026-08-06T19:16:50.473629Z","title":"Mixed-state phases from local reversibility,","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2507.06218","last_updated":"2025-07-08T17:51:00Z","snapshot_observed_at":"2026-08-09T21:58:35.635565Z","submitted_at":"2025-07-08T17:51:00Z","title":"Topological Holography for Mixed-State Phases and Phase Transitions","version":1},"reference_index":65,"source":"pdf_text","source_observed_at":"2026-08-06T19:16:50.473629Z"},"links":{"cited_paper":"/paper/2507.02292","citing_paper":"/paper/2507.06218"},"observation_digest":"sha256:b4fe1a6de5b468839df0e9218c74eef2f3ca7487f9ee6abaa541f5bd7de8d1cc","observation_id":"4dfc2ff1-aba1-49c4-bc9b-d205a32da615","resolution":{"observed_at":"2026-08-06T19:16:50.473629Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2507.02292","last_updated":"2025-07-25T18:39:08Z","snapshot_observed_at":"2026-08-08T00:49:34.815340Z","submitted_at":"2025-07-03T03:59:07Z","title":"Mixed-state phases from local reversibility","version":2},"cited_work":{"arxiv_id":"2507.02292","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2507.02292","snapshot_observed_at":"2026-07-03T13:18:12.883835Z","title":"Mixed-state phases from local reversibility","venue":null,"work_id":"55cdd57e-0130-4140-a6a0-0fe08c42f11b","year":2025},"citing_paper":{"arxiv_id":"2509.24179","last_updated":"2026-04-16T02:12:27Z","snapshot_observed_at":"2026-08-08T08:52:22.219118Z","submitted_at":"2025-09-29T01:53:18Z","title":"Strong-to-weak spontaneous symmetry breaking of higher-form non-invertible symmetries in Kitaev's quantum double model","version":2},"reference_index":63,"source":"pdf_text","source_observed_at":"2026-05-18T13:37:19.604351Z"},"links":{"cited_paper":"/paper/2507.02292","citing_paper":"/paper/2509.24179"},"observation_digest":"sha256:3ec52b9db7b72a2664499aa45a4a827830352e4d3bebb8683b9c0b46efd03c22","observation_id":"c05a5516-ffe1-4849-a6dc-3f76b38db015","resolution":{"observed_at":"2026-05-18T13:41:25.789078Z","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"}},{"citation":{"cited_paper":{"arxiv_id":"2507.02292","last_updated":"2025-07-25T18:39:08Z","snapshot_observed_at":"2026-08-08T00:49:34.815340Z","submitted_at":"2025-07-03T03:59:07Z","title":"Mixed-state phases from local reversibility","version":2},"cited_work":{"arxiv_id":"2507.02292","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2507.02292","snapshot_observed_at":"2026-07-03T13:18:12.883835Z","title":"Mixed-state phases from local reversibility","venue":null,"work_id":"55cdd57e-0130-4140-a6a0-0fe08c42f11b","year":2025},"citing_paper":{"arxiv_id":"2510.22542","last_updated":"2026-05-22T01:39:25Z","snapshot_observed_at":"2026-07-06T22:34:03.489056Z","submitted_at":"2025-10-26T05:46:34Z","title":"Krylov Complexity and Mixed-State Phase Transition","version":4},"reference_index":69,"source":"pdf_text","source_observed_at":"2026-05-25T07:50:05.277937Z"},"links":{"cited_paper":"/paper/2507.02292","citing_paper":"/paper/2510.22542"},"observation_digest":"sha256:8f004ea4a877df1bc240a24fc3b84b261b3e2d0b0d2f4e7e9e679dffeac80b57","observation_id":"50dd8e82-c3e3-4543-95ed-7f3458a5be2e","resolution":{"observed_at":"2026-05-25T07:50:28.858909Z","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"}},{"citation":{"cited_paper":{"arxiv_id":"2507.02292","last_updated":"2025-07-25T18:39:08Z","snapshot_observed_at":"2026-08-08T00:49:34.815340Z","submitted_at":"2025-07-03T03:59:07Z","title":"Mixed-state phases from local reversibility","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2507.02292","snapshot_observed_at":"2026-08-03T14:57:26.123845Z","title":null,"venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2512.18783","last_updated":"2026-05-27T01:10:57Z","snapshot_observed_at":"2026-08-05T12:56:41.283918Z","submitted_at":"2025-12-21T15:55:12Z","title":"Noisy Monitored Quantum Circuits","version":2},"reference_index":196,"source":"pdf_text","source_observed_at":"2026-08-03T14:57:26.123845Z"},"links":{"cited_paper":"/paper/2507.02292","citing_paper":"/paper/2512.18783"},"observation_digest":"sha256:23878b46a7683d9b324a6baf1be7f2d2bd7903a3897ae3c1f0e128c9fd032a1c","observation_id":"faf304cc-c03f-43fc-b85a-a69c99c7c7fe","resolution":{"observed_at":"2026-08-03T14:57:26.123845Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2507.02292","last_updated":"2025-07-25T18:39:08Z","snapshot_observed_at":"2026-08-08T00:49:34.815340Z","submitted_at":"2025-07-03T03:59:07Z","title":"Mixed-state phases from local reversibility","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2507.02292","snapshot_observed_at":"2026-08-04T06:17:14.058033Z","title":null,"venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2602.04961","last_updated":"2026-08-02T04:25:53Z","snapshot_observed_at":"2026-08-06T23:24:19.558707Z","submitted_at":"2026-02-04T19:00:03Z","title":"Non-perturbative constraints on stability and renormalization group flows in nonequilibrium matter","version":2},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-04T06:17:14.058033Z"},"links":{"cited_paper":"/paper/2507.02292","citing_paper":"/paper/2602.04961"},"observation_digest":"sha256:d1a70bcc2094577690fcdce20267dd5da654d63787e48abf19a222bb3fc40e13","observation_id":"ce4ba85f-8f66-4109-8bbd-294d7ca162b1","resolution":{"observed_at":"2026-08-04T06:17:14.058033Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2507.02292","last_updated":"2025-07-25T18:39:08Z","snapshot_observed_at":"2026-08-08T00:49:34.815340Z","submitted_at":"2025-07-03T03:59:07Z","title":"Mixed-state phases from local reversibility","version":2},"cited_work":{"arxiv_id":"2507.02292","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2507.02292","snapshot_observed_at":"2026-07-03T13:18:12.883835Z","title":"Mixed-state phases from local reversibility","venue":null,"work_id":"55cdd57e-0130-4140-a6a0-0fe08c42f11b","year":2025},"citing_paper":{"arxiv_id":"2605.00088","last_updated":"2026-04-30T18:00:00Z","snapshot_observed_at":"2026-07-06T23:13:33.799847Z","submitted_at":"2026-04-30T18:00:00Z","title":"A Unified Framework for Locally Stable Phases","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-05-09T20:55:48.768028Z"},"links":{"cited_paper":"/paper/2507.02292","citing_paper":"/paper/2605.00088"},"observation_digest":"sha256:2c6c8910448c0b99306563dc8dd062e4fbc7cfb9a31110f1494e1d5e93cf95be","observation_id":"d8c7c7aa-139f-4b99-97f5-e4f6f0e9d8c3","resolution":{"observed_at":"2026-05-11T14:51:11.183922Z","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"}},{"citation":{"cited_paper":{"arxiv_id":"2507.02292","last_updated":"2025-07-25T18:39:08Z","snapshot_observed_at":"2026-08-08T00:49:34.815340Z","submitted_at":"2025-07-03T03:59:07Z","title":"Mixed-state phases from local reversibility","version":2},"cited_work":{"arxiv_id":"2507.02292","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2507.02292","snapshot_observed_at":"2026-07-03T13:18:12.883835Z","title":"Mixed-state phases from local reversibility","venue":null,"work_id":"55cdd57e-0130-4140-a6a0-0fe08c42f11b","year":2025},"citing_paper":{"arxiv_id":"2605.15201","last_updated":"2026-05-14T17:59:59Z","snapshot_observed_at":"2026-08-06T18:52:01.855027Z","submitted_at":"2026-05-14T17:59:59Z","title":"Mixed-State Long-Range Entanglement from Dimensional Constraints","version":1},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-05-15T03:07:01.857791Z"},"links":{"cited_paper":"/paper/2507.02292","citing_paper":"/paper/2605.15201"},"observation_digest":"sha256:2ce54c85b85cb35f3cd56af9aec918662e82da0df668377dc62212feace62e65","observation_id":"0b72e7a7-0f5c-4567-8fce-b080bc716163","resolution":{"observed_at":"2026-05-15T03:08:58.292928Z","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"}},{"citation":{"cited_paper":{"arxiv_id":"2507.02292","last_updated":"2025-07-25T18:39:08Z","snapshot_observed_at":"2026-08-08T00:49:34.815340Z","submitted_at":"2025-07-03T03:59:07Z","title":"Mixed-state phases from local reversibility","version":2},"cited_work":{"arxiv_id":"2507.02292","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2507.02292","snapshot_observed_at":"2026-07-03T13:18:12.883835Z","title":"Mixed-state phases from local reversibility","venue":null,"work_id":"55cdd57e-0130-4140-a6a0-0fe08c42f11b","year":2025},"citing_paper":{"arxiv_id":"2605.28925","last_updated":"2026-05-27T18:00:00Z","snapshot_observed_at":"2026-08-06T07:30:36.589203Z","submitted_at":"2026-05-27T18:00:00Z","title":"A local description of strong symmetries and strong-to-weak symmetry breaking in quantum many-body systems","version":1},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-06-29T11:42:51.655279Z"},"links":{"cited_paper":"/paper/2507.02292","citing_paper":"/paper/2605.28925"},"observation_digest":"sha256:a4136d58a1a88b8591d5d1bbe51b4a445224b75bf5b0a9e0ad260eaedaa6930a","observation_id":"4064080c-4efb-48b2-8e9d-4f4e338fa788","resolution":{"observed_at":"2026-06-29T11:43:23.202378Z","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"}},{"citation":{"cited_paper":{"arxiv_id":"2507.02292","last_updated":"2025-07-25T18:39:08Z","snapshot_observed_at":"2026-08-08T00:49:34.815340Z","submitted_at":"2025-07-03T03:59:07Z","title":"Mixed-state phases from local reversibility","version":2},"cited_work":{"arxiv_id":"2507.02292","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2507.02292","snapshot_observed_at":"2026-07-03T13:18:12.883835Z","title":"Mixed-state phases from local reversibility","venue":null,"work_id":"55cdd57e-0130-4140-a6a0-0fe08c42f11b","year":2025},"citing_paper":{"arxiv_id":"2605.28967","last_updated":"2026-05-27T18:16:15Z","snapshot_observed_at":"2026-07-31T08:37:11.901056Z","submitted_at":"2026-05-27T18:16:15Z","title":"Local Strong-to-Weak Spontaneous Symmetry