{"as_of":"2026-08-04T19:24:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:52472b4660c55a074c7a06c3382e79fbed7c00698bd92d69054a94b5604b57d3","coverage":[{"denominator":68,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":68,"source":"paper_references, paper_reference_links","source_observed_at":"2026-05-10T02:30:01.593171Z","state":"measured"},{"denominator":69,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":69,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-04T06:34:03.388597+00:00","state":"measured"},{"denominator":1,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":1,"source":"paper_references, paper_reference_links","source_observed_at":"2026-07-03T11:51:57.387946Z","state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"pith","source_observed_at":"2026-07-03T11:58:05.587434Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2604.19889","last_updated":"2026-04-21T18:11:19Z","snapshot_observed_at":"2026-07-06T23:06:26.596990Z","submitted_at":"2026-04-21T18:11:19Z","title":"Quantum-to-Classical Computability Transition via Negative Markov Chains","version":1},"cited_work":{"arxiv_id":"2604.19889","doi":null,"metadata_source":"pith","pith_arxiv_id":"2604.19889","snapshot_observed_at":"2026-07-03T11:58:05.587434Z","title":"Quantum-to-Classical Computability Transition via Negative Markov Chains","venue":"quant-ph","work_id":"cfd05f3e-142b-4150-a5c2-3de2b347e4a1","year":2026},"citing_paper":{"arxiv_id":"2607.02341","last_updated":"2026-07-02T15:48:06Z","snapshot_observed_at":"2026-07-07T00:07:47.719699Z","submitted_at":"2026-07-02T15:48:06Z","title":"Kardar-Parisi-Zhang dynamics in an open integrable system: beyond the spontaneous-symmetry-breaking ansatz","version":1},"reference_index":50,"source":"pdf_text","source_observed_at":"2026-07-03T11:51:57.387946Z"},"links":{"cited_paper":"/paper/2604.19889","citing_paper":"/paper/2607.02341"},"observation_digest":"sha256:4c3b5d36558a596ba6a3be6b49e3db9c6eb39c5b9b956b7ea5d13ff94e04f894","observation_id":"1efa8a0f-b3d1-46bf-823a-1a508c756d2a","resolution":{"observed_at":"2026-07-03T11:58:05.589201Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+00:00","source":"retraction_watch"}],"state":"measured"}}],"links":{"evidence":"/evidence","html":"/paper/2604.19889/citation-record","integrity":"/paper/2604.19889/integrity","json":"/paper/2604.19889/citation-record.json","paper":"/paper/2604.19889"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Aaronson and A","venue":null,"work_id":"c11999b0-ecbe-44cb-9818-24b57dea7698","year":2011},"citing_paper":{"arxiv_id":"2604.19889","last_updated":"2026-04-21T18:11:19Z","snapshot_observed_at":"2026-07-06T23:06:26.596990Z","submitted_at":"2026-04-21T18:11:19Z","title":"Quantum-to-Classical Computability Transition via Negative Markov Chains","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-05-10T02:30:01.593171Z"},"links":{"citing_paper":"/paper/2604.19889"},"observation_digest":"sha256:3774302482392e4079fed097a15f3a1fced0a1edd1d22b5e0f68ec63201d081b","observation_id":"62810c12-9948-43ff-959e-1707799017c7","resolution":{"observed_at":"2026-05-22T21:57:11.662714Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+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":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"7b23ecfb-5554-4289-ae31-a433aa47720f","year":2016},"citing_paper":{"arxiv_id":"2604.19889","last_updated":"2026-04-21T18:11:19Z","snapshot_observed_at":"2026-07-06T23:06:26.596990Z","submitted_at":"2026-04-21T18:11:19Z","title":"Quantum-to-Classical Computability Transition via Negative Markov Chains","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-05-10T02:30:01.593171Z"},"links":{"citing_paper":"/paper/2604.19889"},"observation_digest":"sha256:ccda334a3876b0108492145ff021b06b217e5a381a68d9581b1b156f11411f38","observation_id":"b11c02b3-2883-49c9-9624-911092605013","resolution":{"observed_at":"2026-05-22T21:57:11.668244Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+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":"2026-06-05T21:23:00.469572Z","title":"Shor, Fault-tolerant quantum computation, inProceed- ings of 37th Conference on Foundations of Computer Sci- ence(1996) pp","venue":null,"work_id":"917f62f3-67da-4c12-baef-1654baf63c5f","year":1996},"citing_paper":{"arxiv_id":"2604.19889","last_updated":"2026-04-21T18:11:19Z","snapshot_observed_at":"2026-07-06T23:06:26.596990Z","submitted_at":"2026-04-21T18:11:19Z","title":"Quantum-to-Classical Computability Transition via Negative Markov Chains","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-05-10T02:30:01.593171Z"},"links":{"citing_paper":"/paper/2604.19889"},"observation_digest":"sha256:e3ba23d50679063671ecec28e176f416b9a18d2099e7b6fb4020cf05edcf0495","observation_id":"501efad3-7fab-4cac-b8de-86fee29f5bdf","resolution":{"observed_at":"2026-05-22T21:57:11.626134Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+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":"2026-07-07T19:14:06.517579Z","title":"Kitaev, Fault-tolerant quantum computation by anyons, Annals of Physics303, 2 (2003)","venue":null,"work_id":"92e4b04d-bb24-461a-9aac-921f73330f58","year":2003},"citing_paper":{"arxiv_id":"2604.19889","last_updated":"2026-04-21T18:11:19Z","snapshot_observed_at":"2026-07-06T23:06:26.596990Z","submitted_at":"2026-04-21T18:11:19Z","title":"Quantum-to-Classical Computability Transition via Negative Markov Chains","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-05-10T02:30:01.593171Z"},"links":{"citing_paper":"/paper/2604.19889"},"observation_digest":"sha256:eed63625f0c5971aba380cd4743314b9d2747f4182a6ae0f4df254c5b621562c","observation_id":"9b552de5-58c3-42b7-b853-bc8e0c992eee","resolution":{"observed_at":"2026-05-22T21:57:11.722474Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+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":"2026-06-05T21:23:00.469572Z","title":"Aharonov and M","venue":null,"work_id":"7c708c6e-a4b9-4690-b08b-0a11ac536625","year":2008},"citing_paper":{"arxiv_id":"2604.19889","last_updated":"2026-04-21T18:11:19Z","snapshot_observed_at":"2026-07-06T23:06:26.596990Z","submitted_at":"2026-04-21T18:11:19Z","title":"Quantum-to-Classical Computability Transition via Negative Markov Chains","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-05-10T02:30:01.593171Z"},"links":{"citing_paper":"/paper/2604.19889"},"observation_digest":"sha256:f62d991500d68fd0115a190d0d23c8ea09ddbfbb5679f90e6f6dc10e57e68a44","observation_id":"6421800f-3a7f-47cc-9c18-ab39355e1640","resolution":{"observed_at":"2026-05-22T21:57:11.717947Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+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":"2026-06-05T21:23:00.469572Z","title":"Preskill, Quantum Computing in the NISQ era and bey- ond, Quantum2, 79 (2018)","venue":null,"work_id":"829eb9a3-acd1-46e5-8cc3-9d6270d32ac2","year":2018},"citing_paper":{"arxiv_id":"2604.19889","last_updated":"2026-04-21T18:11:19Z","snapshot_observed_at":"2026-07-06T23:06:26.596990Z","submitted_at":"2026-04-21T18:11:19Z","title":"Quantum-to-Classical Computability Transition via Negative Markov Chains","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-05-10T02:30:01.593171Z"},"links":{"citing_paper":"/paper/2604.19889"},"observation_digest":"sha256:893f83b8a4d7d16f0b84d288adbc874d6ddcaa59bdf8eae46dd82f7c2e509c1c","observation_id":"9452ea77-f6f7-427b-a540-2b5776961551","resolution":{"observed_at":"2026-05-22T21:57:11.659666Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+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":"2026-07-07T09:13:35.468700Z","title":"Arute, K","venue":null,"work_id":"7fd32d1d-9618-4154-b202-d09ed0e9b1f0","year":2019},"citing_paper":{"arxiv_id":"2604.19889","last_updated":"2026-04-21T18:11:19Z","snapshot_observed_at":"2026-07-06T23:06:26.596990Z","submitted_at":"2026-04-21T18:11:19Z","title":"Quantum-to-Classical Computability Transition via Negative Markov