{"as_of":"2026-08-10T04:54:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:4dddc4cd9e76b0403b25f917850e14435e51a036fd274c2015a4cc1bd59600aa","coverage":[{"denominator":66,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":66,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-04T11:01:10.435807Z","state":"measured"},{"denominator":66,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":66,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-09T06:31:02.800959+00:00","state":"measured"},{"denominator":0,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":0,"source":"paper_references, paper_reference_links","source_observed_at":null,"state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"cited_works","source_observed_at":null,"state":"measured"}],"external_citation_measurements":[],"inbound":[],"links":{"evidence":"/evidence","html":"/paper/2510.07396/citation-record","integrity":"/paper/2510.07396/integrity","json":"/paper/2510.07396/citation-record.json","paper":"/paper/2510.07396"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T11:01:05.664097Z","title":"Shor, Fault-tolerant quantum computation, inPro- ceedings of 37th Conference on Foundations of Computer Science(1996) pp","venue":null,"work_id":null,"year":1996},"citing_paper":{"arxiv_id":"2510.07396","last_updated":"2026-05-28T21:14:00Z","snapshot_observed_at":"2026-08-08T11:49:39.116792Z","submitted_at":"2025-10-08T18:00:13Z","title":"Spectral properties and coding transitions of Haar-random quantum codes","version":3},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-04T11:01:05.664097Z"},"links":{"citing_paper":"/paper/2510.07396"},"observation_digest":"sha256:a4add50787eddc0ac21d8c1e88c2cf1829390cbcfb0d7c9791f0b1b648a0df4b","observation_id":"04d15ecb-cca5-4a3a-9509-5d1d6a3c97dd","resolution":{"observed_at":"2026-08-04T11:01:05.664097Z","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":"2026-08-04T11:01:05.716604Z","title":"Aharonov and M","venue":null,"work_id":null,"year":1997},"citing_paper":{"arxiv_id":"2510.07396","last_updated":"2026-05-28T21:14:00Z","snapshot_observed_at":"2026-08-08T11:49:39.116792Z","submitted_at":"2025-10-08T18:00:13Z","title":"Spectral properties and coding transitions of Haar-random quantum codes","version":3},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-04T11:01:05.716604Z"},"links":{"citing_paper":"/paper/2510.07396"},"observation_digest":"sha256:6a87250202440b31c10d828b236e42e21482e83b831babecfe84a3d357e94741","observation_id":"53a5d9bb-eb9a-4dac-a955-b00e1bc5a281","resolution":{"observed_at":"2026-08-04T11:01:05.716604Z","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":"2026-08-04T11:01:05.780732Z","title":null,"venue":null,"work_id":null,"year":1997},"citing_paper":{"arxiv_id":"2510.07396","last_updated":"2026-05-28T21:14:00Z","snapshot_observed_at":"2026-08-08T11:49:39.116792Z","submitted_at":"2025-10-08T18:00:13Z","title":"Spectral properties and coding transitions of Haar-random quantum codes","version":3},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-04T11:01:05.780732Z"},"links":{"citing_paper":"/paper/2510.07396"},"observation_digest":"sha256:19d1356e2f0d57c3d2143770988810ce9b05472e8fcdc4b03f5b27a80507d8e1","observation_id":"b06862a9-ae55-4c6e-9e9c-baf6fcda310d","resolution":{"observed_at":"2026-08-04T11:01:05.780732Z","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":"2026-08-04T11:01:05.833031Z","title":"Knill, R","venue":null,"work_id":null,"year":1998},"citing_paper":{"arxiv_id":"2510.07396","last_updated":"2026-05-28T21:14:00Z","snapshot_observed_at":"2026-08-08T11:49:39.116792Z","submitted_at":"2025-10-08T18:00:13Z","title":"Spectral properties and coding transitions of Haar-random quantum codes","version":3},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-04T11:01:05.833031Z"},"links":{"citing_paper":"/paper/2510.07396"},"observation_digest":"sha256:4b83c146caf7c71b5e069237313cb6c1a1ba929c5361d1bcdbb537cdf5c4b805","observation_id":"0f083d72-3e0f-449c-bd66-24cc7d5c4e9d","resolution":{"observed_at":"2026-08-04T11:01:05.833031Z","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":"2026-08-04T11:01:05.920829Z","title":"Aharonov and M","venue":null,"work_id":null,"year":2008},"citing_paper":{"arxiv_id":"2510.07396","last_updated":"2026-05-28T21:14:00Z","snapshot_observed_at":"2026-08-08T11:49:39.116792Z","submitted_at":"2025-10-08T18:00:13Z","title":"Spectral properties and coding transitions of Haar-random quantum codes","version":3},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-04T11:01:05.920829Z"},"links":{"citing_paper":"/paper/2510.07396"},"observation_digest":"sha256:77316729701c1293471397c63370df74e3e28e9ad80f5f76050ae63e7b64c505","observation_id":"65dd5397-e76e-445b-8482-0b7dfacb4cd8","resolution":{"observed_at":"2026-08-04T11:01:05.920829Z","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":"2026-08-04T11:01:06.012160Z","title":null,"venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2510.07396","last_updated":"2026-05-28T21:14:00Z","snapshot_observed_at":"2026-08-08T11:49:39.116792Z","submitted_at":"2025-10-08T18:00:13Z","title":"Spectral properties and coding transitions of Haar-random quantum codes","version":3},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-04T11:01:06.012160Z"},"links":{"citing_paper":"/paper/2510.07396"},"observation_digest":"sha256:4191f04ab9a0de60076167dae1042a9bfb8257de93cc24e6954481682e863f94","observation_id":"636b445d-a30e-486f-a63e-b8ea61ff3fb5","resolution":{"observed_at":"2026-08-04T11:01:06.012160Z","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":"2026-08-04T11:01:06.082048Z","title":"Rakovszky, S","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2510.07396","last_updated":"2026-05-28T21:14:00Z","snapshot_observed_at":"2026-08-08T11:49:39.116792Z","submitted_at":"2025-10-08T18:00:13Z","title":"Spectral properties and coding transitions of Haar-random quantum codes","version":3},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-04T11:01:06.082048Z"},"links":{"citing_paper":"/paper/2510.07396"},"observation_digest":"sha256:f68f92d7951a469f2ef8ae37e7e54383f29340dd32c3cacac8a5e63ff22c888d","observation_id":"966ad4c0-e2f4-488c-9889-127e29b80855","resolution":{"observed_at":"2026-08-04T11:01:06.082048Z","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":"2026-08-04T11:01:06.172652Z","title":"Ma, J.