{"as_of":"2026-08-09T14:24:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:66da4a72b49f5824f924296c8d259e123d258cbfe80d459e1dc1729d173acba9","coverage":[{"denominator":119,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":100,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-04T20:12:38.382792Z","state":"measured"},{"denominator":101,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":101,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-09T06:31:02.800959+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":"2026-06-28T14:27:33.470813Z","state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"arxiv_reference","source_observed_at":"2026-07-01T23:26:21.529269Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2509.08911","last_updated":"2025-09-10T18:15:41Z","snapshot_observed_at":"2026-08-08T00:35:55.880889Z","submitted_at":"2025-09-10T18:15:41Z","title":"Instance-Optimal Matrix Multiplicative Weight Update and Its Quantum Applications","version":1},"cited_work":{"arxiv_id":"2509.08911","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2509.08911","snapshot_observed_at":"2026-07-01T23:26:21.529269Z","title":"Instance-optimal matrix multiplicative weight update and its quantum applications","venue":null,"work_id":"1f0e299a-b539-4e79-9bcb-00c1691e5ebd","year":2025},"citing_paper":{"arxiv_id":"2606.02655","last_updated":"2026-06-01T05:06:12Z","snapshot_observed_at":"2026-08-08T08:43:43.712484Z","submitted_at":"2026-06-01T05:06:12Z","title":"Coherent Swap Regret and Channel-Proof Learning","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-06-28T14:27:33.470813Z"},"links":{"cited_paper":"/paper/2509.08911","citing_paper":"/paper/2606.02655"},"observation_digest":"sha256:7cfc75ebfd7c7213a6421c16c628dc5eeaf2659727f49df1be2c08a04c1e2ca2","observation_id":"a98dfcdb-8ce1-49b7-9810-4ed5716400c1","resolution":{"observed_at":"2026-07-01T23:26:21.531513Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}}],"links":{"evidence":"/evidence","html":"/paper/2509.08911/citation-record","integrity":"/paper/2509.08911/integrity","json":"/paper/2509.08911/citation-record.json","paper":"/paper/2509.08911"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T20:12:37.325720Z","title":"Shadow tomography of quantum states","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2509.08911","last_updated":"2025-09-10T18:15:41Z","snapshot_observed_at":"2026-08-08T00:35:55.880889Z","submitted_at":"2025-09-10T18:15:41Z","title":"Instance-Optimal Matrix Multiplicative Weight Update and Its Quantum Applications","version":1},"reference_index":1,"source":"arxiv_source","source_observed_at":"2026-08-04T20:12:37.325720Z"},"links":{"citing_paper":"/paper/2509.08911"},"observation_digest":"sha256:bc1a9eccf68b4cf9ed8b7fcaf28ee575f1c23b630cfa2ceb9d0c4fd27aab723b","observation_id":"9d6e62a6-3953-4838-b6a0-e8f232693e72","resolution":{"observed_at":"2026-08-04T20:12:37.325720Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T20:12:37.334872Z","title":"Online learning of quantum states","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2509.08911","last_updated":"2025-09-10T18:15:41Z","snapshot_observed_at":"2026-08-08T00:35:55.880889Z","submitted_at":"2025-09-10T18:15:41Z","title":"Instance-Optimal Matrix Multiplicative Weight Update and Its Quantum