Chains","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-05-10T02:30:01.593171Z"},"links":{"citing_paper":"/paper/2604.19889"},"observation_digest":"sha256:2966de4456f799cb87f62671c0744b0ae3895be3bd4afc02708e7af738f31e1d","observation_id":"87a655be-ed8d-4243-97a8-9ae79754d386","resolution":{"observed_at":"2026-05-22T21:57:11.832291Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+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":"2026-06-05T21:23:00.469572Z","title":"Zhong, H","venue":null,"work_id":"45b1d8c7-6097-4bf4-9292-345164685589","year":2020},"citing_paper":{"arxiv_id":"2604.19889","last_updated":"2026-04-21T18:11:19Z","snapshot_observed_at":"2026-07-06T23:06:26.596990Z","submitted_at":"2026-04-21T18:11:19Z","title":"Quantum-to-Classical Computability Transition via Negative Markov Chains","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-05-10T02:30:01.593171Z"},"links":{"citing_paper":"/paper/2604.19889"},"observation_digest":"sha256:72f4094bf6f15f52ae244735d6c6a2799f25f974ffcfe2ee970c51fc70f949c3","observation_id":"ada75070-3b13-4e67-b116-49f3e607600e","resolution":{"observed_at":"2026-05-22T21:57:11.622856Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+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":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"b0a211de-9a7e-4412-a8c9-7689104ed510","year":2023},"citing_paper":{"arxiv_id":"2604.19889","last_updated":"2026-04-21T18:11:19Z","snapshot_observed_at":"2026-07-06T23:06:26.596990Z","submitted_at":"2026-04-21T18:11:19Z","title":"Quantum-to-Classical Computability Transition via Negative Markov Chains","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-05-10T02:30:01.593171Z"},"links":{"citing_paper":"/paper/2604.19889"},"observation_digest":"sha256:cd6fdc4c85c7db582c1adca2e053eba2742e59c407244b43b5d32fca2b8cd3cb","observation_id":"06ed8bde-e175-4b49-b20b-4ca1c09a09ce","resolution":{"observed_at":"2026-05-22T21:57:11.620132Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+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":"2026-06-05T21:23:00.469572Z","title":"Morvan, B","venue":null,"work_id":"42e1836a-24f9-41e5-b4fc-f31023516a64","year":2024},"citing_paper":{"arxiv_id":"2604.19889","last_updated":"2026-04-21T18:11:19Z","snapshot_observed_at":"2026-07-06T23:06:26.596990Z","submitted_at":"2026-04-21T18:11:19Z","title":"Quantum-to-Classical Computability Transition via Negative Markov Chains","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-05-10T02:30:01.593171Z"},"links":{"citing_paper":"/paper/2604.19889"},"observation_digest":"sha256:8a1521eae0bda40062ddf2ee3def290f84c432738f50b18da11a1f12c6b2efd1","observation_id":"56763dd7-9a58-4a81-b2d0-c754271931b1","resolution":{"observed_at":"2026-05-22T21:57:11.656260Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+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":"2026-06-05T21:23:00.469572Z","title":"Zhong, Y.-H","venue":null,"work_id":"ba13bc02-58f1-41fa-93f4-3029ae4907ea","year":2021},"citing_paper":{"arxiv_id":"2604.19889","last_updated":"2026-04-21T18:11:19Z","snapshot_observed_at":"2026-07-06T23:06:26.596990Z","submitted_at":"2026-04-21T18:11:19Z","title":"Quantum-to-Classical Computability Transition via Negative Markov Chains","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-05-10T02:30:01.593171Z"},"links":{"citing_paper":"/paper/2604.19889"},"observation_digest":"sha256:4009834124000fcd387c16df9f5fee42f3ca49a944445e62a8893b1b377e57c6","observation_id":"89a1dc30-6810-4095-a647-2c0a7e5cfb49","resolution":{"observed_at":"2026-05-22T21:57:11.665395Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+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":"2026-06-05T21:23:00.469572Z","title":"Deng, Y.-C","venue":null,"work_id":"7f5d3105-3d51-46e6-a302-87ebc29f559b","year":2023},"citing_paper":{"arxiv_id":"2604.19889","last_updated":"2026-04-21T18:11:19Z","snapshot_observed_at":"2026-07-06T23:06:26.596990Z","submitted_at":"2026-04-21T18:11:19Z","title":"Quantum-to-Classical Computability Transition via Negative Markov Chains","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-05-10T02:30:01.593171Z"},"links":{"citing_paper":"/paper/2604.19889"},"observation_digest":"sha256:fa3e68ec566f271ce033ac55256122e9d0042db9b6e55db66bcc50f0fb0fc3ee","observation_id":"6212d0bd-8ced-481a-b9f0-21368f3b4857","resolution":{"observed_at":"2026-05-22T21:57:11.766750Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2508.09092","last_updated":"2025-08-24T08:50:25Z","snapshot_observed_at":"2026-08-03T12:26:07.017285Z","submitted_at":"2025-08-12T17:17:40Z","title":"Robust quantum computational advantage with programmable 3050-photon Gaussian boson sampling","version":3},"cited_work":{"arxiv_id":"2508.09092","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2508.09092","snapshot_observed_at":"2026-07-03T14:28:31.416477Z","title":"Robust quantum computational advantage with programmable 3050- photon gaussian boson sampling","venue":null,"work_id":"36ac3535-e169-45b7-8fa0-8e1f536447b9","year":2025},"citing_paper":{"arxiv_id":"2604.19889","last_updated":"2026-04-21T18:11:19Z","snapshot_observed_at":"2026-07-06T23:06:26.596990Z","submitted_at":"2026-04-21T18:11:19Z","title":"Quantum-to-Classical Computability Transition via Negative Markov Chains","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-05-10T02:30:01.593171Z"},"links":{"cited_paper":"/paper/2508.09092","citing_paper":"/paper/2604.19889"},"observation_digest":"sha256:8ebf438ccff0b4052fcebe4d12277dab3f75f0d61ada4b51a5e913be5f5c391e","observation_id":"d358afe3-916b-4c19-8dde-83205cde339f","resolution":{"observed_at":"2026-05-11T13:01:04.612291Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+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":"2026-06-05T21:23:00.469572Z","title":"DeCross, R","venue":null,"work_id":"1fcc7464-63bc-4007-a0d3-ba151834cfea","year":2025},"citing_paper":{"arxiv_id":"2604.19889","last_updated":"2026-04-21T18:11:19Z","snapshot_observed_at":"2026-07-06T23:06:26.596990Z","submitted_at":"2026-04-21T18:11:19Z","title":"Quantum-to-Classical Computability Transition via Negative Markov Chains","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-05-10T02:30:01.593171Z"},"links":{"citing_paper":"/paper/2604.19889"},"observation_digest":"sha256:e358e1cb9b6dbe8d29462862b1a934ece7fd23745ef801714e1e1f2bcc8bc58f","observation_id":"e6a3ed9c-1ee0-4b4a-883d-deb0953897b3","resolution":{"observed_at":"2026-05-22T21:57:11.646041Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+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":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"634ac0af-91d4-4373-9cec-dc11212b1bdf","year":2025},"citing_paper":{"arxiv_id":"2604.19889","last_updated":"2026-04-21T18:11:19Z","snapshot_observed_at":"2026-07-06T23:06:26.596990Z","submitted_at":"2026-04-21T18:11:19Z","title":"Quantum-to-Classical Computability Transition via Negative Markov Chains","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-05-10T02:30:01.593171Z"},"links":{"citing_paper":"/paper/2604.19889"},"observation_digest":"sha256:0bcb93b4d74adb7b094df4d9b4ddc9b37f4338f3712e38c42a5e93ff38c04a16","observation_id":"07ccce99-dedb-499e-a45c-754de33931c0","resolution":{"observed_at":"2026-05-22T21:57:11.632498Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1810.03176","last_updated":"2018-10-07T16:44:18Z","snapshot_observed_at":"2026-07-06T07:06:32.994889Z","submitted_at":"2018-10-07T16:44:18Z","title":"Efficient classical simulation of noisy quantum computation","version":1},"cited_work":{"arxiv_id":"1810.03176","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"1810.03176","snapshot_observed_at":"2026-07-04T23:06:22.283601Z","title":"Gao and L","venue":null,"work_id":"fe15e995-6ad1-4969-a143-3d125d94ae1f","year":2018},"citing_paper":{"arxiv_id":"2604.19889","last_updated":"2026-04-21T18:11:19Z","snapshot_observed_at":"2026-07-06T23:06:26.596990Z","submitted_at":"2026-04-21T18:11:19Z","title":"Quantum-to-Classical Computability Transition via Negative