-H","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2510.07396","last_updated":"2026-05-28T21:14:00Z","snapshot_observed_at":"2026-08-08T11:49:39.116792Z","submitted_at":"2025-10-08T18:00:13Z","title":"Spectral properties and coding transitions of Haar-random quantum codes","version":3},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-04T11:01:06.172652Z"},"links":{"citing_paper":"/paper/2510.07396"},"observation_digest":"sha256:6a2c1e2729ea98ff113a65dfb4fa7b0cedff0fffdd3c2cee4d8493509f6dbeec","observation_id":"e29ae633-fc43-46db-b996-8267ea7495d3","resolution":{"observed_at":"2026-08-04T11:01:06.172652Z","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":"2026-08-04T11:01:06.245591Z","title":null,"venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2510.07396","last_updated":"2026-05-28T21:14:00Z","snapshot_observed_at":"2026-08-08T11:49:39.116792Z","submitted_at":"2025-10-08T18:00:13Z","title":"Spectral properties and coding transitions of Haar-random quantum codes","version":3},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-04T11:01:06.245591Z"},"links":{"citing_paper":"/paper/2510.07396"},"observation_digest":"sha256:00492c78c72739ea3707ff67a55d724543be658ff39df040d363c41f518be5c4","observation_id":"dec8106c-bc51-4461-b074-5107d2e11a06","resolution":{"observed_at":"2026-08-04T11:01:06.245591Z","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":"2026-08-04T11:01:06.330111Z","title":"Niwa and J","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2510.07396","last_updated":"2026-05-28T21:14:00Z","snapshot_observed_at":"2026-08-08T11:49:39.116792Z","submitted_at":"2025-10-08T18:00:13Z","title":"Spectral properties and coding transitions of Haar-random quantum codes","version":3},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-04T11:01:06.330111Z"},"links":{"citing_paper":"/paper/2510.07396"},"observation_digest":"sha256:5b45b851c2b4e968882b781462ec4a2abb21a8e93d62a73923e71f29ec850e1b","observation_id":"dd364863-11c1-4487-81b0-8c2309fee283","resolution":{"observed_at":"2026-08-04T11:01:06.330111Z","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":"2026-08-04T11:01:06.402297Z","title":null,"venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2510.07396","last_updated":"2026-05-28T21:14:00Z","snapshot_observed_at":"2026-08-08T11:49:39.116792Z","submitted_at":"2025-10-08T18:00:13Z","title":"Spectral properties and coding transitions of Haar-random quantum codes","version":3},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-04T11:01:06.402297Z"},"links":{"citing_paper":"/paper/2510.07396"},"observation_digest":"sha256:4432f1d93e92b3d5414d4741e1887b34c9da600d51cb069fb1ae86352208783b","observation_id":"224ee2c9-ca27-4f7b-a95a-007e1f7d447c","resolution":{"observed_at":"2026-08-04T11:01:06.402297Z","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":"2026-08-04T11:01:06.494742Z","title":null,"venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2510.07396","last_updated":"2026-05-28T21:14:00Z","snapshot_observed_at":"2026-08-08T11:49:39.116792Z","submitted_at":"2025-10-08T18:00:13Z","title":"Spectral properties and coding transitions of Haar-random quantum codes","version":3},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-04T11:01:06.494742Z"},"links":{"cited_paper":"/paper/2301.05687","citing_paper":"/paper/2510.07396"},"observation_digest":"sha256:7f02f3919d7dc687038fb16278f97002a872334af44ba3dd83443633edbf8955","observation_id":"d038d694-7c23-4f7b-a6dd-f12d8434453c","resolution":{"observed_at":"2026-08-04T11:01:06.494742Z","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":"2026-08-04T11:01:06.565761Z","title":null,"venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2510.07396","last_updated":"2026-05-28T21:14:00Z","snapshot_observed_at":"2026-08-08T11:49:39.116792Z","submitted_at":"2025-10-08T18:00:13Z","title":"Spectral properties and coding transitions of Haar-random quantum codes","version":3},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-04T11:01:06.565761Z"},"links":{"citing_paper":"/paper/2510.07396"},"observation_digest":"sha256:f54a3ac3501cb89447759d14ee2dee5ad8f6f78d7c7c61bba2d3464301d61e68","observation_id":"226ec5da-1c78-4d61-b347-1d2faf38a70f","resolution":{"observed_at":"2026-08-04T11:01:06.565761Z","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":"2026-08-04T11:01:06.644845Z","title":"Chen and T","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2510.07396","last_updated":"2026-05-28T21:14:00Z","snapshot_observed_at":"2026-08-08T11:49:39.116792Z","submitted_at":"2025-10-08T18:00:13Z","title":"Spectral properties and coding transitions of Haar-random quantum codes","version":3},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-04T11:01:06.644845Z"},"links":{"citing_paper":"/paper/2510.07396"},"observation_digest":"sha256:f51575c87b35514dccddb63a24a62e6cbbc6c7c997c5856002797c0dd4bdbc9b","observation_id":"7592381a-de20-49b8-b54b-82748daa11b9","resolution":{"observed_at":"2026-08-04T11:01:06.644845Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2403.03955","last_updated":"2024-03-06T18:59:00Z","snapshot_observed_at":"2026-08-07T21:23:42.220466Z","submitted_at":"2024-03-06T18:59:00Z","title":"Understanding Stabilizer Codes Under Local Decoherence Through a General Statistical Mechanics Mapping","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2403.03955","snapshot_observed_at":"2026-08-04T11:01:06.722874Z","title":"Lyons, Understanding stabilizer codes under local de- coherence through a general statistical mechanics map- ping (2024), arXiv:2403.03955 [quant-ph]","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2510.07396","last_updated":"2026-05-28T21:14:00Z","snapshot_observed_at":"2026-08-08T11:49:39.116792Z","submitted_at":"2025-10-08T18:00:13Z","title":"Spectral properties and coding transitions of Haar-random quantum codes","version":3},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-04T11:01:06.722874Z"},"links":{"cited_paper":"/paper/2403.03955","citing_paper":"/paper/2510.07396"},"observation_digest":"sha256:570041f3a81ed7249b7c69c41f8faa456073c49771cd929a9927d70e5c4b22b2","observation_id":"cb207874-6746-49f7-9a0a-64d2d681640c","resolution":{"observed_at":"2026-08-04T11:01:06.722874Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2407.07882","last_updated":"2024-07-10T17:48:54Z","snapshot_observed_at":"2026-08-06T08:50:35.102664Z","submitted_at":"2024-07-10T17:48:54Z","title":"Information dynamics in decohered quantum memory with repeated syndrome measurements: a dual approach","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2407.07882","snapshot_observed_at":"2026-08-04T11:01:06.789766Z","title":"Hauser, Y","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2510.07396","last_updated":"2026-05-28T21:14:00Z","snapshot_observed_at":"2026-08-08T11:49:39.116792Z","submitted_at":"2025-10-08T18:00:13Z","title":"Spectral properties and coding transitions of Haar-random quantum codes","version":3},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-04T11:01:06.789766Z"},"links":{"cited_paper":"/paper/2407.07882","citing_paper":"/paper/2510.07396"},"observation_digest":"sha256:5e01e30bef3c307f6d8f003f57f89deca9f6a053cc4988d7acdeb026ef2c8d07","observation_id":"2ffeb61c-5765-4a9e-bbeb-7cebe5325ae0","resolution":{"observed_at":"2026-08-04T11:01:06.789766Z","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":"2026-08-04T11:01:06.858470Z","title":"Kitaev, Fault-tolerant