Breaking","version":1},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-06-29T11:20:30.695407Z"},"links":{"cited_paper":"/paper/2507.02292","citing_paper":"/paper/2605.28967"},"observation_digest":"sha256:be66fecf3d8e9fb983ebfc980450da2d59b34a693235a69788961ca087e56b22","observation_id":"578ca573-912e-4ec1-9518-b0ff75222742","resolution":{"observed_at":"2026-06-29T11:23:20.745769Z","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"}},{"citation":{"cited_paper":{"arxiv_id":"2507.02292","last_updated":"2025-07-25T18:39:08Z","snapshot_observed_at":"2026-08-08T00:49:34.815340Z","submitted_at":"2025-07-03T03:59:07Z","title":"Mixed-state phases from local reversibility","version":2},"cited_work":{"arxiv_id":"2507.02292","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2507.02292","snapshot_observed_at":"2026-07-03T13:18:12.883835Z","title":"Mixed-state phases from local reversibility","venue":null,"work_id":"55cdd57e-0130-4140-a6a0-0fe08c42f11b","year":2025},"citing_paper":{"arxiv_id":"2605.29113","last_updated":"2026-05-27T21:20:59Z","snapshot_observed_at":"2026-07-06T23:38:37.178378Z","submitted_at":"2026-05-27T21:20:59Z","title":"Local diagnostics for strong-to-weak spontaneous symmetry breaking and non-equilibrium phase transitions","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-06-29T11:23:01.230345Z"},"links":{"cited_paper":"/paper/2507.02292","citing_paper":"/paper/2605.29113"},"observation_digest":"sha256:bf7a31377bd7579c312da4acd10b263143bbf25eeadf263eeb7c1f39f55b6418","observation_id":"224ac9d1-f697-4c97-8446-e2a1e4d24584","resolution":{"observed_at":"2026-06-29T11:23:20.558207Z","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"}},{"citation":{"cited_paper":{"arxiv_id":"2507.02292","last_updated":"2025-07-25T18:39:08Z","snapshot_observed_at":"2026-08-08T00:49:34.815340Z","submitted_at":"2025-07-03T03:59:07Z","title":"Mixed-state phases from local reversibility","version":2},"cited_work":{"arxiv_id":"2507.02292","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2507.02292","snapshot_observed_at":"2026-07-03T13:18:12.883835Z","title":"Mixed-state phases from local reversibility","venue":null,"work_id":"55cdd57e-0130-4140-a6a0-0fe08c42f11b","year":2025},"citing_paper":{"arxiv_id":"2606.02555","last_updated":"2026-06-08T05:12:17Z","snapshot_observed_at":"2026-07-06T23:42:58.036516Z","submitted_at":"2026-06-01T17:51:09Z","title":"Strong-to-Weak Spontaneous Symmetry Breaking","version":2},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-06-28T14:16:27.400490Z"},"links":{"cited_paper":"/paper/2507.02292","citing_paper":"/paper/2606.02555"},"observation_digest":"sha256:b893debf7f886ae179dc5a8e58c8884284d4a61a1323324c5d04a9502d3e5ba3","observation_id":"3977683c-8221-4a40-877d-56f240796c84","resolution":{"observed_at":"2026-07-01T23:36:22.093151Z","resolver_source":"arxiv_id","status":"metadata_mismatch"},"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":"2507.02292","last_updated":"2025-07-25T18:39:08Z","snapshot_observed_at":"2026-08-08T00:49:34.815340Z","submitted_at":"2025-07-03T03:59:07Z","title":"Mixed-state phases from local reversibility","version":2},"cited_work":{"arxiv_id":"2507.02292","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2507.02292","snapshot_observed_at":"2026-07-03T13:18:12.883835Z","title":"Mixed-state phases from local reversibility","venue":null,"work_id":"55cdd57e-0130-4140-a6a0-0fe08c42f11b","year":2025},"citing_paper":{"arxiv_id":"2606.12132","last_updated":"2026-06-29T15:52:52Z","snapshot_observed_at":"2026-07-06T23:51:07.629939Z","submitted_at":"2026-06-10T14:26:18Z","title":"From Topological Order to Mixed-State Phases: A Ground-State Probe of Fractionalized Excitations","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-06-27T08:17:02.156089Z"},"links":{"cited_paper":"/paper/2507.02292","citing_paper":"/paper/2606.12132"},"observation_digest":"sha256:9333e288d4fa41937933aba85501f1ee79ba1f7d295f03990de68b71330cd62c","observation_id":"3d3d14a8-e1e5-4b20-8639-e97d32e218c4","resolution":{"observed_at":"2026-07-03T13:18:12.885367Z","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"}},{"citation":{"cited_paper":{"arxiv_id":"2507.02292","last_updated":"2025-07-25T18:39:08Z","snapshot_observed_at":"2026-08-08T00:49:34.815340Z","submitted_at":"2025-07-03T03:59:07Z","title":"Mixed-state phases from local reversibility","version":2},"cited_work":{"arxiv_id":"2507.02292","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2507.02292","snapshot_observed_at":"2026-07-03T13:18:12.883835Z","title":"Mixed-state phases from local reversibility","venue":null,"work_id":"55cdd57e-0130-4140-a6a0-0fe08c42f11b","year":2025},"citing_paper":{"arxiv_id":"2606.12132","last_updated":"2026-06-29T15:52:52Z","snapshot_observed_at":"2026-07-06T23:51:07.629939Z","submitted_at":"2026-06-10T14:26:18Z","title":"From Topological Order to Mixed-State Phases: A Ground-State Probe of Fractionalized Excitations","version":2},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-06-30T10:28:39.040228Z"},"links":{"cited_paper":"/paper/2507.02292","citing_paper":"/paper/2606.12132"},"observation_digest":"sha256:953fa08aedef175ea1130cb69f4d0416a3972858a3bbba8629baaca734eb0cc6","observation_id":"c05c31d8-fcf5-4e25-9695-913c10d45b68","resolution":{"observed_at":"2026-06-30T10:44:37.369889Z","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"}},{"citation":{"cited_paper":{"arxiv_id":"2507.02292","last_updated":"2025-07-25T18:39:08Z","snapshot_observed_at":"2026-08-08T00:49:34.815340Z","submitted_at":"2025-07-03T03:59:07Z","title":"Mixed-state phases from local reversibility","version":2},"cited_work":{"arxiv_id":"2507.02292","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2507.02292","snapshot_observed_at":"2026-07-03T13:18:12.883835Z","title":"Mixed-state phases from local reversibility","venue":null,"work_id":"55cdd57e-0130-4140-a6a0-0fe08c42f11b","year":2025},"citing_paper":{"arxiv_id":"2606.28054","last_updated":"2026-07-07T08:48:59Z","snapshot_observed_at":"2026-08-05T06:39:21.063341Z","submitted_at":"2026-06-26T12:56:57Z","title":"Static features from mixing in short- and long-range Lindbladians: Markov property and correlations","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-06-29T04:10:02.479489Z"},"links":{"cited_paper":"/paper/2507.02292","citing_paper":"/paper/2606.28054"},"observation_digest":"sha256:747eb77ba6452a923c19ea202b57b6b952f493e426fb8ca009cb9eb58dee8c77","observation_id":"bdc017e7-df09-4653-89a5-ebd8b3b3c874","resolution":{"observed_at":"2026-07-01T17:05:51.374747Z","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"}},{"citation":{"cited_paper":{"arxiv_id":"2507.02292","last_updated":"2025-07-25T18:39:08Z","snapshot_observed_at":"2026-08-08T00:49:34.815340Z","submitted_at":"2025-07-03T03:59:07Z","title":"Mixed-state phases from local reversibility","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2507.02292","snapshot_observed_at":"2026-07-12T11:34:29.323923Z","title":"Mixed-state phases from local reversibilityarXiv:2507.02292 [quant-ph]","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2606.28054","last_updated":"2026-07-07T08:48:59Z","snapshot_observed_at":"2026-08-05T06:39:21.063341Z","submitted_at":"2026-06-26T12:56:57Z","title":"Static features from mixing in short- and long-range Lindbladians: Markov property and correlations","version":2},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-07-12T11:34:29.323923Z"},"links":{"cited_paper":"/paper/2507.02292","citing_paper":"/paper/2606.28054"},"observation_digest":"sha256:1b7bc8f1d1faa10fb0b5ff9651d3fcd24fdb3a769fa43ea33ee0c44d8973af61","observation_id":"0473cbeb-a7c3-4d2d-abe7-cca7469272e9","resolution":{"observed_at":"2026-07-12T11:34:29.323923Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2507.02292","last_updated":"2025-07-25T18:39:08Z","snapshot_observed_at":"2026-08-08T00:49:34.815340Z","submitted_at":"2025-07-03T03:59:07Z","title":"Mixed-state phases from local reversibility","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2507.02292","snapshot_observed_at":"2026-08-08T19:23:26.275182Z","title":null,"venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2608.04350","last_updated":"2026-08-05T01:49:48Z","snapshot_observed_at":"2026-08-10T03:31:17.242014Z","submitted_at":"2026-08-05T01:49:48Z","title":"Quantized topological invariant of symmetry-projected Gibbs states","version":1},"reference_index":39,"source":"pdf_text","source_observed_at":"2026-08-08T19:23:26.275182Z"},"links":{"cited_paper":"/paper/2507.02292","citing_paper":"/paper/2608.04350"},"observation_digest":"sha256:ec6baa5b46f94e372b77288723567343ce85837d9eb75ca05d65fadc8245e1ef","observation_id":"bcf49092-5114-4361-875b-4906fdf412de","resolution":{"observed_at":"2026-08-08T19:23:26.275182Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"links":{"evidence":"/evidence","html":"/paper/2507.02292/citation-record","integrity":"/paper/2507.02292/integrity","json":"/paper/2507.02292/citation-record.json","paper":"/paper/2507.02292"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T20:44:24.289721Z","title":null,"venue":null,"work_id":"c1c5a118-a558-4c16-a4d0-3f06bf7af60d","year":null},"citing_paper":{"arxiv_id":"2507.02292","last_updated":"2025-07-25T18:39:08Z","snapshot_observed_at":"2026-08-08T00:49:34.815340Z","submitted_at":"2025-07-03T03:59:07Z","title":"Mixed-state phases from local reversibility","version":2},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-06T20:44:22.996716Z"},"links":{"citing_paper":"/paper/2507.02292"},"observation_digest":"sha256:ead2fc7a9e0da177ff43b38e44ffe3c15811f261b53e0b27996a6ef512c8bd09","observation_id":"50018b6a-81a0-495e-95c5-20e453f39ec2","resolution":{"observed_at":"2026-08-06T20:44:24.293186Z","resolver_source":"raw_fallback","status":"unresolved"},"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":"2026-08-06T20:44:24.278345Z","title":null,"venue":null,"work_id":"9175f0c9-cd5a-46eb-a5a9-51d2f52f9be3","year":null},"citing_paper":{"arxiv_id":"2507.02292","last_updated":"2025-07-25T18:39:08Z","snapshot_observed_at":"2026-08-08T00:49:34.815340Z","submitted_at":"2025-07-03T03:59:07Z","title":"Mixed-state phases from local