Markov Chains","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-05-10T02:30:01.593171Z"},"links":{"cited_paper":"/paper/1810.03176","citing_paper":"/paper/2604.19889"},"observation_digest":"sha256:738b929de6f36df1cd23f78370fadc72d31d2173ceee3286efc37d0f7dab8e7e","observation_id":"086c7d6a-fbde-4bdc-954b-832205766b10","resolution":{"observed_at":"2026-07-04T23:06:22.283601Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2005.06787","last_updated":"2020-05-14T07:57:38Z","snapshot_observed_at":"2026-07-06T09:20:15.010776Z","submitted_at":"2020-05-14T07:57:38Z","title":"Classical Simulation of Quantum Supremacy Circuits","version":1},"cited_work":{"arxiv_id":"2005.06787","doi":"10.48550/arxiv.2005.06787","metadata_source":"arxiv_reference","pith_arxiv_id":"2005.06787","snapshot_observed_at":"2026-07-10T06:15:00.866473Z","title":"Huang, F","venue":null,"work_id":"86f1f41c-ebfa-4b46-bfd5-81be9c10f314","year":2020},"citing_paper":{"arxiv_id":"2604.19889","last_updated":"2026-04-21T18:11:19Z","snapshot_observed_at":"2026-07-06T23:06:26.596990Z","submitted_at":"2026-04-21T18:11:19Z","title":"Quantum-to-Classical Computability Transition via Negative Markov Chains","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-05-10T02:30:01.593171Z"},"links":{"cited_paper":"/paper/2005.06787","citing_paper":"/paper/2604.19889"},"observation_digest":"sha256:b2fc327c3861833be82ad63a85fcc21ec744f0c9a2a9be2afdea2ede67ec7fbd","observation_id":"50e1f825-3d61-4fbe-8f65-8f1854a38d5a","resolution":{"observed_at":"2026-05-11T13:01:04.634982Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2103.03074","last_updated":"2021-03-04T14:55:15Z","snapshot_observed_at":"2026-07-06T10:46:50.440586Z","submitted_at":"2021-03-04T14:55:15Z","title":"Simulating the Sycamore quantum supremacy circuits","version":1},"cited_work":{"arxiv_id":"2103.03074","doi":"10.48550/arxiv.2103.03074","metadata_source":"arxiv_reference","pith_arxiv_id":"2103.03074","snapshot_observed_at":"2026-07-10T06:15:00.866473Z","title":"Pan and P","venue":null,"work_id":"47d2a7aa-559e-447c-9fcf-30c6f84a5649","year":2021},"citing_paper":{"arxiv_id":"2604.19889","last_updated":"2026-04-21T18:11:19Z","snapshot_observed_at":"2026-07-06T23:06:26.596990Z","submitted_at":"2026-04-21T18:11:19Z","title":"Quantum-to-Classical Computability Transition via Negative Markov Chains","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-05-10T02:30:01.593171Z"},"links":{"cited_paper":"/paper/2103.03074","citing_paper":"/paper/2604.19889"},"observation_digest":"sha256:72ab73fabdbd509df879464f330e7083f8cd3c3caec4d4f3187c1e8fe99faeb9","observation_id":"cd777725-d58c-4d3a-b0a1-b74a1a0a3598","resolution":{"observed_at":"2026-05-11T13:01:04.651141Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+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":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"47d5e3c6-068d-44ae-9b39-e2c926ab8615","year":2022},"citing_paper":{"arxiv_id":"2604.19889","last_updated":"2026-04-21T18:11:19Z","snapshot_observed_at":"2026-07-06T23:06:26.596990Z","submitted_at":"2026-04-21T18:11:19Z","title":"Quantum-to-Classical Computability Transition via Negative Markov Chains","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-05-10T02:30:01.593171Z"},"links":{"citing_paper":"/paper/2604.19889"},"observation_digest":"sha256:f34697b57998c2dcab9bc9ceede63c65d806660833fde2d4a2ce8375f7b6f944","observation_id":"682e516b-1f4d-48ed-9629-da0755c17892","resolution":{"observed_at":"2026-05-22T21:57:11.713848Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+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":"2026-06-05T21:23:00.469572Z","title":"Pan and P","venue":null,"work_id":"f7b7848c-0428-4802-be95-13b1f98d2dbb","year":2022},"citing_paper":{"arxiv_id":"2604.19889","last_updated":"2026-04-21T18:11:19Z","snapshot_observed_at":"2026-07-06T23:06:26.596990Z","submitted_at":"2026-04-21T18:11:19Z","title":"Quantum-to-Classical Computability Transition via Negative Markov Chains","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-05-10T02:30:01.593171Z"},"links":{"citing_paper":"/paper/2604.19889"},"observation_digest":"sha256:acba73ecb00cb2fbc2f7808e60ab9ff15daa36a13098114bccf859697d00b5c5","observation_id":"b9dda432-7cac-4570-972b-589a8e5c686b","resolution":{"observed_at":"2026-05-22T21:57:11.839510Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+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":"2026-06-05T21:23:00.469572Z","title":"quantum supremacy","venue":null,"work_id":"a942383e-3bf5-4532-9549-d2b14a94d701","year":2021},"citing_paper":{"arxiv_id":"2604.19889","last_updated":"2026-04-21T18:11:19Z","snapshot_observed_at":"2026-07-06T23:06:26.596990Z","submitted_at":"2026-04-21T18:11:19Z","title":"Quantum-to-Classical Computability Transition via Negative Markov Chains","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-05-10T02:30:01.593171Z"},"links":{"citing_paper":"/paper/2604.19889"},"observation_digest":"sha256:23e224b89384deb2b08355da0d358f106b13c2f622555622583d391822092566","observation_id":"cde3d15d-35de-472c-ae9f-9cb8ef381a61","resolution":{"observed_at":"2026-05-22T21:57:11.785171Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+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":"2026-06-05T21:23:00.469572Z","title":"Tindall, M","venue":null,"work_id":"7dacb70e-308c-4fe8-9dee-fec9add6f954","year":2024},"citing_paper":{"arxiv_id":"2604.19889","last_updated":"2026-04-21T18:11:19Z","snapshot_observed_at":"2026-07-06T23:06:26.596990Z","submitted_at":"2026-04-21T18:11:19Z","title":"Quantum-to-Classical Computability Transition via Negative Markov Chains","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-05-10T02:30:01.593171Z"},"links":{"citing_paper":"/paper/2604.19889"},"observation_digest":"sha256:efd1e6fb7131ea37820c53b894b0798ee65b2e1fe696e03c11c2ee6d48341529","observation_id":"e54eb8a3-1394-45e5-8123-016f3b2c8aad","resolution":{"observed_at":"2026-05-22T21:57:11.835949Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+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":"2026-06-05T21:23:00.469572Z","title":"Begušić, J","venue":null,"work_id":"5a2fc9ec-76e0-4d13-9415-5e142fe52d18","year":2024},"citing_paper":{"arxiv_id":"2604.19889","last_updated":"2026-04-21T18:11:19Z","snapshot_observed_at":"2026-07-06T23:06:26.596990Z","submitted_at":"2026-04-21T18:11:19Z","title":"Quantum-to-Classical Computability Transition via Negative Markov Chains","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-05-10T02:30:01.593171Z"},"links":{"citing_paper":"/paper/2604.19889"},"observation_digest":"sha256:a7c7cd105e09444158f54e05e95ccba63159cdee1bc23d7073adff1163318e78","observation_id":"e8520902-6f57-4c84-9080-2baeba800af3","resolution":{"observed_at":"2026-05-22T21:57:11.755006Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+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":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"656628c3-50d6-445c-94d3-4584b04e1116","year":2022},"citing_paper":{"arxiv_id":"2604.19889","last_updated":"2026-04-21T18:11:19Z","snapshot_observed_at":"2026-07-06T23:06:26.596990Z","submitted_at":"2026-04-21T18:11:19Z","title":"Quantum-to-Classical Computability Transition via Negative Markov Chains","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-05-10T02:30:01.593171Z"},"links":{"citing_paper":"/paper/2604.19889"},"observation_digest":"sha256:98588419b98a03f71de10507cfb7d768f728723d94833c373edb22d5b4d83b82","observation_id":"fb88e6c7-8677-4570-bea2-7fc0c36b5fec","resolution":{"observed_at":"2026-05-22T21:57:11.744346Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+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":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"b4fc61c7-e101-48b4-a42f-92d85f0db55c","year":2024},"citing_paper":{"arxiv_id":"2604.19889","last_updated":"2026-04-21T18:11:19Z","snapshot_observed_at":"2026-07-06T23:06:26.596990Z","submitted_at":"2026-04-21T18:11:19Z","title":"Quantum-to-Classical