quantum computation by anyons, Annals of Physics303, 2–30 (2003)","venue":null,"work_id":null,"year":2003},"citing_paper":{"arxiv_id":"2510.07396","last_updated":"2026-05-28T21:14:00Z","snapshot_observed_at":"2026-08-08T11:49:39.116792Z","submitted_at":"2025-10-08T18:00:13Z","title":"Spectral properties and coding transitions of Haar-random quantum codes","version":3},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-04T11:01:06.858470Z"},"links":{"citing_paper":"/paper/2510.07396"},"observation_digest":"sha256:6a219c7575b67c0f8f3be8d86a2b2420266e323ba0bffb7e80567f128b4f8acf","observation_id":"c768ac1f-3759-41a0-b289-021f76267f37","resolution":{"observed_at":"2026-08-04T11:01:06.858470Z","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":"2026-08-04T11:01:06.927206Z","title":"Dennis, A","venue":null,"work_id":null,"year":2002},"citing_paper":{"arxiv_id":"2510.07396","last_updated":"2026-05-28T21:14:00Z","snapshot_observed_at":"2026-08-08T11:49:39.116792Z","submitted_at":"2025-10-08T18:00:13Z","title":"Spectral properties and coding transitions of Haar-random quantum codes","version":3},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-04T11:01:06.927206Z"},"links":{"citing_paper":"/paper/2510.07396"},"observation_digest":"sha256:eec55b6cf063973f6a45bcf3e5203cbe258a80a35277ede30a120700e7d9ae01","observation_id":"ede12e26-d0e8-4f93-a324-f2e4f5372148","resolution":{"observed_at":"2026-08-04T11:01:06.927206Z","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":"2026-08-04T11:01:06.989793Z","title":"Bombin, R","venue":null,"work_id":null,"year":2012},"citing_paper":{"arxiv_id":"2510.07396","last_updated":"2026-05-28T21:14:00Z","snapshot_observed_at":"2026-08-08T11:49:39.116792Z","submitted_at":"2025-10-08T18:00:13Z","title":"Spectral properties and coding transitions of Haar-random quantum codes","version":3},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-04T11:01:06.989793Z"},"links":{"citing_paper":"/paper/2510.07396"},"observation_digest":"sha256:eb73368bc55be38435f9dc5999a2775f479acec8aff43e2f3a3b7f2c9f4d12db","observation_id":"d8f5b9d4-24f4-43be-b18e-36f260203e8b","resolution":{"observed_at":"2026-08-04T11:01:06.989793Z","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":"2026-08-04T11:01:07.076571Z","title":"Chen and T","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2510.07396","last_updated":"2026-05-28T21:14:00Z","snapshot_observed_at":"2026-08-08T11:49:39.116792Z","submitted_at":"2025-10-08T18:00:13Z","title":"Spectral properties and coding transitions of Haar-random quantum codes","version":3},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-04T11:01:07.076571Z"},"links":{"citing_paper":"/paper/2510.07396"},"observation_digest":"sha256:8f2b83670da88c669dfed17e80a8b2c46b27362784efd37c4092da26ec397ac7","observation_id":"a52a4090-c9bc-4653-9318-bf55e59ecc49","resolution":{"observed_at":"2026-08-04T11:01:07.076571Z","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":"2026-08-04T11:01:07.168052Z","title":"Sang and T","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2510.07396","last_updated":"2026-05-28T21:14:00Z","snapshot_observed_at":"2026-08-08T11:49:39.116792Z","submitted_at":"2025-10-08T18:00:13Z","title":"Spectral properties and coding transitions of Haar-random quantum codes","version":3},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-04T11:01:07.168052Z"},"links":{"citing_paper":"/paper/2510.07396"},"observation_digest":"sha256:fa18befeb8189823e35212d32698d7177a3f296cdeaa1daf3e91ac3cb267f519","observation_id":"a868c5b4-2cb4-438d-9fd9-b9eb16db0d75","resolution":{"observed_at":"2026-08-04T11:01:07.168052Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2412.00193","last_updated":"2025-06-05T14:50:47Z","snapshot_observed_at":"2026-08-06T04:42:32.447758Z","submitted_at":"2024-11-29T19:00:03Z","title":"Spacetime Markov length: a diagnostic for fault tolerance via mixed-state phases","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2412.00193","snapshot_observed_at":"2026-08-04T11:01:07.247808Z","title":"Negari, T","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2510.07396","last_updated":"2026-05-28T21:14:00Z","snapshot_observed_at":"2026-08-08T11:49:39.116792Z","submitted_at":"2025-10-08T18:00:13Z","title":"Spectral properties and coding transitions of Haar-random quantum codes","version":3},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-04T11:01:07.247808Z"},"links":{"cited_paper":"/paper/2412.00193","citing_paper":"/paper/2510.07396"},"observation_digest":"sha256:ae71a1410220bd810ffd2828dc5256f302c63d19780e98016590f6998be4e089","observation_id":"922dfe13-11df-4643-aa24-fe040e1c6dd9","resolution":{"observed_at":"2026-08-04T11:01:07.247808Z","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":"2026-08-04T11:01:07.305845Z","title":null,"venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2510.07396","last_updated":"2026-05-28T21:14:00Z","snapshot_observed_at":"2026-08-08T11:49:39.116792Z","submitted_at":"2025-10-08T18:00:13Z","title":"Spectral properties and coding transitions of Haar-random quantum codes","version":3},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-04T11:01:07.305845Z"},"links":{"citing_paper":"/paper/2510.07396"},"observation_digest":"sha256:edc2fb82a21cce20babde6d25f6ebfbbc2104651ccb2696efb2e35ea0fc21358","observation_id":"fb71540a-2f52-42a2-9446-2e305021ea3b","resolution":{"observed_at":"2026-08-04T11:01:07.305845Z","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":"2026-08-04T11:01:07.384497Z","title":null,"venue":null,"work_id":null,"year":1996},"citing_paper":{"arxiv_id":"2510.07396","last_updated":"2026-05-28T21:14:00Z","snapshot_observed_at":"2026-08-08T11:49:39.116792Z","submitted_at":"2025-10-08T18:00:13Z","title":"Spectral properties and coding transitions of Haar-random quantum codes","version":3},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-04T11:01:07.384497Z"},"links":{"citing_paper":"/paper/2510.07396"},"observation_digest":"sha256:cd84c4a24b58dd743893c72bb0bb3a1a230c63e12ee358dbed8779d3b16ee193","observation_id":"0d8dbcc2-1bcf-4065-9692-b905ede96d0e","resolution":{"observed_at":"2026-08-04T11:01:07.384497Z","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":"2026-08-04T11:01:07.472706Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2510.07396","last_updated":"2026-05-28T21:14:00Z","snapshot_observed_at":"2026-08-08T11:49:39.116792Z","submitted_at":"2025-10-08T18:00:13Z","title":"Spectral properties and coding transitions of Haar-random quantum