Applications","version":1},"reference_index":2,"source":"arxiv_source","source_observed_at":"2026-08-04T20:12:37.334872Z"},"links":{"citing_paper":"/paper/2509.08911"},"observation_digest":"sha256:ee0466eced209de620f3ceca4c54c691ba6608171be9b5b0e302f05ed9fd832c","observation_id":"ea4076f6-83d4-41eb-91f9-054aba2675a4","resolution":{"observed_at":"2026-08-04T20:12:37.334872Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T20:12:37.343265Z","title":"Rothblum","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2509.08911","last_updated":"2025-09-10T18:15:41Z","snapshot_observed_at":"2026-08-08T00:35:55.880889Z","submitted_at":"2025-09-10T18:15:41Z","title":"Instance-Optimal Matrix Multiplicative Weight Update and Its Quantum Applications","version":1},"reference_index":3,"source":"arxiv_source","source_observed_at":"2026-08-04T20:12:37.343265Z"},"links":{"citing_paper":"/paper/2509.08911"},"observation_digest":"sha256:f8718c1cb4f7f36d1009e82bf22218920eb8c3c32b6da82dbedeb0d3614e2987","observation_id":"3535d467-5733-4a28-b5fc-809949020245","resolution":{"observed_at":"2026-08-04T20:12:37.343265Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T20:12:37.350719Z","title":"A polynomial-time classical algorithm for noisy random circuit sampling","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2509.08911","last_updated":"2025-09-10T18:15:41Z","snapshot_observed_at":"2026-08-08T00:35:55.880889Z","submitted_at":"2025-09-10T18:15:41Z","title":"Instance-Optimal Matrix Multiplicative Weight Update and Its Quantum Applications","version":1},"reference_index":4,"source":"arxiv_source","source_observed_at":"2026-08-04T20:12:37.350719Z"},"links":{"citing_paper":"/paper/2509.08911"},"observation_digest":"sha256:d4e7f109e5d3d0dd40bb989ab9820a1d1f9f73909c9057c24a39b6d5909b047c","observation_id":"0f4c5a59-e773-42a5-8de6-3fb61d6b1c64","resolution":{"observed_at":"2026-08-04T20:12:37.350719Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T20:12:37.365588Z","title":"Some bounds for expected values of order statistics","venue":null,"work_id":null,"year":1965},"citing_paper":{"arxiv_id":"2509.08911","last_updated":"2025-09-10T18:15:41Z","snapshot_observed_at":"2026-08-08T00:35:55.880889Z","submitted_at":"2025-09-10T18:15:41Z","title":"Instance-Optimal Matrix Multiplicative Weight Update and Its Quantum Applications","version":1},"reference_index":5,"source":"arxiv_source","source_observed_at":"2026-08-04T20:12:37.365588Z"},"links":{"citing_paper":"/paper/2509.08911"},"observation_digest":"sha256:ec6063ee2d00138adca9761190fad441ad8dbf032cddb0848e572111a3102567","observation_id":"a619cd1f-736c-4499-8403-4831f4440c38","resolution":{"observed_at":"2026-08-04T20:12:37.365588Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T20:12:37.379998Z","title":"Follow the compressed leader: Faster online learning of eigenvectors and faster MMWU","venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2509.08911","last_updated":"2025-09-10T18:15:41Z","snapshot_observed_at":"2026-08-08T00:35:55.880889Z","submitted_at":"2025-09-10T18:15:41Z","title":"Instance-Optimal Matrix Multiplicative Weight Update and Its Quantum Applications","version":1},"reference_index":6,"source":"arxiv_source","source_observed_at":"2026-08-04T20:12:37.379998Z"},"links":{"citing_paper":"/paper/2509.08911"},"observation_digest":"sha256:04fd073542aeb6c0697a3cbbdeeb3943be031b09900d3fcdd0d8e13b5937201b","observation_id":"d5cef8ec-863f-4089-92f9-474a50c900fa","resolution":{"observed_at":"2026-08-04T20:12:37.379998Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T20:12:37.394347Z","title":"Spectral sparsification and regret minimization beyond matrix multiplicative updates","venue":null,"work_id":null,"year":2015},"citing_paper":{"arxiv_id":"2509.08911","last_updated":"2025-09-10T18:15:41Z","snapshot_observed_at":"2026-08-08T00:35:55.880889Z","submitted_at":"2025-09-10T18:15:41Z","title":"Instance-Optimal