reversibility","version":2},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-06T20:44:23.002885Z"},"links":{"citing_paper":"/paper/2507.02292"},"observation_digest":"sha256:aa0cfc659ba8a24d02aecea38166392b47a908affea262b2f8935085d1fc64ed","observation_id":"ddd76d28-6716-4dbb-b9f5-09b1173b2e5f","resolution":{"observed_at":"2026-08-06T20:44:24.282306Z","resolver_source":"raw_fallback","status":"parse_uncertain"},"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":"2507.02292","last_updated":"2025-07-25T18:39:08Z","snapshot_observed_at":"2026-08-08T00:49:34.815340Z","submitted_at":"2025-07-03T03:59:07Z","title":"Mixed-state phases from local reversibility","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2507.02292","snapshot_observed_at":"2026-08-06T20:44:23.007884Z","title":"INTRODUCTION Quantum information insights have led to substantial progress in understanding quantum many-body phenom- ena","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2507.02292","last_updated":"2025-07-25T18:39:08Z","snapshot_observed_at":"2026-08-08T00:49:34.815340Z","submitted_at":"2025-07-03T03:59:07Z","title":"Mixed-state phases from local reversibility","version":2},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-06T20:44:23.007884Z"},"links":{"cited_paper":"/paper/2507.02292","citing_paper":"/paper/2507.02292"},"observation_digest":"sha256:0664033e8909f8c8eabec0293a6f0d07f1a80dd0c2b8a0a8ff37142dbca364f7","observation_id":"5be803aa-4e6a-4b78-a7dd-9c37b22389c4","resolution":{"observed_at":"2026-08-06T20:44:23.007884Z","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":"2026-08-06T20:44:24.267040Z","title":"III the topological degeneracy of mixed-states via local indistinguishability, which gen- eralizes the topological degeneracy in topologically or- dered ground states","venue":null,"work_id":"100eab4b-c65a-4114-bbe4-d0461c59c050","year":null},"citing_paper":{"arxiv_id":"2507.02292","last_updated":"2025-07-25T18:39:08Z","snapshot_observed_at":"2026-08-08T00:49:34.815340Z","submitted_at":"2025-07-03T03:59:07Z","title":"Mixed-state phases from local reversibility","version":2},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-06T20:44:23.013454Z"},"links":{"citing_paper":"/paper/2507.02292"},"observation_digest":"sha256:cce11ef9ab2fc65743e8095fbb51e69e8e14c8d27283235061cf99f9d73da029","observation_id":"d30a71ef-7a0f-4ad1-8fb4-e743e8c34e4a","resolution":{"observed_at":"2026-08-06T20:44:24.270987Z","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":"2026-08-06T20:44:24.254586Z","title":"IV that the spontaneous symme- try breaking of 1-form symmetries, or equivalently the ’t Hooft anomaly associated with the symmetries, is also a phase invariant","venue":null,"work_id":"44d45cab-99fe-41b8-ab9d-dee3e8339fdb","year":null},"citing_paper":{"arxiv_id":"2507.02292","last_updated":"2025-07-25T18:39:08Z","snapshot_observed_at":"2026-08-08T00:49:34.815340Z","submitted_at":"2025-07-03T03:59:07Z","title":"Mixed-state phases from local reversibility","version":2},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-06T20:44:23.018538Z"},"links":{"citing_paper":"/paper/2507.02292"},"observation_digest":"sha256:d6b84b1fb1f3d93ae77153407c8c0630a1692c5f9a2f67ff792cee78d1d9be85","observation_id":"2704849a-77dd-4ea2-8215-7da0613f5caa","resolution":{"observed_at":"2026-08-06T20:44:24.258907Z","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":"2026-08-06T20:44:24.242302Z","title":"topological entanglement entropy","venue":null,"work_id":"b6647bec-90fd-4109-adce-5f1b99f6de4d","year":null},"citing_paper":{"arxiv_id":"2507.02292","last_updated":"2025-07-25T18:39:08Z","snapshot_observed_at":"2026-08-08T00:49:34.815340Z","submitted_at":"2025-07-03T03:59:07Z","title":"Mixed-state phases from local reversibility","version":2},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-06T20:44:23.023462Z"},"links":{"citing_paper":"/paper/2507.02292"},"observation_digest":"sha256:69f6cc0e6807f288b47e70480b42aa0b2bda568028443dfbe73f37d3317a6548","observation_id":"8a175fd5-46fc-425b-9bb5-623068147d48","resolution":{"observed_at":"2026-08-06T20:44:24.246489Z","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":"2026-08-06T20:44:24.231176Z","title":"As we will illustrate with the ρcl example, the constraint removes ‘unphys- ical’ locally indistinguishable states","venue":null,"work_id":"ac77f65e-825a-43e1-8168-dc425850c6b1","year":null},"citing_paper":{"arxiv_id":"2507.02292","last_updated":"2025-07-25T18:39:08Z","snapshot_observed_at":"2026-08-08T00:49:34.815340Z","submitted_at":"2025-07-03T03:59:07Z","title":"Mixed-state phases from local reversibility","version":2},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-06T20:44:23.028989Z"},"links":{"citing_paper":"/paper/2507.02292"},"observation_digest":"sha256:dd2beb5f21a5cd27066084ea9c85caa0faab01164e53b14df283ea96022fe8c8","observation_id":"eee7aa4c-43b3-4430-abbe-eb691e2b3bbe","resolution":{"observed_at":"2026-08-06T20:44:24.234974Z","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":"2026-08-06T20:44:24.218434Z","title":"To see this, it suffices to check that σ3 is locally indistinguishable from ρ and has a finite Markov length","venue":null,"work_id":"94c5a98c-ed09-492d-881c-d0175136efd1","year":null},"citing_paper":{"arxiv_id":"2507.02292","last_updated":"2025-07-25T18:39:08Z","snapshot_observed_at":"2026-08-08T00:49:34.815340Z","submitted_at":"2025-07-03T03:59:07Z","title":"Mixed-state phases from local reversibility","version":2},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-06T20:44:23.036171Z"},"links":{"citing_paper":"/paper/2507.02292"},"observation_digest":"sha256:99972164b1263f5945ae975a9019951866476e47924d5b64557ff3a6b55fdaa3","observation_id":"513ca5af-0a36-47fb-98ca-8d3b05c2155d","resolution":{"observed_at":"2026-08-06T20:44:24.223763Z","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":"2026-08-06T20:44:24.207782Z","title":null,"venue":null,"work_id":"e0c057b1-2442-4e8d-a9cb-e22e0fd6d459","year":null},"citing_paper":{"arxiv_id":"2507.02292","last_updated":"2025-07-25T18:39:08Z","snapshot_observed_at":"2026-08-08T00:49:34.815340Z","submitted_at":"2025-07-03T03:59:07Z","title":"Mixed-state phases from local reversibility","version":2},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-06T20:44:23.040323Z"},"links":{"citing_paper":"/paper/2507.02292"},"observation_digest":"sha256:247ac53da120605b081bd95bb2dd795fecb3bc300df55c563db87e0a8f64a7c3","observation_id":"61078f81-4631-4870-b2ec-a29efce3c0e6","resolution":{"observed_at":"2026-08-06T20:44:24.211284Z","resolver_source":"raw_fallback","status":"unresolved"},"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":"2026-08-06T20:44:24.194952Z","title":"fidelity observable","venue":null,"work_id":"91fba56c-f5a3-4050-86bf-29a0c959cbe8","year":null},"citing_paper":{"arxiv_id":"2507.02292","last_updated":"2025-07-25T18:39:08Z","snapshot_observed_at":"2026-08-08T00:49:34.815340Z","submitted_at":"2025-07-03T03:59:07Z","title":"Mixed-state phases from local reversibility","version":2},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-06T20:44:23.045954Z"},"links":{"citing_paper":"/paper/2507.02292"},"observation_digest":"sha256:112ffc7d4cc5e5c46023a4c9968d41cf8000d0b56879adca663111593e86ccb5","observation_id":"1f7379d9-0731-4fce-8145-a0fea25b8048","resolution":{"observed_at":"2026-08-06T20:44:24.199278Z","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":"2412.19803","last_updated":"2026-05-23T04:03:12Z","snapshot_observed_at":"2026-08-10T07:58:44.726750Z","submitted_at":"2024-12-27T18:59:57Z","title":"A local automaton for the 2D toric code","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2412.19803","snapshot_observed_at":"2026-08-06T20:44:23.142786Z","title":"Balasubramanian, M","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2507.02292","last_updated":"2025-07-25T18:39:08Z","snapshot_observed_at":"2026-08-08T00:49:34.815340Z","submitted_at":"2025-07-03T03:59:07Z","title":"Mixed-state phases from local reversibility","version":2},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-06T20:44:23.142786Z"},"links":{"cited_paper":"/paper/2412.19803","citing_paper":"/paper/2507.02292"},"observation_digest":"sha256:1f152850e2052a588e258d2e560b6c073b996922324b79b33807ca0e688c6d53","observation_id":"7c473780-36fb-4986-9015-50d3f1118f2d","resolution":{"observed_at":"2026-08-06T20:44:23.142786Z","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":"2026-08-06T20:44:24.173232Z","title":null,"venue":null,"work_id":"c64c21da-49f6-4c16-9473-1495b3d56f74","year":null},"citing_paper":{"arxiv_id":"2507.02292","last_updated":"2025-07-25T18:39:08Z","snapshot_observed_at":"2026-08-08T00:49:34.815340Z","submitted_at":"2025-07-03T03:59:07Z","title":"Mixed-state phases from local reversibility","version":2},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-06T20:44:23.057784Z"},"links":{"citing_paper":"/paper/2507.02292"},"observation_digest":"sha256:bc8fa71680424e46fc7ce504bd4a280c86d2f1ede83a2dbc8e0f4b465a35924a","observation_id":"d792f1b4-a6d4-4095-8d6e-30016394af42","resolution":{"observed_at":"2026-08-06T20:44:24.177244Z","resolver_source":"raw_fallback","status":"unresolved"},"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":"2026-08-06T20:44:24.162574Z","title":"For q = 1 /2, the classical loop state with no non-contractible loops ρcl = ρ00 cl is reached","venue":null,"work_id":"db6ca70c-e5de-49e3-8964-55296e9c0cf5","year":null},"citing_paper":{"arxiv_id":"2507.02292","last_updated":"2025-07-25T18:39:08Z","snapshot_observed_at":"2026-08-08T00:49:34.815340Z","submitted_at":"2025-07-03T03:59:07Z","title":"Mixed-state phases from local reversibility","version":2},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-06T20:44:23.063467Z"},"links":{"citing_paper":"/paper/2507.02292"},"observation_digest":"sha256:b8cc10a4b056bf0317803afc363e3415386dede0407b24ad1b2036eed5d04200","observation_id":"7938b4c9-b6b4-4d4f-af15-847c6ae08a0e","resolution":{"observed_at":"2026-08-06T20:44:24.166191Z","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":"2026-08-06T20:44:24.151283Z","title":null,"venue":null,"work_id":"7bb36f2b-384f-4204-b186-d688f41df92f","year":null},"citing_paper":{"arxiv_id":"2507.02292","last_updated":"2025-07-25T18:39:08Z","snapshot_observed_at":"2026-08-08T00:49:34.815340Z","submitted_at":"2025-07-03T03:59:07Z","title":"Mixed-state