codes","version":3},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-04T11:01:07.472706Z"},"links":{"citing_paper":"/paper/2510.07396"},"observation_digest":"sha256:0bb9aed4908d5ea113911bd1c3a5cf008e1e0656fe164a4613b6b6e722d53001","observation_id":"4c20fb90-b04a-4004-9b79-e0cd873141cb","resolution":{"observed_at":"2026-08-04T11:01:07.472706Z","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":"2026-08-04T11:01:07.534874Z","title":null,"venue":null,"work_id":null,"year":1997},"citing_paper":{"arxiv_id":"2510.07396","last_updated":"2026-05-28T21:14:00Z","snapshot_observed_at":"2026-08-08T11:49:39.116792Z","submitted_at":"2025-10-08T18:00:13Z","title":"Spectral properties and coding transitions of Haar-random quantum codes","version":3},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-04T11:01:07.534874Z"},"links":{"citing_paper":"/paper/2510.07396"},"observation_digest":"sha256:d04d8b6a515feeed2a7c43afe2e28af2856f1ba27379790cfe942b5d7bcdc881","observation_id":"1f4d8d46-ceb7-40d0-b50e-6e8e7402c251","resolution":{"observed_at":"2026-08-04T11:01:07.534874Z","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":"2026-08-04T11:01:07.606687Z","title":"Shor and R","venue":null,"work_id":null,"year":1997},"citing_paper":{"arxiv_id":"2510.07396","last_updated":"2026-05-28T21:14:00Z","snapshot_observed_at":"2026-08-08T11:49:39.116792Z","submitted_at":"2025-10-08T18:00:13Z","title":"Spectral properties and coding transitions of Haar-random quantum codes","version":3},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-04T11:01:07.606687Z"},"links":{"citing_paper":"/paper/2510.07396"},"observation_digest":"sha256:8769a5dbd16f1e9d199bd68f794a5dad51a08048333ac5939af9edf4fc453906","observation_id":"bf64f5c6-4871-42f3-be3e-4592a7387aa2","resolution":{"observed_at":"2026-08-04T11:01:07.606687Z","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":"2026-08-04T11:01:07.727180Z","title":"Rains, Quantum weight enumerators, IEEE Transac- tions on Information Theory44, 1388 (1998)","venue":null,"work_id":null,"year":1998},"citing_paper":{"arxiv_id":"2510.07396","last_updated":"2026-05-28T21:14:00Z","snapshot_observed_at":"2026-08-08T11:49:39.116792Z","submitted_at":"2025-10-08T18:00:13Z","title":"Spectral properties and coding transitions of Haar-random quantum codes","version":3},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-04T11:01:07.727180Z"},"links":{"citing_paper":"/paper/2510.07396"},"observation_digest":"sha256:cb3bdf9bdd238498fd5b7a5151101a3f9ec9557f036e1a79d1e29be433075843","observation_id":"4221c4d9-be0e-4959-88cf-fa2246d72053","resolution":{"observed_at":"2026-08-04T11:01:07.727180Z","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":"2026-08-04T11:01:07.840580Z","title":null,"venue":null,"work_id":null,"year":1999},"citing_paper":{"arxiv_id":"2510.07396","last_updated":"2026-05-28T21:14:00Z","snapshot_observed_at":"2026-08-08T11:49:39.116792Z","submitted_at":"2025-10-08T18:00:13Z","title":"Spectral properties and coding transitions of Haar-random quantum codes","version":3},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-04T11:01:07.840580Z"},"links":{"citing_paper":"/paper/2510.07396"},"observation_digest":"sha256:ee8d184f9cc241eefa278e41bb734a53d87e9e1d79609b3177fbc01c37bf33cf","observation_id":"17ff8add-4aa2-4fc3-9898-32309047e418","resolution":{"observed_at":"2026-08-04T11:01:07.840580Z","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":"2026-08-04T11:01:07.892748Z","title":"Cao and B","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2510.07396","last_updated":"2026-05-28T21:14:00Z","snapshot_observed_at":"2026-08-08T11:49:39.116792Z","submitted_at":"2025-10-08T18:00:13Z","title":"Spectral properties and coding transitions of Haar-random quantum codes","version":3},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-04T11:01:07.892748Z"},"links":{"citing_paper":"/paper/2510.07396"},"observation_digest":"sha256:d38c3a1e647e7c95dd807335dcb5042c12ad822a0c8995a522b0ad40de4e6b96","observation_id":"b80c23b7-ce44-4549-9b04-6820ba0ff355","resolution":{"observed_at":"2026-08-04T11:01:07.892748Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2308.05152","last_updated":"2024-03-02T04:29:13Z","snapshot_observed_at":"2026-08-02T02:54:51.296388Z","submitted_at":"2023-08-09T18:00:02Z","title":"Quantum Lego Expansion Pack: Enumerators from Tensor Networks","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2308.05152","snapshot_observed_at":"2026-08-04T11:01:07.948968Z","title":null,"venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2510.07396","last_updated":"2026-05-28T21:14:00Z","snapshot_observed_at":"2026-08-08T11:49:39.116792Z","submitted_at":"2025-10-08T18:00:13Z","title":"Spectral properties and coding transitions of Haar-random quantum codes","version":3},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-04T11:01:07.948968Z"},"links":{"cited_paper":"/paper/2308.05152","citing_paper":"/paper/2510.07396"},"observation_digest":"sha256:9cbdbd2bd17c95c05b65faa11262d6d89cbddd03ae02d46c4d18b0d752ab6f6b","observation_id":"40abb42b-6741-4137-b9b0-197ea5d3318b","resolution":{"observed_at":"2026-08-04T11:01:07.948968Z","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":"2026-08-04T11:01:08.029578Z","title":"MacWilliams and N","venue":null,"work_id":null,"year":1978},"citing_paper":{"arxiv_id":"2510.07396","last_updated":"2026-05-28T21:14:00Z","snapshot_observed_at":"2026-08-08T11:49:39.116792Z","submitted_at":"2025-10-08T18:00:13Z","title":"Spectral properties and coding transitions of Haar-random quantum codes","version":3},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-04T11:01:08.029578Z"},"links":{"citing_paper":"/paper/2510.07396"},"observation_digest":"sha256:ade0abc6a7e241078cebc52b323bfdecb97c0c24d43255920bd8565e7dc3d56a","observation_id":"f65a4a26-c179-4d4a-a6f2-d26a153a7d78","resolution":{"observed_at":"2026-08-04T11:01:08.029578Z","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":"2026-08-04T11:01:08.082974Z","title":"However, in practice, all such quanti- ties are self-averaging in the thermodynamic limit","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2510.07396","last_updated":"2026-05-28T21:14:00Z","snapshot_observed_at":"2026-08-08T11:49:39.116792Z","submitted_at":"2025-10-08T18:00:13Z","title":"Spectral properties and coding transitions of Haar-random quantum codes","version":3},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-04T11:01:08.082974Z"},"links":{"citing_paper":"/paper/2510.07396"},"observation_digest":"sha256:26ae145d53a171ea17c54502aada4d2ca8857bee8b99dcf4b4dabeeb67d8df08","observation_id":"7b93b7a7-b787-4d88-b91d-186a1349b04a","resolution":{"observed_at":"2026-08-04T11:01:08.082974Z","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":"2026-08-04T11:01:08.139959Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2510.07396","last_updated":"2026-05-28T21:14:00Z","snapshot_observed_at":"2026-08-08T11:49:39.116792Z","submitted_at":"2025-10-08T18:00:13Z","title":"Spectral properties and coding transitions of Haar-random quantum