Matrix Multiplicative Weight Update and Its Quantum Applications","version":1},"reference_index":7,"source":"arxiv_source","source_observed_at":"2026-08-04T20:12:37.394347Z"},"links":{"citing_paper":"/paper/2509.08911"},"observation_digest":"sha256:2962a8ba8597dbd102efe9f243f5dd64e7f6dc1ca19736cd50d687de43c4e155","observation_id":"5c6ccb7e-89ed-4f92-962d-228b2b0556dc","resolution":{"observed_at":"2026-08-04T20:12:37.394347Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T20:12:37.402924Z","title":"Anderson, Alice Guionnet, and Ofer Zeitouni","venue":null,"work_id":null,"year":2010},"citing_paper":{"arxiv_id":"2509.08911","last_updated":"2025-09-10T18:15:41Z","snapshot_observed_at":"2026-08-08T00:35:55.880889Z","submitted_at":"2025-09-10T18:15:41Z","title":"Instance-Optimal Matrix Multiplicative Weight Update and Its Quantum Applications","version":1},"reference_index":8,"source":"arxiv_source","source_observed_at":"2026-08-04T20:12:37.402924Z"},"links":{"citing_paper":"/paper/2509.08911"},"observation_digest":"sha256:28aa854bf55adf2106de522c9655e37bea7e834b3efe4ad212d173fa949a334d","observation_id":"74ea6042-3c0d-46c0-9488-285c8b5cb80d","resolution":{"observed_at":"2026-08-04T20:12:37.402924Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T20:12:37.411304Z","title":"A survey on the complexity of learning quantum states","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2509.08911","last_updated":"2025-09-10T18:15:41Z","snapshot_observed_at":"2026-08-08T00:35:55.880889Z","submitted_at":"2025-09-10T18:15:41Z","title":"Instance-Optimal Matrix Multiplicative Weight Update and Its Quantum Applications","version":1},"reference_index":9,"source":"arxiv_source","source_observed_at":"2026-08-04T20:12:37.411304Z"},"links":{"citing_paper":"/paper/2509.08911"},"observation_digest":"sha256:2b15096333824ff0901b9d24b19941ef25e06f4b7cca6a41163bcfd7d0adce30","observation_id":"0e36e92c-2f10-4dbf-9301-6ff47f9105a3","resolution":{"observed_at":"2026-08-04T20:12:37.411304Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T20:12:37.428846Z","title":"A combinatorial, primal-dual approach to semidefinite programs","venue":null,"work_id":null,"year":2007},"citing_paper":{"arxiv_id":"2509.08911","last_updated":"2025-09-10T18:15:41Z","snapshot_observed_at":"2026-08-08T00:35:55.880889Z","submitted_at":"2025-09-10T18:15:41Z","title":"Instance-Optimal Matrix Multiplicative Weight Update and Its Quantum Applications","version":1},"reference_index":10,"source":"arxiv_source","source_observed_at":"2026-08-04T20:12:37.428846Z"},"links":{"citing_paper":"/paper/2509.08911"},"observation_digest":"sha256:ab5bab8dc1a3bb5c3b702fb9b24f432a0ad558cba0b06c1eb7d27cd070afc0ab","observation_id":"7c1c605e-5ac6-4197-af85-934a7d9be082","resolution":{"observed_at":"2026-08-04T20:12:37.428846Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T20:12:37.436279Z","title":"Bardin, Rami Barends, Rupak Biswas, Sergio Boixo, Fernando G","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2509.08911","last_updated":"2025-09-10T18:15:41Z","snapshot_observed_at":"2026-08-08T00:35:55.880889Z","submitted_at":"2025-09-10T18:15:41Z","title":"Instance-Optimal Matrix Multiplicative Weight Update and Its Quantum Applications","version":1},"reference_index":11,"source":"arxiv_source","source_observed_at":"2026-08-04T20:12:37.436279Z"},"links":{"citing_paper":"/paper/2509.08911"},"observation_digest":"sha256:15a42958193871b572ee9889b62abda48e08ab2c23b2fde9c9a71042dc4ecba6","observation_id":"8c3a970d-9f15-4ad6-b5be-b2a78be7fcbf","resolution":{"observed_at":"2026-08-04T20:12:37.436279Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T20:12:37.445258Z","title":"Improved