phases from local reversibility","version":2},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-06T20:44:23.067972Z"},"links":{"citing_paper":"/paper/2507.02292"},"observation_digest":"sha256:452bd8b65bfd587f055d898f8890c9988e62e832a8a33f33df988a49b5e870e7","observation_id":"f722e1e6-8c79-4b62-ab6e-e4f5eff9a9f0","resolution":{"observed_at":"2026-08-06T20:44:24.154770Z","resolver_source":"raw_fallback","status":"unresolved"},"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":"2026-08-06T20:44:24.139213Z","title":"(B17) not only gives the correct critical behavior at q ≈ qc, but is also accurate even for q/qc ≪ 1 (and |A| large), far from the regime ( q ≈ qc) it was initially derived from","venue":null,"work_id":"da74c73f-4bb7-4006-8b99-ea351c97bfb2","year":null},"citing_paper":{"arxiv_id":"2507.02292","last_updated":"2025-07-25T18:39:08Z","snapshot_observed_at":"2026-08-08T00:49:34.815340Z","submitted_at":"2025-07-03T03:59:07Z","title":"Mixed-state phases from local reversibility","version":2},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-06T20:44:23.072922Z"},"links":{"citing_paper":"/paper/2507.02292"},"observation_digest":"sha256:5ec108e19704e1efc6a391557c24cff214bb215435a5edb6338d472aa20046e6","observation_id":"57e0f18c-49d7-4a9b-a375-7c2aea92f59e","resolution":{"observed_at":"2026-08-06T20:44:24.144045Z","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":"2026-08-06T20:44:24.126840Z","title":null,"venue":null,"work_id":"87b098f9-d1f3-4a38-87f2-6aa63f8fc3e0","year":null},"citing_paper":{"arxiv_id":"2507.02292","last_updated":"2025-07-25T18:39:08Z","snapshot_observed_at":"2026-08-08T00:49:34.815340Z","submitted_at":"2025-07-03T03:59:07Z","title":"Mixed-state phases from local reversibility","version":2},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-06T20:44:23.085125Z"},"links":{"citing_paper":"/paper/2507.02292"},"observation_digest":"sha256:b2e9c3bba5c302263f33d18ff92590313e353a7fd0de09ec51a0c7f776df9d3c","observation_id":"4d06ccd5-d9b9-4d6c-847f-02361eb9f582","resolution":{"observed_at":"2026-08-06T20:44:24.130876Z","resolver_source":"raw_fallback","status":"unresolved"},"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":"2026-08-06T20:44:24.115633Z","title":"Chen, Z.-C","venue":null,"work_id":"346e07be-976f-4f56-935c-951f293e8e1a","year":2010},"citing_paper":{"arxiv_id":"2507.02292","last_updated":"2025-07-25T18:39:08Z","snapshot_observed_at":"2026-08-08T00:49:34.815340Z","submitted_at":"2025-07-03T03:59:07Z","title":"Mixed-state phases from local reversibility","version":2},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-06T20:44:23.090822Z"},"links":{"citing_paper":"/paper/2507.02292"},"observation_digest":"sha256:364ad268ed8f84ae1deb10ee29a0624be0c8a537122a4390d745b00d92ef5648","observation_id":"bc49acaf-9f7d-45ba-b277-14dd38ce1bbb","resolution":{"observed_at":"2026-08-06T20:44:24.119331Z","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":"2026-08-06T20:44:24.103453Z","title":null,"venue":null,"work_id":"5653a919-91b9-4e59-ace3-c8dd0023d316","year":2005},"citing_paper":{"arxiv_id":"2507.02292","last_updated":"2025-07-25T18:39:08Z","snapshot_observed_at":"2026-08-08T00:49:34.815340Z","submitted_at":"2025-07-03T03:59:07Z","title":"Mixed-state phases from local reversibility","version":2},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-06T20:44:23.095496Z"},"links":{"citing_paper":"/paper/2507.02292"},"observation_digest":"sha256:208b33948cd8aa3d2562cf0d53115284c988382e98596adc8f4a8bded6accf1c","observation_id":"a6ca4b47-2fb3-49eb-9314-9057eadd58b8","resolution":{"observed_at":"2026-08-06T20:44:24.107112Z","resolver_source":"raw_fallback","status":"unresolved"},"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":"2026-08-06T20:44:23.100876Z","title":"Verstraete, M","venue":null,"work_id":null,"year":2009},"citing_paper":{"arxiv_id":"2507.02292","last_updated":"2025-07-25T18:39:08Z","snapshot_observed_at":"2026-08-08T00:49:34.815340Z","submitted_at":"2025-07-03T03:59:07Z","title":"Mixed-state phases from local reversibility","version":2},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-06T20:44:23.100876Z"},"links":{"citing_paper":"/paper/2507.02292"},"observation_digest":"sha256:a69997ec43bb77fca0747edb9d3e710c6ab46ff9291242a586b7a9e2a8f9dde1","observation_id":"690e5edf-acf7-41a2-a4ab-beef4beb7b67","resolution":{"observed_at":"2026-08-06T20:44:23.100876Z","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":"2026-08-06T20:44:23.105740Z","title":"Diehl, A","venue":null,"work_id":null,"year":2008},"citing_paper":{"arxiv_id":"2507.02292","last_updated":"2025-07-25T18:39:08Z","snapshot_observed_at":"2026-08-08T00:49:34.815340Z","submitted_at":"2025-07-03T03:59:07Z","title":"Mixed-state phases from local reversibility","version":2},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-06T20:44:23.105740Z"},"links":{"citing_paper":"/paper/2507.02292"},"observation_digest":"sha256:c9e6ac7df611a383a2277eb864329edfa2f86dfe338256d4e68699839cc77baa","observation_id":"92470c78-6320-4fda-9fd7-a42359f65bc8","resolution":{"observed_at":"2026-08-06T20:44:23.105740Z","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":"2026-08-06T20:44:24.183810Z","title":"symmetry pullback","venue":null,"work_id":"a39676d6-b2c8-4692-ad2a-d287eb19cfa1","year":2020},"citing_paper":{"arxiv_id":"2507.02292","last_updated":"2025-07-25T18:39:08Z","snapshot_observed_at":"2026-08-08T00:49:34.815340Z","submitted_at":"2025-07-03T03:59:07Z","title":"Mixed-state phases from local reversibility","version":2},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-06T20:44:23.052347Z"},"links":{"citing_paper":"/paper/2507.02292"},"observation_digest":"sha256:30955fc918843920a0204fdd4977305ce871e4436bc670a7229b1a7192d15283","observation_id":"f70f7079-8f6a-4d1c-8fb9-d18b6c6c0f2c","resolution":{"observed_at":"2026-08-06T20:44:24.187462Z","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":"2301.05689","last_updated":"2024-03-12T06:20:34Z","snapshot_observed_at":"2026-07-06T14:41:10.087407Z","submitted_at":"2023-01-13T18:21:23Z","title":"Diagnostics of mixed-state topological order and breakdown of quantum memory","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2301.05689","snapshot_observed_at":"2026-08-06T20:44:23.111006Z","title":null,"venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2507.02292","last_updated":"2025-07-25T18:39:08Z","snapshot_observed_at":"2026-08-08T00:49:34.815340Z","submitted_at":"2025-07-03T03:59:07Z","title":"Mixed-state phases from local reversibility","version":2},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-06T20:44:23.111006Z"},"links":{"cited_paper":"/paper/2301.05689","citing_paper":"/paper/2507.02292"},"observation_digest":"sha256:d19ecc307d4ec50fcf3cbcf07d9c204581c576e449f09845886ed0c90e0179a8","observation_id":"58ec2a67-c83c-4401-9c46-d16e5b52845b","resolution":{"observed_at":"2026-08-06T20:44:23.111006Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2301.05238","last_updated":"2023-07-27T00:27:35Z","snapshot_observed_at":"2026-07-06T14:40:50.270024Z","submitted_at":"2023-01-12T19:00:00Z","title":"Quantum criticality under decoherence or weak measurement","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2301.05238","snapshot_observed_at":"2026-08-06T20:44:23.115748Z","title":null,"venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2507.02292","last_updated":"2025-07-25T18:39:08Z","snapshot_observed_at":"2026-08-08T00:49:34.815340Z","submitted_at":"2025-07-03T03:59:07Z","title":"Mixed-state phases from local reversibility","version":2},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-06T20:44:23.115748Z"},"links":{"cited_paper":"/paper/2301.05238","citing_paper":"/paper/2507.02292"},"observation_digest":"sha256:cb9bd55dbcad0ae76bda92e07a7e08d971566dbd3087556995b7d2a05206ee7e","observation_id":"bec7d4c8-87d0-4a01-9a56-b65152c8a7ea","resolution":{"observed_at":"2026-08-06T20:44:23.115748Z","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":"2026-08-06T20:44:24.078132Z","title":null,"venue":null,"work_id":"e34c7e68-4ff0-49d1-853f-97807de4c213","year":2023},"citing_paper":{"arxiv_id":"2507.02292","last_updated":"2025-07-25T18:39:08Z","snapshot_observed_at":"2026-08-08T00:49:34.815340Z","submitted_at":"2025-07-03T03:59:07Z","title":"Mixed-state phases from local reversibility","version":2},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-06T20:44:23.121743Z"},"links":{"citing_paper":"/paper/2507.02292"},"observation_digest":"sha256:09287a8e472d6a660b19f6d2f77433ef83cd8a6f20f795f5e73475de56eefd86","observation_id":"39f26c93-d856-430e-9cc6-af2dfb91b98a","resolution":{"observed_at":"2026-08-06T20:44:24.081944Z","resolver_source":"raw_fallback","status":"unresolved"},"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":"2026-08-06T20:44:23.127518Z","title":null,"venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2507.02292","last_updated":"2025-07-25T18:39:08Z","snapshot_observed_at":"2026-08-08T00:49:34.815340Z","submitted_at":"2025-07-03T03:59:07Z","title":"Mixed-state phases from local reversibility","version":2},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-06T20:44:23.127518Z"},"links":{"citing_paper":"/paper/2507.02292"},"observation_digest":"sha256:97c0106a33ca0aa8d53ee2e086509ab04a69cd2dae0d439a0cd36f3c2375e886","observation_id":"b623984c-b16a-49b1-bb78-7a9971109038","resolution":{"observed_at":"2026-08-06T20:44:23.127518Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2208.11699","last_updated":"2022-09-06T16:28:58Z","snapshot_observed_at":"2026-07-06T13:45:08.197247Z","submitted_at":"2022-08-24T17:59:58Z","title":"Decoding Measurement-Prepared Quantum Phases and Transitions: from Ising model to gauge theory, and