codes","version":3},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-04T11:01:08.139959Z"},"links":{"citing_paper":"/paper/2510.07396"},"observation_digest":"sha256:2fd915f4f89368aa3478cf590156d55b895857a4e1d9a00e28e6c88a4ad5df24","observation_id":"26123e8f-b451-4ffc-86f7-484141a6550f","resolution":{"observed_at":"2026-08-04T11:01:08.139959Z","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":"2026-08-04T11:01:08.191160Z","title":null,"venue":null,"work_id":null,"year":1967},"citing_paper":{"arxiv_id":"2510.07396","last_updated":"2026-05-28T21:14:00Z","snapshot_observed_at":"2026-08-08T11:49:39.116792Z","submitted_at":"2025-10-08T18:00:13Z","title":"Spectral properties and coding transitions of Haar-random quantum codes","version":3},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-08-04T11:01:08.191160Z"},"links":{"citing_paper":"/paper/2510.07396"},"observation_digest":"sha256:6b5ed2bbc068317706b33059effd69f19a293227e7085adff9e73465084f2926","observation_id":"5998a8dc-b4ac-411a-83ab-9c53f86439d9","resolution":{"observed_at":"2026-08-04T11:01:08.191160Z","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":"2026-08-04T11:01:08.242982Z","title":"Livan, M","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2510.07396","last_updated":"2026-05-28T21:14:00Z","snapshot_observed_at":"2026-08-08T11:49:39.116792Z","submitted_at":"2025-10-08T18:00:13Z","title":"Spectral properties and coding transitions of Haar-random quantum codes","version":3},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-08-04T11:01:08.242982Z"},"links":{"citing_paper":"/paper/2510.07396"},"observation_digest":"sha256:82fe3a5761791265947d6fcd0d5117fd36d4901c3067a554a609a7cc90763599","observation_id":"98bfdf5a-530b-4912-8c9c-987607d2ae70","resolution":{"observed_at":"2026-08-04T11:01:08.242982Z","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":"2026-08-04T11:01:08.323091Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2510.07396","last_updated":"2026-05-28T21:14:00Z","snapshot_observed_at":"2026-08-08T11:49:39.116792Z","submitted_at":"2025-10-08T18:00:13Z","title":"Spectral properties and coding transitions of Haar-random quantum codes","version":3},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-08-04T11:01:08.323091Z"},"links":{"citing_paper":"/paper/2510.07396"},"observation_digest":"sha256:532fe2958d18cf86d21bffda24be4a86cf91079efcfc7db8ed301c932f6ab479","observation_id":"97763099-7f4d-4e45-826a-72f76d609a85","resolution":{"observed_at":"2026-08-04T11:01:08.323091Z","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":"2026-08-04T11:01:08.378948Z","title":"Turkeshi and P","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2510.07396","last_updated":"2026-05-28T21:14:00Z","snapshot_observed_at":"2026-08-08T11:49:39.116792Z","submitted_at":"2025-10-08T18:00:13Z","title":"Spectral properties and coding transitions of Haar-random quantum codes","version":3},"reference_index":38,"source":"pdf_text","source_observed_at":"2026-08-04T11:01:08.378948Z"},"links":{"citing_paper":"/paper/2510.07396"},"observation_digest":"sha256:d4dbbe586d32b62984792780c8dd37854813b4f48c0c47790a1feb1c426626f2","observation_id":"b4d31005-0d9b-4bef-b0ac-b32e77238fef","resolution":{"observed_at":"2026-08-04T11:01:08.378948Z","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":"2026-08-04T11:01:08.458958Z","title":"Barr´ e, D","venue":null,"work_id":null,"year":2001},"citing_paper":{"arxiv_id":"2510.07396","last_updated":"2026-05-28T21:14:00Z","snapshot_observed_at":"2026-08-08T11:49:39.116792Z","submitted_at":"2025-10-08T18:00:13Z","title":"Spectral properties and coding transitions of Haar-random quantum codes","version":3},"reference_index":39,"source":"pdf_text","source_observed_at":"2026-08-04T11:01:08.458958Z"},"links":{"citing_paper":"/paper/2510.07396"},"observation_digest":"sha256:ed81a6f9d7d9e12423798afa560d0559457d288739beb12eaed862fc9f509360","observation_id":"f18c4dce-1e33-46c8-b098-936cd6168e05","resolution":{"observed_at":"2026-08-04T11:01:08.458958Z","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":"2026-08-04T11:01:08.545540Z","title":"Defenu, D","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2510.07396","last_updated":"2026-05-28T21:14:00Z","snapshot_observed_at":"2026-08-08T11:49:39.116792Z","submitted_at":"2025-10-08T18:00:13Z","title":"Spectral properties and coding transitions of Haar-random quantum codes","version":3},"reference_index":40,"source":"pdf_text","source_observed_at":"2026-08-04T11:01:08.545540Z"},"links":{"citing_paper":"/paper/2510.07396"},"observation_digest":"sha256:5556f2ad4898561e8604d84d7dcc49c3ddb436031b593c54a1f477de00d059fb","observation_id":"4b8e7643-4a13-4457-b421-c1c60396009f","resolution":{"observed_at":"2026-08-04T11:01:08.545540Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2504.14008","last_updated":"2026-04-08T16:12:50Z","snapshot_observed_at":"2026-08-04T08:19:15.519880Z","submitted_at":"2025-04-18T18:01:26Z","title":"Ensemble Inequivalence in Long-Range Quantum Spin Systems","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2504.14008","snapshot_observed_at":"2026-08-04T11:01:08.609521Z","title":"Arrufat-Vicente, D","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2510.07396","last_updated":"2026-05-28T21:14:00Z","snapshot_observed_at":"2026-08-08T11:49:39.116792Z","submitted_at":"2025-10-08T18:00:13Z","title":"Spectral properties and coding transitions of Haar-random quantum codes","version":3},"reference_index":41,"source":"pdf_text","source_observed_at":"2026-08-04T11:01:08.609521Z"},"links":{"cited_paper":"/paper/2504.14008","citing_paper":"/paper/2510.07396"},"observation_digest":"sha256:408aece425aeb71099356170292b417b0c2a1d54b63b9439dee95257d3636b17","observation_id":"5edacad2-cf10-4b84-8cbb-fdb401288360","resolution":{"observed_at":"2026-08-04T11:01:08.609521Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2502.14974","last_updated":"2025-02-20T19:07:31Z","snapshot_observed_at":"2026-08-07T18:00:51.353780Z","submitted_at":"2025-02-20T19:07:31Z","title":"Universal Quantum Computation with the $S_3$ Quantum Double: A Pedagogical Exposition","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2502.14974","snapshot_observed_at":"2026-08-04T11:01:08.683621Z","title":null,"venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2510.07396","last_updated":"2026-05-28T21:14:00Z","snapshot_observed_at":"2026-08-08T11:49:39.116792Z","submitted_at":"2025-10-08T18:00:13Z","title":"Spectral properties and coding transitions of Haar-random quantum codes","version":3},"reference_index":42,"source":"pdf_text","source_observed_at":"2026-08-04T11:01:08.683621Z"},"links":{"cited_paper":"/paper/2502.14974","citing_paper":"/paper/2510.07396"},"observation_digest":"sha256:d126fb81e618bfcc86324358e13f3a37609bd206e4046bfa9a5af7e22d649b89","observation_id":"79314a23-4ecb-4367-8aaa-66c45b33b5c1","resolution":{"observed_at":"2026-08-04T11:01:08.683621Z","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":"2026-08-04T11:01:08.746102Z","title":null,"venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2510.07396","last_updated":"2026-05-28T21:14:00Z","snapshot_observed_at":"2026-08-08T11:49:39.116792Z","submitted_at":"2025-10-08T18:00:13Z","title":"Spectral