quantum data analysis","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2509.08911","last_updated":"2025-09-10T18:15:41Z","snapshot_observed_at":"2026-08-08T00:35:55.880889Z","submitted_at":"2025-09-10T18:15:41Z","title":"Instance-Optimal Matrix Multiplicative Weight Update and Its Quantum Applications","version":1},"reference_index":12,"source":"arxiv_source","source_observed_at":"2026-08-04T20:12:37.445258Z"},"links":{"citing_paper":"/paper/2509.08911"},"observation_digest":"sha256:e0b501b986cbe1351bfee5512a2fb8b770098a34d2113079d8fa123b3aba2562","observation_id":"3776eeeb-b450-4a41-8e3a-0887c536f194","resolution":{"observed_at":"2026-08-04T20:12:37.445258Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T20:12:37.457151Z","title":"Bandeira, March T","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2509.08911","last_updated":"2025-09-10T18:15:41Z","snapshot_observed_at":"2026-08-08T00:35:55.880889Z","submitted_at":"2025-09-10T18:15:41Z","title":"Instance-Optimal Matrix Multiplicative Weight Update and Its Quantum Applications","version":1},"reference_index":13,"source":"arxiv_source","source_observed_at":"2026-08-04T20:12:37.457151Z"},"links":{"citing_paper":"/paper/2509.08911"},"observation_digest":"sha256:a2af5cd8d77dec0a6ed9784bbf6ae2303f24355db9fb3241fcf4967ff4f285ae","observation_id":"3dffcb12-8bef-4b67-8190-88a0ce2b1d40","resolution":{"observed_at":"2026-08-04T20:12:37.457151Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T20:12:37.471073Z","title":"Pseudospectral shattering, the sign function, and diagonalization in nearly matrix multiplication time","venue":null,"work_id":null,"year":1959},"citing_paper":{"arxiv_id":"2509.08911","last_updated":"2025-09-10T18:15:41Z","snapshot_observed_at":"2026-08-08T00:35:55.880889Z","submitted_at":"2025-09-10T18:15:41Z","title":"Instance-Optimal Matrix Multiplicative Weight Update and Its Quantum Applications","version":1},"reference_index":14,"source":"arxiv_source","source_observed_at":"2026-08-04T20:12:37.471073Z"},"links":{"citing_paper":"/paper/2509.08911"},"observation_digest":"sha256:8ee32cd2a7a613e669d286a541500920c6a78326726979be2f7b44c524f70074","observation_id":"85dc5a53-e19a-427e-88e4-47166cd34f54","resolution":{"observed_at":"2026-08-04T20:12:37.471073Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T20:12:37.480383Z","title":"Online learning of a panoply of quantum objects","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2509.08911","last_updated":"2025-09-10T18:15:41Z","snapshot_observed_at":"2026-08-08T00:35:55.880889Z","submitted_at":"2025-09-10T18:15:41Z","title":"Instance-Optimal Matrix Multiplicative Weight Update and Its Quantum Applications","version":1},"reference_index":15,"source":"arxiv_source","source_observed_at":"2026-08-04T20:12:37.480383Z"},"links":{"citing_paper":"/paper/2509.08911"},"observation_digest":"sha256:7530aa303d9ddc994253ed1e53b519cac9cfa30fe94d75e1ac88d5abd6cebd3c","observation_id":"493fd54c-d3a1-4fd5-9c64-bfef83490178","resolution":{"observed_at":"2026-08-04T20:12:37.480383Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T20:12:37.488361Z","title":"Boyd and Lieven Vandenberghe","venue":null,"work_id":null,"year":2004},"citing_paper":{"arxiv_id":"2509.08911","last_updated":"2025-09-10T18:15:41Z","snapshot_observed_at":"2026-08-08T00:35:55.880889Z","submitted_at":"2025-09-10T18:15:41Z","title":"Instance-Optimal Matrix Multiplicative Weight Update and Its Quantum