Computability Transition via Negative Markov Chains","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-05-10T02:30:01.593171Z"},"links":{"citing_paper":"/paper/2604.19889"},"observation_digest":"sha256:5f9f459542abf1708d28b017c0329bdfd760063a4ccf2f38877034234e4fcdd4","observation_id":"af50f098-8392-42c1-b6fa-2777fd9eba97","resolution":{"observed_at":"2026-05-22T21:57:11.828544Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2503.08247","last_updated":"2025-03-11T10:09:37Z","snapshot_observed_at":"2026-07-06T20:50:33.513259Z","submitted_at":"2025-03-11T10:09:37Z","title":"Challenging the Quantum Advantage Frontier with Large-Scale Classical Simulations of Annealing Dynamics","version":1},"cited_work":{"arxiv_id":"2503.08247","doi":"10.48550/arxiv.2503.08247","metadata_source":"pith","pith_arxiv_id":"2503.08247","snapshot_observed_at":"2026-07-10T21:57:37.293512Z","title":"Mauron and G","venue":"quant-ph","work_id":"5b75608d-2c0d-4e94-8639-9e508331d349","year":2025},"citing_paper":{"arxiv_id":"2604.19889","last_updated":"2026-04-21T18:11:19Z","snapshot_observed_at":"2026-07-06T23:06:26.596990Z","submitted_at":"2026-04-21T18:11:19Z","title":"Quantum-to-Classical Computability Transition via Negative Markov Chains","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-05-10T02:30:01.593171Z"},"links":{"cited_paper":"/paper/2503.08247","citing_paper":"/paper/2604.19889"},"observation_digest":"sha256:03594dfdf0bd38ed99d4bd53501fb22722a7149bd2da651c8cce45b68592c6f4","observation_id":"4077b6fd-28c3-42cb-898c-b2f50cd99b11","resolution":{"observed_at":"2026-05-11T13:01:04.643694Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2503.05693","last_updated":"2026-05-27T20:25:50Z","snapshot_observed_at":"2026-07-06T20:48:45.592525Z","submitted_at":"2025-03-07T18:58:03Z","title":"Dynamics of disordered quantum systems with two- and three-dimensional tensor networks","version":4},"cited_work":{"arxiv_id":"2503.05693","doi":null,"metadata_source":"pith","pith_arxiv_id":"2503.05693","snapshot_observed_at":"2026-07-04T05:49:37.855550Z","title":"Tindall, A","venue":"quant-ph","work_id":"5aa96b39-3e5e-4bc0-80f6-599c72d97a6b","year":2025},"citing_paper":{"arxiv_id":"2604.19889","last_updated":"2026-04-21T18:11:19Z","snapshot_observed_at":"2026-07-06T23:06:26.596990Z","submitted_at":"2026-04-21T18:11:19Z","title":"Quantum-to-Classical Computability Transition via Negative Markov Chains","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-05-10T02:30:01.593171Z"},"links":{"cited_paper":"/paper/2503.05693","citing_paper":"/paper/2604.19889"},"observation_digest":"sha256:ed00992c51477afcaa4303dbcd9e844062c2b16e0184a6612d8c11d650f4bd61","observation_id":"e2ab52ec-03fd-40b1-88c9-14e4234dadef","resolution":{"observed_at":"2026-05-29T02:04:38.744947Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+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":"2026-06-05T21:23:00.469572Z","title":"Hosseinabadi, O","venue":null,"work_id":"b40c9f1d-7c72-4177-a81d-eca031cdbabf","year":2025},"citing_paper":{"arxiv_id":"2604.19889","last_updated":"2026-04-21T18:11:19Z","snapshot_observed_at":"2026-07-06T23:06:26.596990Z","submitted_at":"2026-04-21T18:11:19Z","title":"Quantum-to-Classical Computability Transition via Negative Markov Chains","version":1},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-05-10T02:30:01.593171Z"},"links":{"citing_paper":"/paper/2604.19889"},"observation_digest":"sha256:5f385e71b35cfad840c8debfc185b14e705632f7e3dd3a3dff67d420cdffc5fd","observation_id":"720736e5-d8f6-4fac-9c9d-eea801167296","resolution":{"observed_at":"2026-05-22T21:57:11.781493Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"quant-ph/9611028","last_updated":"1996-11-17T16:40:20Z","snapshot_observed_at":"2026-07-07T07:26:30.090183Z","submitted_at":"1996-11-17T16:40:20Z","title":"Limitations of Noisy Reversible Computation","version":1},"cited_work":{"arxiv_id":"quant-ph/9611028","doi":null,"metadata_source":"pith","pith_arxiv_id":"quant-ph/9611028","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Limitations of Noisy Reversible Computation","venue":"quant-ph","work_id":"c0eadea5-7014-4bf7-8052-518a25ea989f","year":1996},"citing_paper":{"arxiv_id":"2604.19889","last_updated":"2026-04-21T18:11:19Z","snapshot_observed_at":"2026-07-06T23:06:26.596990Z","submitted_at":"2026-04-21T18:11:19Z","title":"Quantum-to-Classical Computability Transition via Negative Markov Chains","version":1},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-05-10T02:30:01.593171Z"},"links":{"cited_paper":"/paper/quant-ph/9611028","citing_paper":"/paper/2604.19889"},"observation_digest":"sha256:3adeefcc6e2d5c4d903862b8faf61a3f23757c0beea740d59ac3d6f4c25cc5c2","observation_id":"286dda98-00f6-4b30-b864-da86b2609a7c","resolution":{"observed_at":"2026-05-11T13:01:04.585970Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+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":"2026-06-05T21:23:00.469572Z","title":"Aharonov, X","venue":null,"work_id":"0580b329-715d-4d47-bb2a-dada5574f4e0","year":2023},"citing_paper":{"arxiv_id":"2604.19889","last_updated":"2026-04-21T18:11:19Z","snapshot_observed_at":"2026-07-06T23:06:26.596990Z","submitted_at":"2026-04-21T18:11:19Z","title":"Quantum-to-Classical Computability Transition via Negative Markov Chains","version":1},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-05-10T02:30:01.593171Z"},"links":{"citing_paper":"/paper/2604.19889"},"observation_digest":"sha256:e425a48a64a3d7356f2fbb68dcdfae8490dda86eaff4fe9a633db416180437d4","observation_id":"6e8edbdb-ab1e-439f-b681-c04a7d0acd13","resolution":{"observed_at":"2026-05-22T21:57:11.747874Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+00:00","source":"retraction_watch"}],"state":"measured"}},{"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":"2407.12768","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2407.12768","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"A polynomial-time classical algorithm for noisy quantum circuits","venue":null,"work_id":"4e55afdd-5b17-487d-afd8-04a7cf1a1315","year":2024},"citing_paper":{"arxiv_id":"2604.19889","last_updated":"2026-04-21T18:11:19Z","snapshot_observed_at":"2026-07-06T23:06:26.596990Z","submitted_at":"2026-04-21T18:11:19Z","title":"Quantum-to-Classical Computability Transition via Negative Markov Chains","version":1},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-05-10T02:30:01.593171Z"},"links":{"cited_paper":"/paper/2407.12768","citing_paper":"/paper/2604.19889"},"observation_digest":"sha256:b0b18b3f590602458c5812666705478521418b33f46292c18012e01c27a41df4","observation_id":"85f2ad64-70ac-4b8a-b01a-735fc26b11ff","resolution":{"observed_at":"2026-05-11T13:01:04.594670Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+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":"2026-06-05T21:23:00.469572Z","title":"Trivedi and J","venue":null,"work_id":"e4b75338-79b0-41fe-b5b6-d40b3deea672","year":2022},"citing_paper":{"arxiv_id":"2604.19889","last_updated":"2026-04-21T18:11:19Z","snapshot_observed_at":"2026-07-06T23:06:26.596990Z","submitted_at":"2026-04-21T18:11:19Z","title":"Quantum-to-Classical Computability Transition via Negative Markov Chains","version":1},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-05-10T02:30:01.593171Z"},"links":{"citing_paper":"/paper/2604.19889"},"observation_digest":"sha256:39c1861615d529588c8a069218cd2fb2d20a5fde77b2e401997c31084b6e2e1b","observation_id":"d8d85b65-5804-46fa-bb38-520d7c85ce92","resolution":{"observed_at":"2026-05-22T21:57:11.733202Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+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":"2026-06-05T21:23:00.469572Z","title":"Rajakumar, J","venue":null,"work_id":"953516b8-4037-4087-9d6d-b5c1155cac83","year":2025},"citing_paper":{"arxiv_id":"2604.19889","last_updated":"2026-04-21T18:11:19Z","snapshot_observed_at":"2026-07-06T23:06:26.596990Z","submitted_at":"2026-04-21T18:11:19Z","title":"Quantum-to-Classical