properties and coding transitions of Haar-random quantum codes","version":3},"reference_index":43,"source":"pdf_text","source_observed_at":"2026-08-04T11:01:08.746102Z"},"links":{"citing_paper":"/paper/2510.07396"},"observation_digest":"sha256:f8f80f997df4dfaf616114bd4e9c94a51160a4148e26784c51420ce5b88aa044","observation_id":"4e691935-84af-4cdd-a81f-579fa46caf1e","resolution":{"observed_at":"2026-08-04T11:01:08.746102Z","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":"2026-08-04T11:01:08.816215Z","title":"Sala and R","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2510.07396","last_updated":"2026-05-28T21:14:00Z","snapshot_observed_at":"2026-08-08T11:49:39.116792Z","submitted_at":"2025-10-08T18:00:13Z","title":"Spectral properties and coding transitions of Haar-random quantum codes","version":3},"reference_index":44,"source":"pdf_text","source_observed_at":"2026-08-04T11:01:08.816215Z"},"links":{"citing_paper":"/paper/2510.07396"},"observation_digest":"sha256:0d35069b076da18d22b12c802e972d5f7f17e763c24ba4da3d936b9b016b939a","observation_id":"add5d1fe-c16a-47a1-bf83-a3a42acba0d8","resolution":{"observed_at":"2026-08-04T11:01:08.816215Z","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":"2026-08-04T11:01:08.870666Z","title":null,"venue":null,"work_id":null,"year":2013},"citing_paper":{"arxiv_id":"2510.07396","last_updated":"2026-05-28T21:14:00Z","snapshot_observed_at":"2026-08-08T11:49:39.116792Z","submitted_at":"2025-10-08T18:00:13Z","title":"Spectral properties and coding transitions of Haar-random quantum codes","version":3},"reference_index":45,"source":"pdf_text","source_observed_at":"2026-08-04T11:01:08.870666Z"},"links":{"citing_paper":"/paper/2510.07396"},"observation_digest":"sha256:875926199cd111a6f693728c77dab24f65b068949c3c04f60936f46741b8de90","observation_id":"322e7688-df51-430b-8611-b1fe6e556af9","resolution":{"observed_at":"2026-08-04T11:01:08.870666Z","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":"2026-08-04T11:01:08.960525Z","title":"Preskill,Lecture Notes for Physics 219: Quantum Computation(2018)","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2510.07396","last_updated":"2026-05-28T21:14:00Z","snapshot_observed_at":"2026-08-08T11:49:39.116792Z","submitted_at":"2025-10-08T18:00:13Z","title":"Spectral properties and coding transitions of Haar-random quantum codes","version":3},"reference_index":46,"source":"pdf_text","source_observed_at":"2026-08-04T11:01:08.960525Z"},"links":{"citing_paper":"/paper/2510.07396"},"observation_digest":"sha256:90fb86a37a1b832a068989b1a6a4b415ffb55492dcfc082521e5a59f44ee8a15","observation_id":"d0c784b2-bc21-498b-ba6f-d75b160cd0a8","resolution":{"observed_at":"2026-08-04T11:01:08.960525Z","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":"2026-08-04T11:01:09.013810Z","title":"Collins and P","venue":null,"work_id":null,"year":2006},"citing_paper":{"arxiv_id":"2510.07396","last_updated":"2026-05-28T21:14:00Z","snapshot_observed_at":"2026-08-08T11:49:39.116792Z","submitted_at":"2025-10-08T18:00:13Z","title":"Spectral properties and coding transitions of Haar-random quantum codes","version":3},"reference_index":47,"source":"pdf_text","source_observed_at":"2026-08-04T11:01:09.013810Z"},"links":{"citing_paper":"/paper/2510.07396"},"observation_digest":"sha256:beb8647a72b451516c15ef626f107ac670a769e77c7ee8bf62306fd452e418ce","observation_id":"55da52a0-a7ff-4b50-b303-319586b55b4c","resolution":{"observed_at":"2026-08-04T11:01:09.013810Z","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":"2026-08-04T11:01:09.066593Z","title":null,"venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2510.07396","last_updated":"2026-05-28T21:14:00Z","snapshot_observed_at":"2026-08-08T11:49:39.116792Z","submitted_at":"2025-10-08T18:00:13Z","title":"Spectral properties and coding transitions of Haar-random quantum codes","version":3},"reference_index":48,"source":"pdf_text","source_observed_at":"2026-08-04T11:01:09.066593Z"},"links":{"citing_paper":"/paper/2510.07396"},"observation_digest":"sha256:3162fb03a2cb73661da0d8d716e77a00c9364f4be04ac45b5123736ec234cdf4","observation_id":"8d7065b8-4587-42d4-adcf-f9ea5c4c0509","resolution":{"observed_at":"2026-08-04T11:01:09.066593Z","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":"2026-08-04T11:01:09.141668Z","title":"Weingarten, Asymptotic behavior of group integrals in the limit of infinite rank, Journal of Mathematical Physics19, 999 (1978)","venue":null,"work_id":null,"year":1978},"citing_paper":{"arxiv_id":"2510.07396","last_updated":"2026-05-28T21:14:00Z","snapshot_observed_at":"2026-08-08T11:49:39.116792Z","submitted_at":"2025-10-08T18:00:13Z","title":"Spectral properties and coding transitions of Haar-random quantum codes","version":3},"reference_index":49,"source":"pdf_text","source_observed_at":"2026-08-04T11:01:09.141668Z"},"links":{"citing_paper":"/paper/2510.07396"},"observation_digest":"sha256:bd51c58f1dc299b95638066d6b2593618001d7212420e5467605cf7b9c95cba3","observation_id":"f0206fa1-a153-4d8e-93e0-736d95726f7c","resolution":{"observed_at":"2026-08-04T11:01:09.141668Z","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":"2026-08-04T11:01:09.201001Z","title":"Schuster and N","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2510.07396","last_updated":"2026-05-28T21:14:00Z","snapshot_observed_at":"2026-08-08T11:49:39.116792Z","submitted_at":"2025-10-08T18:00:13Z","title":"Spectral properties and coding transitions of Haar-random quantum codes","version":3},"reference_index":50,"source":"pdf_text","source_observed_at":"2026-08-04T11:01:09.201001Z"},"links":{"citing_paper":"/paper/2510.07396"},"observation_digest":"sha256:62156cafeae843a164d7322a2ad23de6cf1d62a8d9f0537fedf8941f77d6c5c8","observation_id":"72b99913-d91f-4dbc-9630-e4b3b6ae949b","resolution":{"observed_at":"2026-08-04T11:01:09.201001Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2407.12768","last_updated":"2024-10-14T16:55:22Z","snapshot_observed_at":"2026-07-06T18:47:56.109836Z","submitted_at":"2024-07-17T17:48:39Z","title":"A polynomial-time classical algorithm for noisy quantum circuits","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2407.12768","snapshot_observed_at":"2026-08-04T11:01:09.281284Z","title":"Schuster, C","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2510.07396","last_updated":"2026-05-28T21:14:00Z","snapshot_observed_at":"2026-08-08T11:49:39.116792Z","submitted_at":"2025-10-08T18:00:13Z","title":"Spectral properties and coding transitions of Haar-random quantum