Applications","version":1},"reference_index":16,"source":"arxiv_source","source_observed_at":"2026-08-04T20:12:37.488361Z"},"links":{"citing_paper":"/paper/2509.08911"},"observation_digest":"sha256:22d9bc1aac62782104f0ab084fbadd267bf7cc023a71d97e3a2ad645ff0bcedb","observation_id":"338c3209-cbc1-4058-9b3c-93788a81978e","resolution":{"observed_at":"2026-08-04T20:12:37.488361Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T20:12:37.497036Z","title":"Universality and sharp matrix concentration inequalities","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2509.08911","last_updated":"2025-09-10T18:15:41Z","snapshot_observed_at":"2026-08-08T00:35:55.880889Z","submitted_at":"2025-09-10T18:15:41Z","title":"Instance-Optimal Matrix Multiplicative Weight Update and Its Quantum Applications","version":1},"reference_index":17,"source":"arxiv_source","source_observed_at":"2026-08-04T20:12:37.497036Z"},"links":{"citing_paper":"/paper/2509.08911"},"observation_digest":"sha256:4178fb03f03b230d207d0a2035c30baa77183315fc8f158b17e01a998b6dcbc3","observation_id":"4a80a15c-b702-43cd-9f0c-977337513d95","resolution":{"observed_at":"2026-08-04T20:12:37.497036Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T20:12:37.506705Z","title":"Brand \\ a o, Amir Kalev, Tongyang Li, Cedric Yen-Yu Lin, Krysta M Svore, and Xiaodi Wu","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2509.08911","last_updated":"2025-09-10T18:15:41Z","snapshot_observed_at":"2026-08-08T00:35:55.880889Z","submitted_at":"2025-09-10T18:15:41Z","title":"Instance-Optimal Matrix Multiplicative Weight Update and Its Quantum Applications","version":1},"reference_index":18,"source":"arxiv_source","source_observed_at":"2026-08-04T20:12:37.506705Z"},"links":{"citing_paper":"/paper/2509.08911"},"observation_digest":"sha256:42c2bab4d6ac81611ec488adac6e3523421fd510104adf5a6c6ffbdc6688c7e6","observation_id":"b0c5018e-d98f-45d3-b263-c2336c95e39b","resolution":{"observed_at":"2026-08-04T20:12:37.506705Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T20:12:37.515460Z","title":"Brandao, Richard Kueng, and Daniel Stilck Fran c a","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2509.08911","last_updated":"2025-09-10T18:15:41Z","snapshot_observed_at":"2026-08-08T00:35:55.880889Z","submitted_at":"2025-09-10T18:15:41Z","title":"Instance-Optimal Matrix Multiplicative Weight Update and Its Quantum Applications","version":1},"reference_index":19,"source":"arxiv_source","source_observed_at":"2026-08-04T20:12:37.515460Z"},"links":{"citing_paper":"/paper/2509.08911"},"observation_digest":"sha256:d1b04a935179be86ab387cdb8e29c94ceb68be8202fde91c312459a93c62650e","observation_id":"14201627-15b8-41aa-8475-6fcc13e04e94","resolution":{"observed_at":"2026-08-04T20:12:37.515460Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T20:12:37.526640Z","title":null,"venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2509.08911","last_updated":"2025-09-10T18:15:41Z","snapshot_observed_at":"2026-08-08T00:35:55.880889Z","submitted_at":"2025-09-10T18:15:41Z","title":"Instance-Optimal Matrix Multiplicative Weight Update and Its Quantum Applications","version":1},"reference_index":20,"source":"arxiv_source","source_observed_at":"2026-08-04T20:12:37.526640Z"},"links":{"citing_paper":"/paper/2509.08911"},"observation_digest":"sha256:d8b20ecc80e190e1edd4daa4a208d56764cc080d9f584be78dc575ae06dc4149","observation_id":"7bc0f985-0bf2-4aad-b2ee-386aa21b6602","resolution":{"observed_at":"2026-08-04T20:12:37.526640Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T20:12:37.542725Z","title":"Lanyon, Peter Zoller, Rainer Blatt, and Christian