Computability Transition via Negative Markov Chains","version":1},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-05-10T02:30:01.593171Z"},"links":{"citing_paper":"/paper/2604.19889"},"observation_digest":"sha256:10e9ce7b363760137b480590094857f6c2d093c760ae51224600bda9028e163e","observation_id":"d1df94c9-7012-4da1-95ca-a1e6866ee3af","resolution":{"observed_at":"2026-05-22T21:57:11.777625Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":"2411.02535","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Nelson, J","venue":null,"work_id":"ea9f6cac-7348-41ee-b4e6-b4706474d9b5","year":2024},"citing_paper":{"arxiv_id":"2604.19889","last_updated":"2026-04-21T18:11:19Z","snapshot_observed_at":"2026-07-06T23:06:26.596990Z","submitted_at":"2026-04-21T18:11:19Z","title":"Quantum-to-Classical Computability Transition via Negative Markov Chains","version":1},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-05-10T02:30:01.593171Z"},"links":{"citing_paper":"/paper/2604.19889"},"observation_digest":"sha256:2f8dbc460bbfa454379ebb3ed0cd8beb06ecf2548945f0e51bf3145234aad467","observation_id":"6602011a-d62b-47f9-8a2e-baa7bee2e796","resolution":{"observed_at":"2026-05-11T13:01:04.575345Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+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":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"8eadc4ab-5879-4df0-b7b3-d7897dc1d9e5","year":2025},"citing_paper":{"arxiv_id":"2604.19889","last_updated":"2026-04-21T18:11:19Z","snapshot_observed_at":"2026-07-06T23:06:26.596990Z","submitted_at":"2026-04-21T18:11:19Z","title":"Quantum-to-Classical Computability Transition via Negative Markov Chains","version":1},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-05-10T02:30:01.593171Z"},"links":{"citing_paper":"/paper/2604.19889"},"observation_digest":"sha256:4a8fd7d8ce374a44100c260dece3bd4fd2ff5ba32f6adcca5826bf470e012457","observation_id":"eb62df66-9bc0-47a6-8576-ed4728e44d82","resolution":{"observed_at":"2026-05-22T21:57:11.759056Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+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":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"90dade60-9f4b-407a-bd52-fc58bbdbbcc2","year":1990},"citing_paper":{"arxiv_id":"2604.19889","last_updated":"2026-04-21T18:11:19Z","snapshot_observed_at":"2026-07-06T23:06:26.596990Z","submitted_at":"2026-04-21T18:11:19Z","title":"Quantum-to-Classical Computability Transition via Negative Markov Chains","version":1},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-05-10T02:30:01.593171Z"},"links":{"citing_paper":"/paper/2604.19889"},"observation_digest":"sha256:20ef6e47e93ad1369068bcad55d3b97180642c0421fef5e2ba8251a0b43457e0","observation_id":"aee269fd-087f-458d-81fb-adb7045038d9","resolution":{"observed_at":"2026-05-22T21:57:11.629364Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+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":"2026-06-05T21:23:00.469572Z","title":"Troyer and U.-J","venue":null,"work_id":"382d178d-aead-4d85-afa1-3f326579ed56","year":2005},"citing_paper":{"arxiv_id":"2604.19889","last_updated":"2026-04-21T18:11:19Z","snapshot_observed_at":"2026-07-06T23:06:26.596990Z","submitted_at":"2026-04-21T18:11:19Z","title":"Quantum-to-Classical Computability Transition via Negative Markov Chains","version":1},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-05-10T02:30:01.593171Z"},"links":{"citing_paper":"/paper/2604.19889"},"observation_digest":"sha256:4654916fe96348300a7a684037b672cb521728cabad1b31086b68606627361c2","observation_id":"8d079091-1799-49fc-aafb-db260b42a965","resolution":{"observed_at":"2026-05-22T21:57:11.774293Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+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":"2026-06-05T21:23:00.469572Z","title":"Chandrasekharan and U.-J","venue":null,"work_id":"8e273848-cf46-4354-9d03-7db7bf197a98","year":1999},"citing_paper":{"arxiv_id":"2604.19889","last_updated":"2026-04-21T18:11:19Z","snapshot_observed_at":"2026-07-06T23:06:26.596990Z","submitted_at":"2026-04-21T18:11:19Z","title":"Quantum-to-Classical Computability Transition via Negative Markov Chains","version":1},"reference_index":38,"source":"pdf_text","source_observed_at":"2026-05-10T02:30:01.593171Z"},"links":{"citing_paper":"/paper/2604.19889"},"observation_digest":"sha256:544d676f3280adf8c56849add98b35b38e41291611b787fd6adf27513fdb328a","observation_id":"789de320-cf50-44a2-b307-f1f9a051164f","resolution":{"observed_at":"2026-05-22T21:57:11.642356Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+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":"2026-06-05T21:23:00.469572Z","title":"Li, Y.-F","venue":null,"work_id":"05b0a204-a452-4f24-b885-bfd6c9160a06","year":2015},"citing_paper":{"arxiv_id":"2604.19889","last_updated":"2026-04-21T18:11:19Z","snapshot_observed_at":"2026-07-06T23:06:26.596990Z","submitted_at":"2026-04-21T18:11:19Z","title":"Quantum-to-Classical Computability Transition via Negative Markov Chains","version":1},"reference_index":39,"source":"pdf_text","source_observed_at":"2026-05-10T02:30:01.593171Z"},"links":{"citing_paper":"/paper/2604.19889"},"observation_digest":"sha256:a669c4f412aad269953bfd80861d070416703ca6989c638a4ecaacce387a11cf","observation_id":"108d46cb-0c20-4753-b5a4-46648a02272c","resolution":{"observed_at":"2026-05-22T21:57:11.652993Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+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":"2026-06-05T21:23:00.469572Z","title":"Marvian, D","venue":null,"work_id":"26000d6c-3fc2-4f11-aec9-fa0f65e47690","year":2019},"citing_paper":{"arxiv_id":"2604.19889","last_updated":"2026-04-21T18:11:19Z","snapshot_observed_at":"2026-07-06T23:06:26.596990Z","submitted_at":"2026-04-21T18:11:19Z","title":"Quantum-to-Classical Computability Transition via Negative Markov Chains","version":1},"reference_index":40,"source":"pdf_text","source_observed_at":"2026-05-10T02:30:01.593171Z"},"links":{"citing_paper":"/paper/2604.19889"},"observation_digest":"sha256:3d93a41f600869e05d01a0eff338380d7fd3f8e458ccb664836044e43f41cc2a","observation_id":"8e901def-9280-4d75-a8d7-51344c8176bd","resolution":{"observed_at":"2026-05-22T21:57:11.710382Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+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":"2026-06-05T21:23:00.469572Z","title":"Völlering, Markov process representation of semigroups whose generators include negative rates, Electronic Com- munications in Probability25, 1 (2020)","venue":null,"work_id":"837d54dc-e895-47a0-a1ba-ba4ff8d6a250","year":2020},"citing_paper":{"arxiv_id":"2604.19889","last_updated":"2026-04-21T18:11:19Z","snapshot_observed_at":"2026-07-06T23:06:26.596990Z","submitted_at":"2026-04-21T18:11:19Z","title":"Quantum-to-Classical Computability Transition via Negative Markov Chains","version":1},"reference_index":41,"source":"pdf_text","source_observed_at":"2026-05-10T02:30:01.593171Z"},"links":{"citing_paper":"/paper/2604.19889"},"observation_digest":"sha256:43702fa96aa1b6b1c242d5598519b0a18e9ffde95a409dd21fc65bf059b51cef","observation_id":"1801beb5-0dc4-46b1-965d-c055dc38f6ea","resolution":{"observed_at":"2026-05-22T21:57:11.810144Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2502.10502","last_updated":"2026-06-09T18:36:08Z","snapshot_observed_at":"2026-07-06T20:36:50.081370Z","submitted_at":"2025-02-14T19:00:11Z","title":"Classical representation of the dynamics of quantum spin chains","version":3},"cited_work":{"arxiv_id":"2502.10502","doi":null,"metadata_source":"pith","pith_arxiv_id":"2502.10502","snapshot_observed_at":"2026-07-03T11:58:05.581122Z","title":"Jin, Classical representation of the dynamics of quantum spin chains (2025), arXiv:2502.10502 [cond-mat.stat-mech]","venue":"cond-mat.stat-mech","work_id":"23b4a137-9bed-4345-a369-ad223bf851c0","year":2025},"citing_paper":{"arxiv_id":"2604.19889","last_updated":"2026-04-21T18:11:19Z","snapshot_observed_at":"2026-07-06T23:06:26.596990Z","submitted_at":"2026-04-21T18:11:19Z","title":"Quantum-to-Classical