codes","version":3},"reference_index":51,"source":"pdf_text","source_observed_at":"2026-08-04T11:01:09.281284Z"},"links":{"cited_paper":"/paper/2407.12768","citing_paper":"/paper/2510.07396"},"observation_digest":"sha256:4a9a2479adcd1791551d5bf9a19d1d5c7f026a7909d57cc439a3fc8163e3c6a6","observation_id":"dbacc578-6f09-454e-9990-bf43fd1cf32f","resolution":{"observed_at":"2026-08-04T11:01:09.281284Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2409.17238","last_updated":"2024-09-25T18:00:07Z","snapshot_observed_at":"2026-08-09T10:41:28.057249Z","submitted_at":"2024-09-25T18:00:07Z","title":"Spectral gaps of local quantum channels in the weak-dissipation limit","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2409.17238","snapshot_observed_at":"2026-08-04T11:01:09.335512Z","title":null,"venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2510.07396","last_updated":"2026-05-28T21:14:00Z","snapshot_observed_at":"2026-08-08T11:49:39.116792Z","submitted_at":"2025-10-08T18:00:13Z","title":"Spectral properties and coding transitions of Haar-random quantum codes","version":3},"reference_index":52,"source":"pdf_text","source_observed_at":"2026-08-04T11:01:09.335512Z"},"links":{"cited_paper":"/paper/2409.17238","citing_paper":"/paper/2510.07396"},"observation_digest":"sha256:f32b12861b91ba7a33c9d8ae9ac51846c25acee40c7ac902646bc7c7298d1699","observation_id":"d5645ab7-cf60-4275-8a8c-5d4eb12c3345","resolution":{"observed_at":"2026-08-04T11:01:09.335512Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2409.17251","last_updated":"2025-03-14T15:56:05Z","snapshot_observed_at":"2026-07-06T19:22:18.873914Z","submitted_at":"2024-09-25T18:07:46Z","title":"Thermalization rates and quantum Ruelle-Pollicott resonances: insights from operator hydrodynamics","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2409.17251","snapshot_observed_at":"2026-08-04T11:01:09.387870Z","title":"Zhang, L","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2510.07396","last_updated":"2026-05-28T21:14:00Z","snapshot_observed_at":"2026-08-08T11:49:39.116792Z","submitted_at":"2025-10-08T18:00:13Z","title":"Spectral properties and coding transitions of Haar-random quantum codes","version":3},"reference_index":53,"source":"pdf_text","source_observed_at":"2026-08-04T11:01:09.387870Z"},"links":{"cited_paper":"/paper/2409.17251","citing_paper":"/paper/2510.07396"},"observation_digest":"sha256:5ad33ddd5cc4419bedcdc5513fdf50ce1af59bb36fc30b3fcdbeb56d18c2e7f4","observation_id":"2d6c7ce2-be4b-485b-a1ac-8bef732ac247","resolution":{"observed_at":"2026-08-04T11:01:09.387870Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1007/jhep08(2024)092","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":null,"venue":"Journal of High Energy Physics","work_id":"1c62aa1d-5950-4d50-9ae9-c717b425fb0f","year":2024},"citing_paper":{"arxiv_id":"2510.07396","last_updated":"2026-05-28T21:14:00Z","snapshot_observed_at":"2026-08-08T11:49:39.116792Z","submitted_at":"2025-10-08T18:00:13Z","title":"Spectral properties and coding transitions of Haar-random quantum codes","version":3},"reference_index":54,"source":"pdf_text","source_observed_at":"2026-08-04T11:01:09.462045Z"},"links":{"citing_paper":"/paper/2510.07396"},"observation_digest":"sha256:16a204af523ad4f90bc3858cf64a929aef44eb5284c1e77d2b642463a4874c1e","observation_id":"36bc3ad6-e891-4d21-9a08-742a7f034dea","resolution":{"observed_at":"2026-08-04T11:04:51.533754Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T11:01:09.518706Z","title":"Schumacher and M","venue":null,"work_id":null,"year":1996},"citing_paper":{"arxiv_id":"2510.07396","last_updated":"2026-05-28T21:14:00Z","snapshot_observed_at":"2026-08-08T11:49:39.116792Z","submitted_at":"2025-10-08T18:00:13Z","title":"Spectral properties and coding transitions of Haar-random quantum codes","version":3},"reference_index":55,"source":"pdf_text","source_observed_at":"2026-08-04T11:01:09.518706Z"},"links":{"citing_paper":"/paper/2510.07396"},"observation_digest":"sha256:a4c14877d4fdb7a18046e5f1b0b425e47dc186ae657d53599476608ab986a3ce","observation_id":"8073bb14-2aa1-4fe9-b748-5b6f188eb934","resolution":{"observed_at":"2026-08-04T11:01:09.518706Z","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":"2026-08-04T11:01:09.575023Z","title":null,"venue":null,"work_id":null,"year":2015},"citing_paper":{"arxiv_id":"2510.07396","last_updated":"2026-05-28T21:14:00Z","snapshot_observed_at":"2026-08-08T11:49:39.116792Z","submitted_at":"2025-10-08T18:00:13Z","title":"Spectral properties and coding transitions of Haar-random quantum codes","version":3},"reference_index":56,"source":"pdf_text","source_observed_at":"2026-08-04T11:01:09.575023Z"},"links":{"citing_paper":"/paper/2510.07396"},"observation_digest":"sha256:ae21c220f3f3a4108e68436922d6cefbabc6d5269f1c391ff296c3cbc1c2ab66","observation_id":"e284cad3-a288-4ee5-bd72-86b052e4e636","resolution":{"observed_at":"2026-08-04T11:01:09.575023Z","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":"2026-08-04T11:01:09.650788Z","title":null,"venue":null,"work_id":null,"year":1996},"citing_paper":{"arxiv_id":"2510.07396","last_updated":"2026-05-28T21:14:00Z","snapshot_observed_at":"2026-08-08T11:49:39.116792Z","submitted_at":"2025-10-08T18:00:13Z","title":"Spectral properties and coding transitions of Haar-random quantum codes","version":3},"reference_index":57,"source":"pdf_text","source_observed_at":"2026-08-04T11:01:09.650788Z"},"links":{"citing_paper":"/paper/2510.07396"},"observation_digest":"sha256:1a36de4a56453b7b0ff81b4ce3677c024c6656897d74fa1cf6a8469bae3a4763","observation_id":"ac53c69c-3ef7-4ecb-9d67-79673cb23724","resolution":{"observed_at":"2026-08-04T11:01:09.650788Z","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":"2026-08-04T11:01:09.705107Z","title":"Steane, Multiple-particle interference and quantum er- ror correction, Proceedings of the Royal Society of Lon- don","venue":null,"work_id":null,"year":1996},"citing_paper":{"arxiv_id":"2510.07396","last_updated":"2026-05-28T21:14:00Z","snapshot_observed_at":"2026-08-08T11:49:39.116792Z","submitted_at":"2025-10-08T18:00:13Z","title":"Spectral properties and coding transitions of Haar-random quantum codes","version":3},"reference_index":58,"source":"pdf_text","source_observed_at":"2026-08-04T11:01:09.705107Z"},"links":{"citing_paper":"/paper/2510.07396"},"observation_digest":"sha256:d3a2a0444e96a131e37bb75cd4a27f9d7bc5e7383341166580c10c2e78a52186","observation_id":"8a6b24d3-3f7a-4f0d-af42-e1165fdfb683","resolution":{"observed_at":"2026-08-04T11:01:09.705107Z","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":"2026-08-04T11:01:09.807328Z","title":null,"venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2510.07396","last_updated":"2026-05-28T21:14:00Z","snapshot_observed_at":"2026-08-08T11:49:39.116792Z","submitted_at":"2025-10-08T18:00:13Z","title":"Spectral properties and coding transitions of Haar-random quantum