beyond","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2208.11699","snapshot_observed_at":"2026-08-06T20:44:23.133494Z","title":null,"venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2507.02292","last_updated":"2025-07-25T18:39:08Z","snapshot_observed_at":"2026-08-08T00:49:34.815340Z","submitted_at":"2025-07-03T03:59:07Z","title":"Mixed-state phases from local reversibility","version":2},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-06T20:44:23.133494Z"},"links":{"cited_paper":"/paper/2208.11699","citing_paper":"/paper/2507.02292"},"observation_digest":"sha256:5b30273e8f71f577e8410be2b56e25cb8a9438385c64fbb4e01fcc622f7c0f9f","observation_id":"6bd696d6-c484-454b-ac77-8708772f5c61","resolution":{"observed_at":"2026-08-06T20:44:23.133494Z","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":"2026-08-06T20:44:23.138501Z","title":null,"venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2507.02292","last_updated":"2025-07-25T18:39:08Z","snapshot_observed_at":"2026-08-08T00:49:34.815340Z","submitted_at":"2025-07-03T03:59:07Z","title":"Mixed-state phases from local reversibility","version":2},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-06T20:44:23.138501Z"},"links":{"citing_paper":"/paper/2507.02292"},"observation_digest":"sha256:bc1d6506f9e7a98f25fe2f45dd1a7ab42f7194c44c073a3051676617fc60a769","observation_id":"ed5b3a75-f83d-4044-b4dd-eeba3c72b015","resolution":{"observed_at":"2026-08-06T20:44:23.138501Z","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":"2026-08-06T20:44:24.051484Z","title":null,"venue":null,"work_id":"38d4b8a5-0bd7-4781-b73f-be1093a6bc98","year":2011},"citing_paper":{"arxiv_id":"2507.02292","last_updated":"2025-07-25T18:39:08Z","snapshot_observed_at":"2026-08-08T00:49:34.815340Z","submitted_at":"2025-07-03T03:59:07Z","title":"Mixed-state phases from local reversibility","version":2},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-06T20:44:23.147520Z"},"links":{"citing_paper":"/paper/2507.02292"},"observation_digest":"sha256:66525d7190e4f4c8a7925616ba83760d31ff390e4661e3f62c8b74540064322a","observation_id":"47e56569-d43f-4a55-aeab-305754b500dc","resolution":{"observed_at":"2026-08-06T20:44:24.055438Z","resolver_source":"raw_fallback","status":"unresolved"},"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":"2026-08-06T20:44:24.039440Z","title":"Coser and D","venue":null,"work_id":"70709c5f-3730-4700-aaf5-01907c818f66","year":2019},"citing_paper":{"arxiv_id":"2507.02292","last_updated":"2025-07-25T18:39:08Z","snapshot_observed_at":"2026-08-08T00:49:34.815340Z","submitted_at":"2025-07-03T03:59:07Z","title":"Mixed-state phases from local reversibility","version":2},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-06T20:44:23.153001Z"},"links":{"citing_paper":"/paper/2507.02292"},"observation_digest":"sha256:7cfe39f4456cf9c3b64125a8296e585b224a9144619164f85f6e12c580775cc1","observation_id":"cc952143-548a-4767-b1e2-985b2700cd9c","resolution":{"observed_at":"2026-08-06T20:44:24.043124Z","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":"2026-08-06T20:44:23.157367Z","title":"Ma and C","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2507.02292","last_updated":"2025-07-25T18:39:08Z","snapshot_observed_at":"2026-08-08T00:49:34.815340Z","submitted_at":"2025-07-03T03:59:07Z","title":"Mixed-state phases from local reversibility","version":2},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-06T20:44:23.157367Z"},"links":{"citing_paper":"/paper/2507.02292"},"observation_digest":"sha256:6c3ef80c7643742e390137c340ab2592a0fd0e026972824276965bea391fe9ea","observation_id":"5fdcce3d-58c2-4a79-80fd-8676803200f4","resolution":{"observed_at":"2026-08-06T20:44:23.157367Z","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":"2026-07-06T15:33:34.832607Z","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":"2026-08-06T20:44:23.162343Z","title":"Ma, J.-H","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2507.02292","last_updated":"2025-07-25T18:39:08Z","snapshot_observed_at":"2026-08-08T00:49:34.815340Z","submitted_at":"2025-07-03T03:59:07Z","title":"Mixed-state phases from local reversibility","version":2},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-06T20:44:23.162343Z"},"links":{"cited_paper":"/paper/2305.16399","citing_paper":"/paper/2507.02292"},"observation_digest":"sha256:5ee9ec10f6a02c523111ef1ec5925196ea4b75e888bbd7d61a70c697759cce4a","observation_id":"d41704a0-cfef-4468-8a0e-93b42623147e","resolution":{"observed_at":"2026-08-06T20:44:23.162343Z","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":"2026-07-06T17:47:26.534826Z","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":"2026-08-06T20:44:23.167696Z","title":"Ma and A","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2507.02292","last_updated":"2025-07-25T18:39:08Z","snapshot_observed_at":"2026-08-08T00:49:34.815340Z","submitted_at":"2025-07-03T03:59:07Z","title":"Mixed-state phases from local reversibility","version":2},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-06T20:44:23.167696Z"},"links":{"cited_paper":"/paper/2403.13280","citing_paper":"/paper/2507.02292"},"observation_digest":"sha256:bb8b6613a2e6a5030a18b169b171251dab771841222b937a2f3472ea06c86ecd","observation_id":"6884052d-f164-4e48-83a8-e92870fa6103","resolution":{"observed_at":"2026-08-06T20:44:23.167696Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2309.11879","last_updated":"2024-04-10T05:46:09Z","snapshot_observed_at":"2026-07-06T16:21:41.556117Z","submitted_at":"2023-09-21T08:28:17Z","title":"Separability transitions in topological states induced by local decoherence","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2309.11879","snapshot_observed_at":"2026-08-06T20:44:23.173216Z","title":"Chen and T","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2507.02292","last_updated":"2025-07-25T18:39:08Z","snapshot_observed_at":"2026-08-08T00:49:34.815340Z","submitted_at":"2025-07-03T03:59:07Z","title":"Mixed-state phases from local reversibility","version":2},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-06T20:44:23.173216Z"},"links":{"cited_paper":"/paper/2309.11879","citing_paper":"/paper/2507.02292"},"observation_digest":"sha256:b287058b3c126ba9b32cf45c4655a47c2a651237442c60f0f7220d9314ccbfe2","observation_id":"e0f5f0ff-e225-4e19-9774-954bf16f4528","resolution":{"observed_at":"2026-08-06T20:44:23.173216Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2310.07286","last_updated":"2024-05-06T01:47:42Z","snapshot_observed_at":"2026-07-06T16:31:03.559653Z","submitted_at":"2023-10-11T08:18:51Z","title":"Symmetry-enforced many-body separability transitions","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2310.07286","snapshot_observed_at":"2026-08-06T20:44:23.177475Z","title":"Chen and T","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2507.02292","last_updated":"2025-07-25T18:39:08Z","snapshot_observed_at":"2026-08-08T00:49:34.815340Z","submitted_at":"2025-07-03T03:59:07Z","title":"Mixed-state phases from local reversibility","version":2},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-06T20:44:23.177475Z"},"links":{"cited_paper":"/paper/2310.07286","citing_paper":"/paper/2507.02292"},"observation_digest":"sha256:31c25759cff2f194a1ef85bb8cd9712e4417ac6290424bfaa38401c1d4b7a7d0","observation_id":"260e3742-a28d-4c41-bb8a-d1c16613f522","resolution":{"observed_at":"2026-08-06T20:44:23.177475Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2403.17069","last_updated":"2024-05-16T01:33:12Z","snapshot_observed_at":"2026-08-09T09:57:57.030883Z","submitted_at":"2024-03-25T18:04:29Z","title":"Tensor network formulation of symmetry protected topological phases in mixed states","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2403.17069","snapshot_observed_at":"2026-08-06T20:44:23.183325Z","title":null,"venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2507.02292","last_updated":"2025-07-25T18:39:08Z","snapshot_observed_at":"2026-08-08T00:49:34.815340Z","submitted_at":"2025-07-03T03:59:07Z","title":"Mixed-state phases from local reversibility","version":2},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-08-06T20:44:23.183325Z"},"links":{"cited_paper":"/paper/2403.17069","citing_paper":"/paper/2507.02292"},"observation_digest":"sha256:aa44fb32603ce12316fb6b7046a41c61625df5990b8790ad3bd56748e2af60c1","observation_id":"5e795b9d-d6a2-4898-8161-26407b410fcd","resolution":{"observed_at":"2026-08-06T20:44:23.183325Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2401.17357","last_updated":"2024-11-29T18:45:44Z","snapshot_observed_at":"2026-08-10T11:34:35.877711Z","submitted_at":"2024-01-30T19:00:02Z","title":"Mixed-state quantum anomaly and multipartite entanglement","version":4},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2401.17357","snapshot_observed_at":"2026-08-06T20:44:23.188019Z","title":null,"venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2507.02292","last_updated":"2025-07-25T18:39:08Z","snapshot_observed_at":"2026-08-08T00:49:34.815340Z","submitted_at":"2025-07-03T03:59:07Z","title":"Mixed-state phases from local reversibility","version":2},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-08-06T20:44:23.188019Z"},"links":{"cited_paper":"/paper/2401.17357","citing_paper":"/paper/2507.02292"},"observation_digest":"sha256:53b3c41e2e0705f3170ee978b98bfc4de857703fe421d94ba010a23580b2b5dd","observation_id":"319b2ff9-8389-4cfd-80c2-4d8e2b69edb7","resolution":{"observed_at":"2026-08-06T20:44:23.188019Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2503.12792","last_updated":"2025-03-17T04:01:17Z","snapshot_observed_at":"2026-08-07T16:59:07.539703Z","submitted_at":"2025-03-17T04:01:17Z","title":"Higher-form anomaly and long-range entanglement of mixed states","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2503.12792","snapshot_observed_at":"2026-08-06T20:44:23.192112Z","title":null,"venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2507.02292","last_updated":"2025-07-25T18:39:08Z","snapshot_observed_at":"2026-08-08T00:49:34.815340Z","submitted_at":"2025-07-03T03:59:07Z","title":"Mixed-state phases from local