Computability Transition via Negative Markov Chains","version":1},"reference_index":42,"source":"pdf_text","source_observed_at":"2026-05-10T02:30:01.593171Z"},"links":{"cited_paper":"/paper/2502.10502","citing_paper":"/paper/2604.19889"},"observation_digest":"sha256:077d1b9e959f8a22fb54379e26e403043dd11af427586094709611c76c67e0a8","observation_id":"d7e8012f-1b5b-4bc8-a182-2c7ea117710c","resolution":{"observed_at":"2026-06-11T01:09:11.336651Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+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":"2026-07-10T10:17:01.778019Z","title":"Lindblad, On the generators of quantum dynamical semigroups, Communications in Mathematical Physics48, 119 (1976)","venue":null,"work_id":"e12ab725-469c-4b94-820f-1075f4151eb1","year":1976},"citing_paper":{"arxiv_id":"2604.19889","last_updated":"2026-04-21T18:11:19Z","snapshot_observed_at":"2026-07-06T23:06:26.596990Z","submitted_at":"2026-04-21T18:11:19Z","title":"Quantum-to-Classical Computability Transition via Negative Markov Chains","version":1},"reference_index":43,"source":"pdf_text","source_observed_at":"2026-05-10T02:30:01.593171Z"},"links":{"citing_paper":"/paper/2604.19889"},"observation_digest":"sha256:e308ff2f43847eb501870eeccb61c8edc2700aba9e8980ccc7e954450e1b92e3","observation_id":"9720721c-78c0-44d3-8816-f5e57e921395","resolution":{"observed_at":"2026-05-22T21:57:11.813991Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+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":"2026-06-05T21:23:00.469572Z","title":"Gorini, A","venue":null,"work_id":"d8301e39-01e1-4774-9382-b39ca8af0bcd","year":1976},"citing_paper":{"arxiv_id":"2604.19889","last_updated":"2026-04-21T18:11:19Z","snapshot_observed_at":"2026-07-06T23:06:26.596990Z","submitted_at":"2026-04-21T18:11:19Z","title":"Quantum-to-Classical Computability Transition via Negative Markov Chains","version":1},"reference_index":44,"source":"pdf_text","source_observed_at":"2026-05-10T02:30:01.593171Z"},"links":{"citing_paper":"/paper/2604.19889"},"observation_digest":"sha256:f4ad3dcff2334acf2b64690d9a941c0294abf7ec23d6a6e3c51f4458befd3a9c","observation_id":"995ff748-f10a-4e37-aae3-5ef31523d9b4","resolution":{"observed_at":"2026-05-22T21:57:11.649879Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+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":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"ef477092-de8c-476a-ab51-899877ec5781","year":null},"citing_paper":{"arxiv_id":"2604.19889","last_updated":"2026-04-21T18:11:19Z","snapshot_observed_at":"2026-07-06T23:06:26.596990Z","submitted_at":"2026-04-21T18:11:19Z","title":"Quantum-to-Classical Computability Transition via Negative Markov Chains","version":1},"reference_index":45,"source":"pdf_text","source_observed_at":"2026-05-10T02:30:01.593171Z"},"links":{"citing_paper":"/paper/2604.19889"},"observation_digest":"sha256:ff6bf599035324e2680b95655f59cab8117775b10a21244a9a8df5630cfd06f1","observation_id":"15becd90-2a0c-4d64-9f93-71b234446179","resolution":{"observed_at":"2026-05-22T21:57:11.617123Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+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":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"03fdfd1c-77ca-4964-9441-eed6ba1b0257","year":1963},"citing_paper":{"arxiv_id":"2604.19889","last_updated":"2026-04-21T18:11:19Z","snapshot_observed_at":"2026-07-06T23:06:26.596990Z","submitted_at":"2026-04-21T18:11:19Z","title":"Quantum-to-Classical Computability Transition via Negative Markov Chains","version":1},"reference_index":46,"source":"pdf_text","source_observed_at":"2026-05-10T02:30:01.593171Z"},"links":{"citing_paper":"/paper/2604.19889"},"observation_digest":"sha256:7eecddb926f588f1aa2d5238ccda0f5beac3de8ff9e2a4ce66895be2ebe92b31","observation_id":"a755792d-fbae-47a1-8b3f-d272f92492a8","resolution":{"observed_at":"2026-05-22T21:57:11.638812Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+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":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"7536295e-c0d2-46e1-87e4-1e897bb3c586","year":1977},"citing_paper":{"arxiv_id":"2604.19889","last_updated":"2026-04-21T18:11:19Z","snapshot_observed_at":"2026-07-06T23:06:26.596990Z","submitted_at":"2026-04-21T18:11:19Z","title":"Quantum-to-Classical Computability Transition via Negative Markov Chains","version":1},"reference_index":47,"source":"pdf_text","source_observed_at":"2026-05-10T02:30:01.593171Z"},"links":{"citing_paper":"/paper/2604.19889"},"observation_digest":"sha256:7e6efd37092140dd6b1ad16c1dbb18b23350ea77c78b3f75c159a199a0cefd9e","observation_id":"04d91af2-89fa-4e5e-aa84-64b472186629","resolution":{"observed_at":"2026-05-22T21:57:11.671067Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+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":"2026-06-05T21:23:00.469572Z","title":"The conservation of probability for the matrix Mtranslates into ⃗1T M= 0, which is equivalent to L∗P C PC = 0","venue":null,"work_id":"1687521d-70d6-4f9f-abb4-56ef8d9af04b","year":null},"citing_paper":{"arxiv_id":"2604.19889","last_updated":"2026-04-21T18:11:19Z","snapshot_observed_at":"2026-07-06T23:06:26.596990Z","submitted_at":"2026-04-21T18:11:19Z","title":"Quantum-to-Classical Computability Transition via Negative Markov Chains","version":1},"reference_index":48,"source":"pdf_text","source_observed_at":"2026-05-10T02:30:01.593171Z"},"links":{"citing_paper":"/paper/2604.19889"},"observation_digest":"sha256:f8ffff3a59c3e6c839c30c12bef51c8e58e373d1b4c62d7114f05929ff567b39","observation_id":"bb6241cc-ecac-4e4c-94ba-e267440b5738","resolution":{"observed_at":"2026-05-22T21:57:11.751555Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+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":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"ea576b74-629c-420d-9d70-b53221e64e1f","year":null},"citing_paper":{"arxiv_id":"2604.19889","last_updated":"2026-04-21T18:11:19Z","snapshot_observed_at":"2026-07-06T23:06:26.596990Z","submitted_at":"2026-04-21T18:11:19Z","title":"Quantum-to-Classical Computability Transition via Negative Markov Chains","version":1},"reference_index":49,"source":"pdf_text","source_observed_at":"2026-05-10T02:30:01.593171Z"},"links":{"citing_paper":"/paper/2604.19889"},"observation_digest":"sha256:37d17c43a356d0613fd3f9d200116ffe3fc288e405633873a91af25c98135093","observation_id":"5ff86d8e-9410-4fda-9d0a-58fa7f2784e7","resolution":{"observed_at":"2026-05-22T21:57:11.849282Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+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":"2026-06-05T21:23:00.469572Z","title":"Indeed, finding the optimal gauge is generally necessary to observe the cor- rect transition to classicality","venue":null,"work_id":"329645c7-9a95-42ab-8a09-4098660967f2","year":null},"citing_paper":{"arxiv_id":"2604.19889","last_updated":"2026-04-21T18:11:19Z","snapshot_observed_at":"2026-07-06T23:06:26.596990Z","submitted_at":"2026-04-21T18:11:19Z","title":"Quantum-to-Classical Computability Transition via Negative Markov Chains","version":1},"reference_index":50,"source":"pdf_text","source_observed_at":"2026-05-10T02:30:01.593171Z"},"links":{"citing_paper":"/paper/2604.19889"},"observation_digest":"sha256:356ab494319bb7822c0b229f4353c7cef98eb56f9b213a22320e5a099a492547","observation_id":"b6508093-52a6-4286-a0e1-94f5f56e5fb8","resolution":{"observed_at":"2026-05-22T21:57:11.792375Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+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":"2026-06-05T21:23:00.469572Z","title":"Chitambar and G","venue":null,"work_id":"721ca662-e1cf-4522-99eb-c26bccc0f6c4","year":2019},"citing_paper":{"arxiv_id":"2604.19889","last_updated":"2026-04-21T18:11:19Z","snapshot_observed_at":"2026-07-06T23:06:26.596990Z","submitted_at":"2026-04-21T18:11:19Z","title":"Quantum-to-Classical Computability Transition via Negative Markov