codes","version":3},"reference_index":59,"source":"pdf_text","source_observed_at":"2026-08-04T11:01:09.807328Z"},"links":{"citing_paper":"/paper/2510.07396"},"observation_digest":"sha256:d16433fb4228d34bb9942f5b53423b8a8f86159f36e3a401514355f7a72c14b1","observation_id":"b9a3d088-3081-4564-bf1d-2ee61cf9c397","resolution":{"observed_at":"2026-08-04T11:01:09.807328Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"quant-ph/9906126","last_updated":"1999-06-30T03:08:19Z","snapshot_observed_at":"2026-07-07T07:29:15.607259Z","submitted_at":"1999-06-30T03:08:19Z","title":"Quantum Error Detection I: Statement of the Problem","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"quant-ph/9906126","snapshot_observed_at":"2026-08-04T11:01:09.915643Z","title":"Ashikhmin, A","venue":null,"work_id":null,"year":1999},"citing_paper":{"arxiv_id":"2510.07396","last_updated":"2026-05-28T21:14:00Z","snapshot_observed_at":"2026-08-08T11:49:39.116792Z","submitted_at":"2025-10-08T18:00:13Z","title":"Spectral properties and coding transitions of Haar-random quantum codes","version":3},"reference_index":60,"source":"pdf_text","source_observed_at":"2026-08-04T11:01:09.915643Z"},"links":{"cited_paper":"/paper/quant-ph/9906126","citing_paper":"/paper/2510.07396"},"observation_digest":"sha256:1d275254da4f8e01231439e726da5dc9556d44e7472accef8f198c54911a5f2c","observation_id":"302eee60-c6fd-4ab5-9124-b338dcc6b6dc","resolution":{"observed_at":"2026-08-04T11:01:09.915643Z","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":"2026-08-04T11:01:10.075369Z","title":null,"venue":null,"work_id":null,"year":2005},"citing_paper":{"arxiv_id":"2510.07396","last_updated":"2026-05-28T21:14:00Z","snapshot_observed_at":"2026-08-08T11:49:39.116792Z","submitted_at":"2025-10-08T18:00:13Z","title":"Spectral properties and coding transitions of Haar-random quantum codes","version":3},"reference_index":61,"source":"pdf_text","source_observed_at":"2026-08-04T11:01:10.075369Z"},"links":{"citing_paper":"/paper/2510.07396"},"observation_digest":"sha256:92b52c9d30342636fd0665d2ec32cdfcbbd26fc3216a39ff171ab963cb7a706b","observation_id":"d46111d7-258b-4f4c-ad25-ef0e7ec48149","resolution":{"observed_at":"2026-08-04T11:01:10.075369Z","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":"2026-08-04T11:01:10.183387Z","title":"microcanonical channel","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2510.07396","last_updated":"2026-05-28T21:14:00Z","snapshot_observed_at":"2026-08-08T11:49:39.116792Z","submitted_at":"2025-10-08T18:00:13Z","title":"Spectral properties and coding transitions of Haar-random quantum codes","version":3},"reference_index":62,"source":"pdf_text","source_observed_at":"2026-08-04T11:01:10.183387Z"},"links":{"citing_paper":"/paper/2510.07396"},"observation_digest":"sha256:1773685cf57ec6f84dc26b0ef2d1db935b883ab1b9c154af2d9a48fbd85b5a50","observation_id":"abc7e30e-8a7c-42e6-98e9-151693d664a1","resolution":{"observed_at":"2026-08-04T11:01:10.183387Z","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":"2026-08-04T11:01:10.270708Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2510.07396","last_updated":"2026-05-28T21:14:00Z","snapshot_observed_at":"2026-08-08T11:49:39.116792Z","submitted_at":"2025-10-08T18:00:13Z","title":"Spectral properties and coding transitions of Haar-random quantum codes","version":3},"reference_index":63,"source":"pdf_text","source_observed_at":"2026-08-04T11:01:10.270708Z"},"links":{"citing_paper":"/paper/2510.07396"},"observation_digest":"sha256:87f97e2c3159742b521efd86e53f6ef4aefad782ba21227ebc45417cb8d93b9a","observation_id":"da7842c9-4dbb-4010-9c5c-781ebededa7c","resolution":{"observed_at":"2026-08-04T11:01:10.270708Z","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":"2026-08-04T11:01:10.327230Z","title":"Namely, projecting the microcanonical density matrices into their corresponding sectors asP wπ(w) RQ ˜ρ(w) RQπ(w) RQ and diagonalizing them, we label the eigenvectors |n(w)⟩","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2510.07396","last_updated":"2026-05-28T21:14:00Z","snapshot_observed_at":"2026-08-08T11:49:39.116792Z","submitted_at":"2025-10-08T18:00:13Z","title":"Spectral properties and coding transitions of Haar-random quantum codes","version":3},"reference_index":64,"source":"pdf_text","source_observed_at":"2026-08-04T11:01:10.327230Z"},"links":{"citing_paper":"/paper/2510.07396"},"observation_digest":"sha256:d3a717452ec712b156783f3742cfb1b5c73f2a3e843f7b32bdf5dcec8421b6a7","observation_id":"a19af21d-2109-4a43-9b61-d89ebb60aa49","resolution":{"observed_at":"2026-08-04T11:01:10.327230Z","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":"2026-08-04T11:01:10.381947Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2510.07396","last_updated":"2026-05-28T21:14:00Z","snapshot_observed_at":"2026-08-08T11:49:39.116792Z","submitted_at":"2025-10-08T18:00:13Z","title":"Spectral properties and coding transitions of Haar-random quantum codes","version":3},"reference_index":65,"source":"pdf_text","source_observed_at":"2026-08-04T11:01:10.381947Z"},"links":{"citing_paper":"/paper/2510.07396"},"observation_digest":"sha256:a49d5054db2e6d9d5aa8f44bdf894b4cafba86277fa393653b6c38f65450aed6","observation_id":"9388ec44-b64c-42bc-b5b3-4ecd64db7560","resolution":{"observed_at":"2026-08-04T11:01:10.381947Z","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":"2026-08-04T11:01:10.435807Z","title":"typical error","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2510.07396","last_updated":"2026-05-28T21:14:00Z","snapshot_observed_at":"2026-08-08T11:49:39.116792Z","submitted_at":"2025-10-08T18:00:13Z","title":"Spectral properties and coding transitions of Haar-random quantum codes","version":3},"reference_index":66,"source":"pdf_text","source_observed_at":"2026-08-04T11:01:10.435807Z"},"links":{"citing_paper":"/paper/2510.07396"},"observation_digest":"sha256:882643ead62985d1526eb675cbc72c8eefae4a968e95415238daf519f556a16d","observation_id":"1e2d69fa-b513-4cc1-88a3-6f611202bddb","resolution":{"observed_at":"2026-08-04T11:01:10.435807Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2510.07396","last_updated":"2026-05-28T21:14:00Z","latest_version":3,"primary_category":"quant-ph","snapshot_observed_at":"2026-08-08T11:49:39.116792Z","submitted_at":"2025-10-08T18:00:13Z","title":"Spectral properties and coding transitions of Haar-random quantum codes"},"reference_resolution":{"displayed":66,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":65,"verified_exact":1,"verified_fuzzy":0},"total_outbound_references":66},"refusal":"A citation records a reference. It does not transfer a finding from one paper to another.","schema":"pith.paper-citation-record.v1","standing_sources":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"thesis":"As of 10 August 2026, this Paper Citation Record lists 66 of 66 outbound references and 0 inbound Pith citation observations for arXiv:2510.07396."}