reversibility","version":2},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-08-06T20:44:23.192112Z"},"links":{"cited_paper":"/paper/2503.12792","citing_paper":"/paper/2507.02292"},"observation_digest":"sha256:06c470e4fea93a4ad005fbaa709b76fbccbab771830af0378681fd6d8f2a4352","observation_id":"876b0cdb-ecf6-4bb0-b170-cf5948e47da3","resolution":{"observed_at":"2026-08-06T20:44:23.192112Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2405.02390","last_updated":"2025-01-21T22:13:24Z","snapshot_observed_at":"2026-08-04T14:52:48.685234Z","submitted_at":"2024-05-03T18:00:00Z","title":"Towards a classification of mixed-state topological orders in two dimensions","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2405.02390","snapshot_observed_at":"2026-08-06T20:44:23.197460Z","title":"Ellison and M","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2507.02292","last_updated":"2025-07-25T18:39:08Z","snapshot_observed_at":"2026-08-08T00:49:34.815340Z","submitted_at":"2025-07-03T03:59:07Z","title":"Mixed-state phases from local reversibility","version":2},"reference_index":38,"source":"pdf_text","source_observed_at":"2026-08-06T20:44:23.197460Z"},"links":{"cited_paper":"/paper/2405.02390","citing_paper":"/paper/2507.02292"},"observation_digest":"sha256:67813ed8773204313505542e1681eb437e28c465d7ea9916b1a9446f9a83f36a","observation_id":"c91a1e2f-728b-48c3-9b16-84f6676cdc4b","resolution":{"observed_at":"2026-08-06T20:44:23.197460Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2307.13758","last_updated":"2025-01-22T06:34:41Z","snapshot_observed_at":"2026-07-06T15:58:27.523039Z","submitted_at":"2023-07-25T18:34:10Z","title":"Intrinsic Mixed-state Topological Order","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2307.13758","snapshot_observed_at":"2026-08-06T20:44:23.203118Z","title":null,"venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2507.02292","last_updated":"2025-07-25T18:39:08Z","snapshot_observed_at":"2026-08-08T00:49:34.815340Z","submitted_at":"2025-07-03T03:59:07Z","title":"Mixed-state phases from local reversibility","version":2},"reference_index":39,"source":"pdf_text","source_observed_at":"2026-08-06T20:44:23.203118Z"},"links":{"cited_paper":"/paper/2307.13758","citing_paper":"/paper/2507.02292"},"observation_digest":"sha256:abf3e059044ebf3a4f09b0c6fd59a73e04671e0c03551850f7564a7cf404e96b","observation_id":"045612a6-456e-496f-8d6d-dcc1e718a9f4","resolution":{"observed_at":"2026-08-06T20:44:23.203118Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2403.14533","last_updated":"2024-06-13T05:29:12Z","snapshot_observed_at":"2026-08-10T02:30:39.418047Z","submitted_at":"2024-03-21T16:34:37Z","title":"Anomaly in open quantum systems and its implications on mixed-state quantum phases","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2403.14533","snapshot_observed_at":"2026-08-06T20:44:23.207645Z","title":"Wang and L","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2507.02292","last_updated":"2025-07-25T18:39:08Z","snapshot_observed_at":"2026-08-08T00:49:34.815340Z","submitted_at":"2025-07-03T03:59:07Z","title":"Mixed-state phases from local reversibility","version":2},"reference_index":40,"source":"pdf_text","source_observed_at":"2026-08-06T20:44:23.207645Z"},"links":{"cited_paper":"/paper/2403.14533","citing_paper":"/paper/2507.02292"},"observation_digest":"sha256:3b81e435644588455570f5b77d001c466c6e6d32aa125ccd335366552da33e78","observation_id":"294c4e80-d6c5-4f20-ad9c-192ea7ea17ef","resolution":{"observed_at":"2026-08-06T20:44:23.207645Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2407.20500","last_updated":"2025-03-21T00:08:04Z","snapshot_observed_at":"2026-08-02T09:22:34.258688Z","submitted_at":"2024-07-30T02:26:45Z","title":"An analog of topological entanglement entropy for mixed states","version":2},"cited_work":{"arxiv_id":"2407.20500","doi":null,"metadata_source":"pith","pith_arxiv_id":"2407.20500","snapshot_observed_at":"2026-08-06T20:44:23.555215Z","title":"An analog of topological entanglement entropy for mixed states","venue":"quant-ph","work_id":"c5c4a9ee-77e9-465e-a615-4c4359aa9d94","year":2024},"citing_paper":{"arxiv_id":"2507.02292","last_updated":"2025-07-25T18:39:08Z","snapshot_observed_at":"2026-08-08T00:49:34.815340Z","submitted_at":"2025-07-03T03:59:07Z","title":"Mixed-state phases from local reversibility","version":2},"reference_index":41,"source":"pdf_text","source_observed_at":"2026-08-06T20:44:23.212608Z"},"links":{"cited_paper":"/paper/2407.20500","citing_paper":"/paper/2507.02292"},"observation_digest":"sha256:5328f62cad680a611ad0ce462b379c2563059254e3f799e004965e90c08432b1","observation_id":"d697106f-6ed0-4e39-9e6e-38d20c66c184","resolution":{"observed_at":"2026-08-06T20:44:23.561235Z","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":"2026-08-06T20:44:24.022451Z","title":"de Groot, A","venue":null,"work_id":"a8910253-2d25-417d-b442-015c7836cec5","year":2022},"citing_paper":{"arxiv_id":"2507.02292","last_updated":"2025-07-25T18:39:08Z","snapshot_observed_at":"2026-08-08T00:49:34.815340Z","submitted_at":"2025-07-03T03:59:07Z","title":"Mixed-state phases from local reversibility","version":2},"reference_index":42,"source":"pdf_text","source_observed_at":"2026-08-06T20:44:23.217268Z"},"links":{"citing_paper":"/paper/2507.02292"},"observation_digest":"sha256:bde2ef7502e3079c188c67122e456928ff981066ddb51c25c76d4ba967b32786","observation_id":"d8361c04-8b51-487b-b16c-e02f528f2c40","resolution":{"observed_at":"2026-08-06T20:44:24.025855Z","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":"2026-08-06T20:44:24.011595Z","title":null,"venue":null,"work_id":"65e105f8-f3ee-41a9-8e04-26ca5c50cfe6","year":2024},"citing_paper":{"arxiv_id":"2507.02292","last_updated":"2025-07-25T18:39:08Z","snapshot_observed_at":"2026-08-08T00:49:34.815340Z","submitted_at":"2025-07-03T03:59:07Z","title":"Mixed-state phases from local reversibility","version":2},"reference_index":43,"source":"pdf_text","source_observed_at":"2026-08-06T20:44:23.221506Z"},"links":{"citing_paper":"/paper/2507.02292"},"observation_digest":"sha256:a8c8ad4e827a8b97e29b6321a010042881968594dd37d8c6c62a143a07d25145","observation_id":"9aa1c7a2-792a-4aaf-8bc4-4c50c1836985","resolution":{"observed_at":"2026-08-06T20:44:24.015125Z","resolver_source":"raw_fallback","status":"unresolved"},"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":"2026-08-06T20:44:24.000278Z","title":"Rakovszky, S","venue":null,"work_id":"a0fc81c9-7632-4e22-80d4-150cb2a206a7","year":2024},"citing_paper":{"arxiv_id":"2507.02292","last_updated":"2025-07-25T18:39:08Z","snapshot_observed_at":"2026-08-08T00:49:34.815340Z","submitted_at":"2025-07-03T03:59:07Z","title":"Mixed-state phases from local reversibility","version":2},"reference_index":44,"source":"pdf_text","source_observed_at":"2026-08-06T20:44:23.226084Z"},"links":{"citing_paper":"/paper/2507.02292"},"observation_digest":"sha256:78938ecbc817de31cf3e64d4be05886870cfffe5923cf122521c193b2acdc453","observation_id":"a36733f7-e3cf-4614-9b71-80d8b4dcbd5b","resolution":{"observed_at":"2026-08-06T20:44:24.004350Z","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":"2026-08-06T20:44:23.231303Z","title":"Sang and T","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2507.02292","last_updated":"2025-07-25T18:39:08Z","snapshot_observed_at":"2026-08-08T00:49:34.815340Z","submitted_at":"2025-07-03T03:59:07Z","title":"Mixed-state phases from local reversibility","version":2},"reference_index":45,"source":"pdf_text","source_observed_at":"2026-08-06T20:44:23.231303Z"},"links":{"citing_paper":"/paper/2507.02292"},"observation_digest":"sha256:f2a515453fa751c633097899c2a18dc557ba9c7502ed0bc8272ca66ba4d292c7","observation_id":"63388687-5877-4898-a45d-37d189147e7d","resolution":{"observed_at":"2026-08-06T20:44:23.231303Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2503.02928","last_updated":"2026-07-14T18:29:52Z","snapshot_observed_at":"2026-08-07T17:29:34.444695Z","submitted_at":"2025-03-04T19:00:00Z","title":"Finite-temperature quantum topological order in three dimensions","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2503.02928","snapshot_observed_at":"2026-08-06T20:44:23.236414Z","title":null,"venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2507.02292","last_updated":"2025-07-25T18:39:08Z","snapshot_observed_at":"2026-08-08T00:49:34.815340Z","submitted_at":"2025-07-03T03:59:07Z","title":"Mixed-state phases from local reversibility","version":2},"reference_index":46,"source":"pdf_text","source_observed_at":"2026-08-06T20:44:23.236414Z"},"links":{"cited_paper":"/paper/2503.02928","citing_paper":"/paper/2507.02292"},"observation_digest":"sha256:535d66ab780fd6fe62206f7b17d6ddc0c843b5e6cabc9bee6386979aae61c9dc","observation_id":"f158fc07-53a7-4f96-9471-43fb509c7bb9","resolution":{"observed_at":"2026-08-06T20:44:23.236414Z","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":"2026-08-06T20:44:23.981025Z","title":"Bravyi, M","venue":null,"work_id":"14dc64ee-2e71-4f57-86c4-067007308651","year":2006},"citing_paper":{"arxiv_id":"2507.02292","last_updated":"2025-07-25T18:39:08Z","snapshot_observed_at":"2026-08-08T00:49:34.815340Z","submitted_at":"2025-07-03T03:59:07Z","title":"Mixed-state phases from local reversibility","version":2},"reference_index":47,"source":"pdf_text","source_observed_at":"2026-08-06T20:44:23.241608Z"},"links":{"citing_paper":"/paper/2507.02292"},"observation_digest":"sha256:20e8ecc71cfe37ef9cc933f007481e6268fa63564c4dfe5883d8631b951c06e4","observation_id":"2d91457c-8bb2-4ef9-b6a9-5b04718a96f2","resolution":{"observed_at":"2026-08-06T20:44:23.984763Z","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":"2026-08-06T20:44:23.246179Z","title":"Levin and X.