Chains","version":1},"reference_index":51,"source":"pdf_text","source_observed_at":"2026-05-10T02:30:01.593171Z"},"links":{"citing_paper":"/paper/2604.19889"},"observation_digest":"sha256:2b4ae41eec39e15ebfb00be92d105ff53d20caf6d77f2dce3d79c339e8ffa429","observation_id":"beb5ee68-7a50-408c-9c11-8dee2d05d9a3","resolution":{"observed_at":"2026-05-22T21:57:11.843483Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+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":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"94c596b0-4a96-4989-9326-86abe26b9fd6","year":2022},"citing_paper":{"arxiv_id":"2604.19889","last_updated":"2026-04-21T18:11:19Z","snapshot_observed_at":"2026-07-06T23:06:26.596990Z","submitted_at":"2026-04-21T18:11:19Z","title":"Quantum-to-Classical Computability Transition via Negative Markov Chains","version":1},"reference_index":52,"source":"pdf_text","source_observed_at":"2026-05-10T02:30:01.593171Z"},"links":{"citing_paper":"/paper/2604.19889"},"observation_digest":"sha256:02f6ea7288fb76fe9eee7b9bc0cc2cd6b51f5a85e957c674a3d2b4c605386b36","observation_id":"ca500183-c2be-4b95-a32d-2280cb7627bc","resolution":{"observed_at":"2026-05-22T21:57:11.805912Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+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":"2026-06-05T21:23:00.469572Z","title":"Leone, S","venue":null,"work_id":"d5a6be7a-7dde-418b-9064-1af22c8a2cb4","year":2022},"citing_paper":{"arxiv_id":"2604.19889","last_updated":"2026-04-21T18:11:19Z","snapshot_observed_at":"2026-07-06T23:06:26.596990Z","submitted_at":"2026-04-21T18:11:19Z","title":"Quantum-to-Classical Computability Transition via Negative Markov Chains","version":1},"reference_index":53,"source":"pdf_text","source_observed_at":"2026-05-10T02:30:01.593171Z"},"links":{"citing_paper":"/paper/2604.19889"},"observation_digest":"sha256:d0fc4e0415a5b98b1b7f3575c41c388c2b7efaaea3ce4495b1fc19e37ec804ad","observation_id":"0594251b-e933-4744-85bd-94c53d651169","resolution":{"observed_at":"2026-05-22T21:57:11.821274Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+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":"2026-06-05T21:23:00.469572Z","title":"Leone and L","venue":null,"work_id":"32cc365a-aad8-463e-952e-9f5f1a5dc7d2","year":2024},"citing_paper":{"arxiv_id":"2604.19889","last_updated":"2026-04-21T18:11:19Z","snapshot_observed_at":"2026-07-06T23:06:26.596990Z","submitted_at":"2026-04-21T18:11:19Z","title":"Quantum-to-Classical Computability Transition via Negative Markov Chains","version":1},"reference_index":54,"source":"pdf_text","source_observed_at":"2026-05-10T02:30:01.593171Z"},"links":{"citing_paper":"/paper/2604.19889"},"observation_digest":"sha256:8618e978c9be6cfb0fe53fe25381c55a7017f5804659fe8f281672b41c02cfe4","observation_id":"324441ce-fa14-4763-bb71-b052f44c90cf","resolution":{"observed_at":"2026-05-22T21:57:11.740412Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+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":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"be06677d-6974-4406-8a46-a15211f8aaa3","year":1992},"citing_paper":{"arxiv_id":"2604.19889","last_updated":"2026-04-21T18:11:19Z","snapshot_observed_at":"2026-07-06T23:06:26.596990Z","submitted_at":"2026-04-21T18:11:19Z","title":"Quantum-to-Classical Computability Transition via Negative Markov Chains","version":1},"reference_index":55,"source":"pdf_text","source_observed_at":"2026-05-10T02:30:01.593171Z"},"links":{"citing_paper":"/paper/2604.19889"},"observation_digest":"sha256:0d8c801624aeb4ec3e809097a3788ea9944f3cf40c854046cb5edd99e616a6b4","observation_id":"84579b56-c059-4123-af6f-cb94bb23a2ac","resolution":{"observed_at":"2026-05-22T21:57:11.706782Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+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":"2026-06-05T21:23:00.469572Z","title":"Orús, A practical introduction to tensor networks: Mat- rix product states and projected entangled pair states, An- nals of Physics349, 117 (2014)","venue":null,"work_id":"9f17ba38-f193-4feb-9c9f-0a73dd3c9454","year":2014},"citing_paper":{"arxiv_id":"2604.19889","last_updated":"2026-04-21T18:11:19Z","snapshot_observed_at":"2026-07-06T23:06:26.596990Z","submitted_at":"2026-04-21T18:11:19Z","title":"Quantum-to-Classical Computability Transition via Negative Markov Chains","version":1},"reference_index":56,"source":"pdf_text","source_observed_at":"2026-05-10T02:30:01.593171Z"},"links":{"citing_paper":"/paper/2604.19889"},"observation_digest":"sha256:ddb62be328224ebe9dbd3066c0b1d4ce65b94f1d80daac71a98fba763f251f6c","observation_id":"07c143dc-890e-47ff-9b93-67fdb4bebb32","resolution":{"observed_at":"2026-05-22T21:57:11.702552Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+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":"2026-06-05T21:23:00.469572Z","title":"Doucet, N","venue":null,"work_id":"94e47861-7cd4-444e-aa92-a94cbf759b8f","year":2001},"citing_paper":{"arxiv_id":"2604.19889","last_updated":"2026-04-21T18:11:19Z","snapshot_observed_at":"2026-07-06T23:06:26.596990Z","submitted_at":"2026-04-21T18:11:19Z","title":"Quantum-to-Classical Computability Transition via Negative Markov Chains","version":1},"reference_index":57,"source":"pdf_text","source_observed_at":"2026-05-10T02:30:01.593171Z"},"links":{"citing_paper":"/paper/2604.19889"},"observation_digest":"sha256:bc5c465151f1298ee84363b41c43031839d90601e29061264b83597dddc7af4d","observation_id":"5d64dd22-8833-4621-a15b-48bb02c4a616","resolution":{"observed_at":"2026-05-22T21:57:11.770808Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+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":"2026-06-05T21:23:00.469572Z","title":"Del Moral, Mean field simulation for monte carlo integ- ration (2013)","venue":null,"work_id":"7ba3e111-762c-4063-ae1f-aa204ca42b03","year":2013},"citing_paper":{"arxiv_id":"2604.19889","last_updated":"2026-04-21T18:11:19Z","snapshot_observed_at":"2026-07-06T23:06:26.596990Z","submitted_at":"2026-04-21T18:11:19Z","title":"Quantum-to-Classical Computability Transition via Negative Markov Chains","version":1},"reference_index":58,"source":"pdf_text","source_observed_at":"2026-05-10T02:30:01.593171Z"},"links":{"citing_paper":"/paper/2604.19889"},"observation_digest":"sha256:6d810a33c831ebff3bc6cead4f2089c62af60820fbcdee8bf21089596804015d","observation_id":"fa20ff73-bf82-415d-8e09-a248777a3273","resolution":{"observed_at":"2026-05-22T21:57:11.796234Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+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":"2026-06-05T21:23:00.469572Z","title":"Seidel and C","venue":null,"work_id":"593014c2-5024-4dbc-b320-3068f60fb6a4","year":1996},"citing_paper":{"arxiv_id":"2604.19889","last_updated":"2026-04-21T18:11:19Z","snapshot_observed_at":"2026-07-06T23:06:26.596990Z","submitted_at":"2026-04-21T18:11:19Z","title":"Quantum-to-Classical Computability Transition via Negative Markov Chains","version":1},"reference_index":59,"source":"pdf_text","source_observed_at":"2026-05-10T02:30:01.593171Z"},"links":{"citing_paper":"/paper/2604.19889"},"observation_digest":"sha256:1c59eb8460a69c9202d9dcba9a299956567cfd884d6700c99c8322a8d7f2aeba","observation_id":"f4883161-82ef-46d3-885f-5e301ef20e89","resolution":{"observed_at":"2026-05-22T21:57:11.824744Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+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":"2026-06-05T21:23:00.469572Z","title":"Apart from the creation rateVC, the other positive terms in (8), corresponding to particle influx, are implicitly handled by simulating the outflux events","venue":null,"work_id":"92ef0ac5-ac86-4cc0-a603-2667591a308f","year":null},"citing_paper":{"arxiv_id":"2604.19889","last_updated":"2026-04-21T18:11:19Z","snapshot_observed_at":"2026-07-06T23:06:26.596990Z","submitted_at":"2026-04-21T18:11:19Z","title":"Quantum-to-Classical Computability Transition via Negative Markov