-G","venue":null,"work_id":null,"year":2006},"citing_paper":{"arxiv_id":"2507.02292","last_updated":"2025-07-25T18:39:08Z","snapshot_observed_at":"2026-08-08T00:49:34.815340Z","submitted_at":"2025-07-03T03:59:07Z","title":"Mixed-state phases from local reversibility","version":2},"reference_index":48,"source":"pdf_text","source_observed_at":"2026-08-06T20:44:23.246179Z"},"links":{"citing_paper":"/paper/2507.02292"},"observation_digest":"sha256:8e64b629bdd4ae4a09636ab9305815b6f8ca84a4d0429545d38c838254b118dc","observation_id":"11afa796-e984-4289-a137-e039d3bf76cc","resolution":{"observed_at":"2026-08-06T20:44:23.246179Z","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":"2026-08-06T20:44:23.959643Z","title":"Castelnovo and C","venue":null,"work_id":"8930450c-5ab1-415b-a812-946fd2686e05","year":2007},"citing_paper":{"arxiv_id":"2507.02292","last_updated":"2025-07-25T18:39:08Z","snapshot_observed_at":"2026-08-08T00:49:34.815340Z","submitted_at":"2025-07-03T03:59:07Z","title":"Mixed-state phases from local reversibility","version":2},"reference_index":49,"source":"pdf_text","source_observed_at":"2026-08-06T20:44:23.250252Z"},"links":{"citing_paper":"/paper/2507.02292"},"observation_digest":"sha256:a911ba60d37c34d59836a292790c04e1997a6b8deedd7dc905396b3eb3565fcc","observation_id":"6453f019-90c2-4c06-b20b-df7e0d39782c","resolution":{"observed_at":"2026-08-06T20:44:23.963736Z","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":"2026-08-06T20:44:23.947132Z","title":"Zhang, Y","venue":null,"work_id":"c1bffdac-658a-453f-9d18-fc2fcd969fc4","year":2025},"citing_paper":{"arxiv_id":"2507.02292","last_updated":"2025-07-25T18:39:08Z","snapshot_observed_at":"2026-08-08T00:49:34.815340Z","submitted_at":"2025-07-03T03:59:07Z","title":"Mixed-state phases from local reversibility","version":2},"reference_index":50,"source":"pdf_text","source_observed_at":"2026-08-06T20:44:23.254829Z"},"links":{"citing_paper":"/paper/2507.02292"},"observation_digest":"sha256:65d2bddf8f6ae71dca968bea69f5ad29ca63a56cf51a54e8676b4bd897197fff","observation_id":"723003ec-5078-471e-abce-192bb1152716","resolution":{"observed_at":"2026-08-06T20:44:23.951350Z","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":"2026-08-06T20:44:23.258589Z","title":"Kitaev and J","venue":null,"work_id":null,"year":2006},"citing_paper":{"arxiv_id":"2507.02292","last_updated":"2025-07-25T18:39:08Z","snapshot_observed_at":"2026-08-08T00:49:34.815340Z","submitted_at":"2025-07-03T03:59:07Z","title":"Mixed-state phases from local reversibility","version":2},"reference_index":51,"source":"pdf_text","source_observed_at":"2026-08-06T20:44:23.258589Z"},"links":{"citing_paper":"/paper/2507.02292"},"observation_digest":"sha256:90561256c55105fc618d68bda84ce07300285e522c86bedf5592bb2b9db4a9db","observation_id":"83f25b7d-12ce-49db-857a-0878b14a6f19","resolution":{"observed_at":"2026-08-06T20:44:23.258589Z","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":"2026-08-06T20:44:23.927433Z","title":"Castelnovo and C","venue":null,"work_id":"d105d87d-1f93-4fd5-a213-88a5f71c6e86","year":2007},"citing_paper":{"arxiv_id":"2507.02292","last_updated":"2025-07-25T18:39:08Z","snapshot_observed_at":"2026-08-08T00:49:34.815340Z","submitted_at":"2025-07-03T03:59:07Z","title":"Mixed-state phases from local reversibility","version":2},"reference_index":52,"source":"pdf_text","source_observed_at":"2026-08-06T20:44:23.262314Z"},"links":{"citing_paper":"/paper/2507.02292"},"observation_digest":"sha256:7de5c9086e5ad48ae206931f02a8e67c3810c3220c97017b95a079bb6e156ba4","observation_id":"7b1611ee-bc84-411b-adb4-666ef7206ef0","resolution":{"observed_at":"2026-08-06T20:44:23.932033Z","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":"2026-08-06T20:44:23.915621Z","title":null,"venue":null,"work_id":"1d51b050-f07a-4fe6-a2da-831e1d5ad2ba","year":2020},"citing_paper":{"arxiv_id":"2507.02292","last_updated":"2025-07-25T18:39:08Z","snapshot_observed_at":"2026-08-08T00:49:34.815340Z","submitted_at":"2025-07-03T03:59:07Z","title":"Mixed-state phases from local reversibility","version":2},"reference_index":53,"source":"pdf_text","source_observed_at":"2026-08-06T20:44:23.266193Z"},"links":{"citing_paper":"/paper/2507.02292"},"observation_digest":"sha256:8cefeb240daf44e048dbdbe9c09b6a50941baa949f3c3905b2e50e11c0e84e54","observation_id":"5476f0ce-5424-4368-80ee-e61c570da7f6","resolution":{"observed_at":"2026-08-06T20:44:23.919645Z","resolver_source":"raw_fallback","status":"unresolved"},"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":"1206.0755","last_updated":"2012-06-04T20:16:35Z","snapshot_observed_at":"2026-07-06T02:49:19.018985Z","submitted_at":"2012-06-04T20:16:35Z","title":"Quantum Markov Networks and Commuting Hamiltonians","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1206.0755","snapshot_observed_at":"2026-08-06T20:44:23.270093Z","title":"Brown and D","venue":null,"work_id":null,"year":2012},"citing_paper":{"arxiv_id":"2507.02292","last_updated":"2025-07-25T18:39:08Z","snapshot_observed_at":"2026-08-08T00:49:34.815340Z","submitted_at":"2025-07-03T03:59:07Z","title":"Mixed-state phases from local reversibility","version":2},"reference_index":54,"source":"pdf_text","source_observed_at":"2026-08-06T20:44:23.270093Z"},"links":{"cited_paper":"/paper/1206.0755","citing_paper":"/paper/2507.02292"},"observation_digest":"sha256:fbfd784196462a0cef23a300349f129984fe8c40b10d701df506fdff38b634ba","observation_id":"7fe8c604-8a02-4eec-84ce-6a55fbaf48cf","resolution":{"observed_at":"2026-08-06T20:44:23.270093Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2405.03639","last_updated":"2024-11-18T02:28:47Z","snapshot_observed_at":"2026-08-08T10:11:26.129762Z","submitted_at":"2024-05-06T16:59:01Z","title":"Strong-to-Weak Spontaneous Symmetry Breaking in Mixed Quantum States","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2405.03639","snapshot_observed_at":"2026-08-06T20:44:23.274117Z","title":null,"venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2507.02292","last_updated":"2025-07-25T18:39:08Z","snapshot_observed_at":"2026-08-08T00:49:34.815340Z","submitted_at":"2025-07-03T03:59:07Z","title":"Mixed-state phases from local reversibility","version":2},"reference_index":55,"source":"pdf_text","source_observed_at":"2026-08-06T20:44:23.274117Z"},"links":{"cited_paper":"/paper/2405.03639","citing_paper":"/paper/2507.02292"},"observation_digest":"sha256:e6d693dea0fe80f8e87e00996dc22b5f8b7997d5a9d4b6b75997942255ba88ee","observation_id":"4201b21a-9794-4393-8a1c-7babb714325f","resolution":{"observed_at":"2026-08-06T20:44:23.274117Z","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":"2026-08-06T20:44:23.902385Z","title":null,"venue":null,"work_id":"ffef608f-5c33-4f0a-9c0d-568520ae6060","year":2024},"citing_paper":{"arxiv_id":"2507.02292","last_updated":"2025-07-25T18:39:08Z","snapshot_observed_at":"2026-08-08T00:49:34.815340Z","submitted_at":"2025-07-03T03:59:07Z","title":"Mixed-state phases from local reversibility","version":2},"reference_index":56,"source":"pdf_text","source_observed_at":"2026-08-06T20:44:23.279014Z"},"links":{"citing_paper":"/paper/2507.02292"},"observation_digest":"sha256:e3d4c4e92b97fbc7df7531074f68dad2c18917f1f9129719614dfcd0b02a2b29","observation_id":"95d26b5e-3ad8-460f-9935-1e1ccdb52fcd","resolution":{"observed_at":"2026-08-06T20:44:23.906960Z","resolver_source":"raw_fallback","status":"unresolved"},"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":"2026-08-06T20:44:23.284619Z","title":null,"venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2507.02292","last_updated":"2025-07-25T18:39:08Z","snapshot_observed_at":"2026-08-08T00:49:34.815340Z","submitted_at":"2025-07-03T03:59:07Z","title":"Mixed-state phases from local reversibility","version":2},"reference_index":57,"source":"pdf_text","source_observed_at":"2026-08-06T20:44:23.284619Z"},"links":{"citing_paper":"/paper/2507.02292"},"observation_digest":"sha256:90f3c4aa7f9c8264d6eddb32e6562c27c0aefd51422f0269420b431b03b294af","observation_id":"6ff32149-9480-44a6-9f99-46ddcad14986","resolution":{"observed_at":"2026-08-06T20:44:23.284619Z","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":"2026-08-06T20:44:23.288896Z","title":"Junge, R","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2507.02292","last_updated":"2025-07-25T18:39:08Z","snapshot_observed_at":"2026-08-08T00:49:34.815340Z","submitted_at":"2025-07-03T03:59:07Z","title":"Mixed-state phases from local reversibility","version":2},"reference_index":58,"source":"pdf_text","source_observed_at":"2026-08-06T20:44:23.288896Z"},"links":{"citing_paper":"/paper/2507.02292"},"observation_digest":"sha256:eb460148c1db91cf925bf244b366caad7712d19a481956b91b3a0b7382203988","observation_id":"30ef6be1-347a-42dd-9361-bde842aae349","resolution":{"observed_at":"2026-08-06T20:44:23.288896Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2402.09516","last_updated":"2024-02-14T19:00:03Z","snapshot_observed_at":"2026-08-09T13:08:37.355962Z","submitted_at":"2024-02-14T19:00:03Z","title":"Replica topological order in quantum mixed states and quantum error correction","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2402.09516","snapshot_observed_at":"2026-08-06T20:44:23.292821Z","title":"Li and R","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2507.02292","last_updated":"2025-07-25T18:39:08Z","snapshot_observed_at":"2026-08-08T00:49:34.815340Z","submitted_at":"2025-07-03T03:59:07Z","title":"Mixed-state phases from local reversibility","version":2},"reference_index":59,"source":"pdf_text","source_observed_at":"2026-08-06T20:44:23.292821Z"},"links":{"cited_paper":"/paper/2402.09516","citing_paper":"/paper/2507.02292"},"observation_digest":"sha256:44059ca20350c2535ef3285fae712fdc2af29bd9bb8aae9a35bead71d93b1dfe","observation_id":"2616a84a-1ca8-4a9c-b9a1-f635a2bf8b08","resolution":{"observed_at":"2026-08-06T20:44:23.292821Z","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":"2026-08-06T20:44:23.872901Z","title":null,"venue":null,"work_id":"1313a6d6-c1a1-476b-97eb-2473f52de6e0","year":2020},"citing_paper":{"arxiv_id":"2507.02292","last_updated":"2025-07-25T18:39:08Z","snapshot_observed_at":"2026-08-08T00:49:34.815340Z","submitted_at":"2025-07-03T03:59:07Z","title":"Mixed-state phases from local