Chains","version":1},"reference_index":60,"source":"pdf_text","source_observed_at":"2026-05-10T02:30:01.593171Z"},"links":{"citing_paper":"/paper/2604.19889"},"observation_digest":"sha256:10624670410c8d5ef6011032511f76205968c565c00b4d07a22137457d57c62d","observation_id":"30af85c2-bbd2-4208-8a09-feda5b969e4c","resolution":{"observed_at":"2026-05-22T21:57:11.802130Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+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":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"b99831f3-3f2c-4906-8e7c-e193277b6a8c","year":null},"citing_paper":{"arxiv_id":"2604.19889","last_updated":"2026-04-21T18:11:19Z","snapshot_observed_at":"2026-07-06T23:06:26.596990Z","submitted_at":"2026-04-21T18:11:19Z","title":"Quantum-to-Classical Computability Transition via Negative Markov Chains","version":1},"reference_index":61,"source":"pdf_text","source_observed_at":"2026-05-10T02:30:01.593171Z"},"links":{"citing_paper":"/paper/2604.19889"},"observation_digest":"sha256:31ced91e044e0d57e26203e61fd83081bd96c84df118b124b844f1ba10247917","observation_id":"2760af93-401f-4956-b523-d6310c6d9235","resolution":{"observed_at":"2026-05-22T21:57:11.686531Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+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":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"99e1a035-ffa7-4d4f-ade9-6bcbbdb3c0ec","year":null},"citing_paper":{"arxiv_id":"2604.19889","last_updated":"2026-04-21T18:11:19Z","snapshot_observed_at":"2026-07-06T23:06:26.596990Z","submitted_at":"2026-04-21T18:11:19Z","title":"Quantum-to-Classical Computability Transition via Negative Markov Chains","version":1},"reference_index":62,"source":"pdf_text","source_observed_at":"2026-05-10T02:30:01.593171Z"},"links":{"citing_paper":"/paper/2604.19889"},"observation_digest":"sha256:8e3d6946cea3bcd64fa2afd202fc0ff337859d39ad5f8f45128732d5933898b2","observation_id":"d8e99600-a334-42d4-9bf8-fe80c44ed549","resolution":{"observed_at":"2026-05-22T21:57:11.788708Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+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":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"b9314132-ea9f-45fc-8dbb-4abb8d7a7d6f","year":null},"citing_paper":{"arxiv_id":"2604.19889","last_updated":"2026-04-21T18:11:19Z","snapshot_observed_at":"2026-07-06T23:06:26.596990Z","submitted_at":"2026-04-21T18:11:19Z","title":"Quantum-to-Classical Computability Transition via Negative Markov Chains","version":1},"reference_index":63,"source":"pdf_text","source_observed_at":"2026-05-10T02:30:01.593171Z"},"links":{"citing_paper":"/paper/2604.19889"},"observation_digest":"sha256:f9bf5a8edb23ce22345d88915835d3da9947bca95f97849a457df5673bc6df58","observation_id":"d4baa28c-8c16-4fee-be49-b94d75ac966d","resolution":{"observed_at":"2026-05-22T21:57:11.698164Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+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":"2026-06-05T21:23:00.469572Z","title":"(a) If the sign+was chosen, simply move the particle to configurationC′","venue":null,"work_id":"66e8e857-82bb-4e84-ae00-8d45ba536b18","year":null},"citing_paper":{"arxiv_id":"2604.19889","last_updated":"2026-04-21T18:11:19Z","snapshot_observed_at":"2026-07-06T23:06:26.596990Z","submitted_at":"2026-04-21T18:11:19Z","title":"Quantum-to-Classical Computability Transition via Negative Markov Chains","version":1},"reference_index":64,"source":"pdf_text","source_observed_at":"2026-05-10T02:30:01.593171Z"},"links":{"citing_paper":"/paper/2604.19889"},"observation_digest":"sha256:a828533c52f2a0badccd44fe898097a3863286c767c5fce94ae4dd62ec0a538d","observation_id":"1abb9e1b-fbe3-4621-8fbe-2435bf514191","resolution":{"observed_at":"2026-05-22T21:57:11.678978Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+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":"2026-06-05T21:23:00.469572Z","title":"Essentially, for any given initial stateρ 0, we need to be able to efficiently sample from the initial probability distributionp C(0) = tr(ρ 0PC)/3N","venue":null,"work_id":"1fd21802-5109-4597-b758-94a8b99b2e4d","year":null},"citing_paper":{"arxiv_id":"2604.19889","last_updated":"2026-04-21T18:11:19Z","snapshot_observed_at":"2026-07-06T23:06:26.596990Z","submitted_at":"2026-04-21T18:11:19Z","title":"Quantum-to-Classical Computability Transition via Negative Markov Chains","version":1},"reference_index":65,"source":"pdf_text","source_observed_at":"2026-05-10T02:30:01.593171Z"},"links":{"citing_paper":"/paper/2604.19889"},"observation_digest":"sha256:79f8f4556a0b8f022c0ca0cbbd9e008f55faa4b4726af60f58f48f280621b372","observation_id":"cb6d348d-9051-4b1f-96e8-7783b91d6c3d","resolution":{"observed_at":"2026-05-22T21:57:11.817583Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+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":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"e81b9b09-1c86-4f51-a88a-83b7bd727ad8","year":null},"citing_paper":{"arxiv_id":"2604.19889","last_updated":"2026-04-21T18:11:19Z","snapshot_observed_at":"2026-07-06T23:06:26.596990Z","submitted_at":"2026-04-21T18:11:19Z","title":"Quantum-to-Classical Computability Transition via Negative Markov Chains","version":1},"reference_index":66,"source":"pdf_text","source_observed_at":"2026-05-10T02:30:01.593171Z"},"links":{"citing_paper":"/paper/2604.19889"},"observation_digest":"sha256:3c86abd857e133977cfe7b78a9351f624cd10f6ddeb2ce8c9f888068033b1ddc","observation_id":"4bed58c1-c3ca-4cd1-adb2-465f26750873","resolution":{"observed_at":"2026-05-22T21:57:11.689975Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+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":"2026-06-05T21:23:00.469572Z","title":"The chosen particle configuration isC= (s1, β1","venue":null,"work_id":"8c1b1c4c-c733-42fc-a614-4876d1ace09b","year":null},"citing_paper":{"arxiv_id":"2604.19889","last_updated":"2026-04-21T18:11:19Z","snapshot_observed_at":"2026-07-06T23:06:26.596990Z","submitted_at":"2026-04-21T18:11:19Z","title":"Quantum-to-Classical Computability Transition via Negative Markov Chains","version":1},"reference_index":67,"source":"pdf_text","source_observed_at":"2026-05-10T02:30:01.593171Z"},"links":{"citing_paper":"/paper/2604.19889"},"observation_digest":"sha256:f79ae67943aca1497952c6b7fa114ef3036aac761c739ba0e30c8dc05884e983","observation_id":"31550a64-a7fc-4abc-94a0-e584825899a8","resolution":{"observed_at":"2026-05-22T21:57:11.682830Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+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":"2026-06-05T21:23:00.469572Z","title":"To do so, we expand the observable in terms of projectorsˆO= P C OCPC (the expansion is not unique)","venue":null,"work_id":"40c10e20-38c3-4758-8bf9-80d45054b527","year":null},"citing_paper":{"arxiv_id":"2604.19889","last_updated":"2026-04-21T18:11:19Z","snapshot_observed_at":"2026-07-06T23:06:26.596990Z","submitted_at":"2026-04-21T18:11:19Z","title":"Quantum-to-Classical Computability Transition via Negative Markov Chains","version":1},"reference_index":68,"source":"pdf_text","source_observed_at":"2026-05-10T02:30:01.593171Z"},"links":{"citing_paper":"/paper/2604.19889"},"observation_digest":"sha256:36152d3eb7d6967e4a036e67dadbaf1339fdaee748e89aad8e0d05bf54f575f3","observation_id":"31da2928-8d57-4fd5-9064-83c367face65","resolution":{"observed_at":"2026-05-22T21:57:11.694214Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2604.19889","last_updated":"2026-04-21T18:11:19Z","latest_version":1,"primary_category":"quant-ph","snapshot_observed_at":"2026-07-06T23:06:26.596990Z","submitted_at":"2026-04-21T18:11:19Z","title":"Quantum-to-Classical Computability Transition via Negative Markov Chains"},"reference_resolution":{"displayed":68,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":18,"verified_exact":10,"verified_fuzzy":40},"total_outbound_references":68},"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":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+00:00","source":"retraction_watch"}],"thesis":"As of 4 August 2026, this Paper Citation Record lists 68 of 68 outbound references and 1 inbound Pith citation observation for arXiv:2604.19889."}