reversibility","version":2},"reference_index":60,"source":"pdf_text","source_observed_at":"2026-08-06T20:44:23.297950Z"},"links":{"citing_paper":"/paper/2507.02292"},"observation_digest":"sha256:3c9eda490ae620bcdbb8eb9a627637e3ce1064ec5b1b1fc7aac871e83a934230","observation_id":"aeba946c-cba4-43c1-b822-bbf6c08f5490","resolution":{"observed_at":"2026-08-06T20:44:23.877402Z","resolver_source":"raw_fallback","status":"unresolved"},"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":"2026-08-06T20:44:23.860516Z","title":null,"venue":null,"work_id":"bd7a83e3-200f-4209-acd3-4c7373e86297","year":2023},"citing_paper":{"arxiv_id":"2507.02292","last_updated":"2025-07-25T18:39:08Z","snapshot_observed_at":"2026-08-08T00:49:34.815340Z","submitted_at":"2025-07-03T03:59:07Z","title":"Mixed-state phases from local reversibility","version":2},"reference_index":61,"source":"pdf_text","source_observed_at":"2026-08-06T20:44:23.301829Z"},"links":{"citing_paper":"/paper/2507.02292"},"observation_digest":"sha256:85d48d249a61534e2cdb8c08cc680f2fff20431470c7ad1b9be5105f7bbcac6c","observation_id":"b46ca795-c076-4bfc-a30f-57f99ad38947","resolution":{"observed_at":"2026-08-06T20:44:23.864361Z","resolver_source":"raw_fallback","status":"unresolved"},"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":"2026-08-06T20:44:23.305743Z","title":null,"venue":null,"work_id":null,"year":2010},"citing_paper":{"arxiv_id":"2507.02292","last_updated":"2025-07-25T18:39:08Z","snapshot_observed_at":"2026-08-08T00:49:34.815340Z","submitted_at":"2025-07-03T03:59:07Z","title":"Mixed-state phases from local reversibility","version":2},"reference_index":62,"source":"pdf_text","source_observed_at":"2026-08-06T20:44:23.305743Z"},"links":{"citing_paper":"/paper/2507.02292"},"observation_digest":"sha256:c342de72bcd9690cbec1cc0417049f303a8caa77f37ec9a69247ea9397ae73d5","observation_id":"e28f019d-f758-42ae-bd97-2b4cedf317e6","resolution":{"observed_at":"2026-08-06T20:44:23.305743Z","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":"2026-08-06T20:44:23.839277Z","title":null,"venue":null,"work_id":"7b75ac7e-49ce-4343-b3d8-d282a9cb1d61","year":2025},"citing_paper":{"arxiv_id":"2507.02292","last_updated":"2025-07-25T18:39:08Z","snapshot_observed_at":"2026-08-08T00:49:34.815340Z","submitted_at":"2025-07-03T03:59:07Z","title":"Mixed-state phases from local reversibility","version":2},"reference_index":63,"source":"pdf_text","source_observed_at":"2026-08-06T20:44:23.309401Z"},"links":{"citing_paper":"/paper/2507.02292"},"observation_digest":"sha256:c089038e44f94ed6590733ad2ad4282e103b07c3d585d7004db5f0ed485f538a","observation_id":"62247036-934d-4a33-b572-d5dd838e254f","resolution":{"observed_at":"2026-08-06T20:44:23.843361Z","resolver_source":"raw_fallback","status":"unresolved"},"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":"2026-08-06T20:44:23.827209Z","title":"Levin, A physical proof of the topological entangle- ment entropy inequality (2024)","venue":null,"work_id":"fde734a2-188d-49ae-b941-22b4b54b50da","year":2024},"citing_paper":{"arxiv_id":"2507.02292","last_updated":"2025-07-25T18:39:08Z","snapshot_observed_at":"2026-08-08T00:49:34.815340Z","submitted_at":"2025-07-03T03:59:07Z","title":"Mixed-state phases from local reversibility","version":2},"reference_index":64,"source":"pdf_text","source_observed_at":"2026-08-06T20:44:23.313343Z"},"links":{"citing_paper":"/paper/2507.02292"},"observation_digest":"sha256:eec4b16ebd2619cdc03123ec77c9753f9b34b4584eb02184608e06387eba11cc","observation_id":"be6f76a7-0bcf-4b16-a76b-9383ca317b0c","resolution":{"observed_at":"2026-08-06T20:44:23.831612Z","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":"2026-08-06T20:44:23.815076Z","title":null,"venue":null,"work_id":"5b050cbe-9082-44d6-86ec-84aca2e7b9d3","year":2013},"citing_paper":{"arxiv_id":"2507.02292","last_updated":"2025-07-25T18:39:08Z","snapshot_observed_at":"2026-08-08T00:49:34.815340Z","submitted_at":"2025-07-03T03:59:07Z","title":"Mixed-state phases from local reversibility","version":2},"reference_index":65,"source":"pdf_text","source_observed_at":"2026-08-06T20:44:23.317213Z"},"links":{"citing_paper":"/paper/2507.02292"},"observation_digest":"sha256:834d64c65c07bc4cb59e84fefc6a530f92cd7aaa0126341745697e5791a20e96","observation_id":"5a4d8280-7eed-4ce9-8e56-a2e4501831cc","resolution":{"observed_at":"2026-08-06T20:44:23.818848Z","resolver_source":"raw_fallback","status":"unresolved"},"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":"2504.02208","last_updated":"2025-04-03T01:54:42Z","snapshot_observed_at":"2026-08-08T00:49:27.432824Z","submitted_at":"2025-04-03T01:54:42Z","title":"Quantum Gibbs states are locally Markovian","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2504.02208","snapshot_observed_at":"2026-08-06T20:44:23.320492Z","title":"Chen and C","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2507.02292","last_updated":"2025-07-25T18:39:08Z","snapshot_observed_at":"2026-08-08T00:49:34.815340Z","submitted_at":"2025-07-03T03:59:07Z","title":"Mixed-state phases from local reversibility","version":2},"reference_index":66,"source":"pdf_text","source_observed_at":"2026-08-06T20:44:23.320492Z"},"links":{"cited_paper":"/paper/2504.02208","citing_paper":"/paper/2507.02292"},"observation_digest":"sha256:6baa116bc5c1d43d758bc348515dc815f8cdb832c745a76ac26296f7ef9a93f9","observation_id":"5c8171f9-bb81-43ab-bb8d-a8af19332479","resolution":{"observed_at":"2026-08-06T20:44:23.320492Z","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":"2026-08-06T20:44:23.803138Z","title":"Kato and F","venue":null,"work_id":"73aa9eba-0b84-4f2e-a4b9-01f60f0f072d","year":2019},"citing_paper":{"arxiv_id":"2507.02292","last_updated":"2025-07-25T18:39:08Z","snapshot_observed_at":"2026-08-08T00:49:34.815340Z","submitted_at":"2025-07-03T03:59:07Z","title":"Mixed-state phases from local reversibility","version":2},"reference_index":67,"source":"pdf_text","source_observed_at":"2026-08-06T20:44:23.324933Z"},"links":{"citing_paper":"/paper/2507.02292"},"observation_digest":"sha256:fae8e71469207a520e66db0452a8cd973e46d87be8971920b27701e88a42961f","observation_id":"0ba1e873-2d8e-48dd-9b04-e966bdf38bcb","resolution":{"observed_at":"2026-08-06T20:44:23.807119Z","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":"2026-08-06T20:44:23.328867Z","title":null,"venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2507.02292","last_updated":"2025-07-25T18:39:08Z","snapshot_observed_at":"2026-08-08T00:49:34.815340Z","submitted_at":"2025-07-03T03:59:07Z","title":"Mixed-state phases from local reversibility","version":2},"reference_index":68,"source":"pdf_text","source_observed_at":"2026-08-06T20:44:23.328867Z"},"links":{"citing_paper":"/paper/2507.02292"},"observation_digest":"sha256:d749d0cac6ba392bd1265603e6c3f98772a4b8e438f775ae09c79693bf488043","observation_id":"3e11a349-078c-4056-b23a-f6fdc7071ae5","resolution":{"observed_at":"2026-08-06T20:44:23.328867Z","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":"2026-08-06T20:44:23.789865Z","title":"Placke, V","venue":null,"work_id":"f60b1d35-84e2-4b62-8ac7-b6dac213a449","year":2025},"citing_paper":{"arxiv_id":"2507.02292","last_updated":"2025-07-25T18:39:08Z","snapshot_observed_at":"2026-08-08T00:49:34.815340Z","submitted_at":"2025-07-03T03:59:07Z","title":"Mixed-state phases from local reversibility","version":2},"reference_index":69,"source":"pdf_text","source_observed_at":"2026-08-06T20:44:23.332947Z"},"links":{"citing_paper":"/paper/2507.02292"},"observation_digest":"sha256:98b867b8069da91cc13bd9937a40224922509149ed5dfec1d0e0b77de8d7db02","observation_id":"3128a38d-fa9a-4b0e-8ad1-e9b5d0d032ae","resolution":{"observed_at":"2026-08-06T20:44:23.794218Z","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":"2026-08-06T20:44:23.336959Z","title":"Dennis, A","venue":null,"work_id":null,"year":2002},"citing_paper":{"arxiv_id":"2507.02292","last_updated":"2025-07-25T18:39:08Z","snapshot_observed_at":"2026-08-08T00:49:34.815340Z","submitted_at":"2025-07-03T03:59:07Z","title":"Mixed-state phases from local reversibility","version":2},"reference_index":70,"source":"pdf_text","source_observed_at":"2026-08-06T20:44:23.336959Z"},"links":{"citing_paper":"/paper/2507.02292"},"observation_digest":"sha256:7feec9a7d0dfbee3125fc688582d4ab9bd3bc1da3a54d50810aae3803a7976cc","observation_id":"6b836f0d-3ec8-46dc-9aef-254080eac457","resolution":{"observed_at":"2026-08-06T20:44:23.336959Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2301.05687","last_updated":"2026-05-01T07:16:30Z","snapshot_observed_at":"2026-08-02T09:51:07.182041Z","submitted_at":"2023-01-13T18:15:04Z","title":"Mixed-state topological order and the errorfield double formulation of decoherence-induced transitions","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2301.05687","snapshot_observed_at":"2026-08-06T20:44:23.341206Z","title":null,"venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2507.02292","last_updated":"2025-07-25T18:39:08Z","snapshot_observed_at":"2026-08-08T00:49:34.815340Z","submitted_at":"2025-07-03T03:59:07Z","title":"Mixed-state phases from local reversibility","version":2},"reference_index":71,"source":"pdf_text","source_observed_at":"2026-08-06T20:44:23.341206Z"},"links":{"cited_paper":"/paper/2301.05687","citing_paper":"/paper/2507.02292"},"observation_digest":"sha256:e40c3d6a01383609798bb2f1ee7fc33c898d4fd54cece625305eb8219cc301c2","observation_id":"e6c40b4c-e4a6-4e77-94b8-02904e3402b7","resolution":{"observed_at":"2026-08-06T20:44:23.341206Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2507.02292","last_updated":"2025-07-25T18:39:08Z","latest_version":2,"primary_category":"quant-ph","snapshot_observed_at":"2026-08-08T00:49:34.815340Z","submitted_at":"2025-07-03T03:59:07Z","title":"Mixed-state phases from local reversibility"},"reference_resolution":{"displayed":71,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":1,"unresolved":49,"verified_exact":1,"verified_fuzzy":20},"total_outbound_references":71},"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 71 of 71 outbound references and 17 inbound Pith citation observations for arXiv:2507.02292."}