F","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2509.08911","last_updated":"2025-09-10T18:15:41Z","snapshot_observed_at":"2026-08-08T00:35:55.880889Z","submitted_at":"2025-09-10T18:15:41Z","title":"Instance-Optimal Matrix Multiplicative Weight Update and Its Quantum Applications","version":1},"reference_index":21,"source":"arxiv_source","source_observed_at":"2026-08-04T20:12:37.542725Z"},"links":{"citing_paper":"/paper/2509.08911"},"observation_digest":"sha256:3cd6f3f43f85289fab5b551b8ce4077dd762591d7d5b49e7139f4ed40cec18e2","observation_id":"9f9024b9-c323-46dd-bda6-06fe729a50a1","resolution":{"observed_at":"2026-08-04T20:12:37.542725Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T20:12:37.551481Z","title":"Benjamin, Suguru Endo, William J","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2509.08911","last_updated":"2025-09-10T18:15:41Z","snapshot_observed_at":"2026-08-08T00:35:55.880889Z","submitted_at":"2025-09-10T18:15:41Z","title":"Instance-Optimal Matrix Multiplicative Weight Update and Its Quantum Applications","version":1},"reference_index":22,"source":"arxiv_source","source_observed_at":"2026-08-04T20:12:37.551481Z"},"links":{"citing_paper":"/paper/2509.08911"},"observation_digest":"sha256:96a0023814b0d0b1fbd67a5e68f0404a59c527253a381745ac707e8ecd8835e6","observation_id":"d62d9527-c716-4c67-a05b-212a031146d3","resolution":{"observed_at":"2026-08-04T20:12:37.551481Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T20:12:37.565360Z","title":"Duchi, Sidford Aaron, and Tian Kevin","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2509.08911","last_updated":"2025-09-10T18:15:41Z","snapshot_observed_at":"2026-08-08T00:35:55.880889Z","submitted_at":"2025-09-10T18:15:41Z","title":"Instance-Optimal Matrix Multiplicative Weight Update and Its Quantum Applications","version":1},"reference_index":23,"source":"arxiv_source","source_observed_at":"2026-08-04T20:12:37.565360Z"},"links":{"citing_paper":"/paper/2509.08911"},"observation_digest":"sha256:55c78e369c5c89fdbbc39b920a6113b798d11fb2cfb928ca4c4959ae9ca11fb6","observation_id":"7699a4c1-e14e-43d0-8cff-9760f78b2150","resolution":{"observed_at":"2026-08-04T20:12:37.565360Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T20:12:37.577753Z","title":"Helmbold, Robert E","venue":null,"work_id":null,"year":1997},"citing_paper":{"arxiv_id":"2509.08911","last_updated":"2025-09-10T18:15:41Z","snapshot_observed_at":"2026-08-08T00:35:55.880889Z","submitted_at":"2025-09-10T18:15:41Z","title":"Instance-Optimal Matrix Multiplicative Weight Update and Its Quantum Applications","version":1},"reference_index":24,"source":"arxiv_source","source_observed_at":"2026-08-04T20:12:37.577753Z"},"links":{"citing_paper":"/paper/2509.08911"},"observation_digest":"sha256:4e9e81db78bfa2adb1277082c489c07d4b257f2cceecee082cfbe0ea711816fb","observation_id":"3caf6959-bde6-4728-9eef-e6852cf85d1d","resolution":{"observed_at":"2026-08-04T20:12:37.577753Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T20:12:37.586183Z","title":"Prediction, learning, and games","venue":null,"work_id":null,"year":2006},"citing_paper":{"arxiv_id":"2509.08911","last_updated":"2025-09-10T18:15:41Z","snapshot_observed_at":"2026-08-08T00:35:55.880889Z","submitted_at":"2025-09-10T18:15:41Z","title":"Instance-Optimal Matrix Multiplicative Weight Update and Its Quantum Applications","version":1},"reference_index":25,"source":"arxiv_source","source_observed_at":"2026-08-04T20:12:37.586183Z"},"links":{"citing_paper":"/paper/2509.08911"},"observation_digest":"sha256:55b28dae81cfa72de8f57091bd57351df091ef0377cc8f58cb34df6cad624aa0","observation_id":"bdb7b51a-f30f-43ec-aa24-60152e896304","resolution":{"observed_at":"2026-08-04T20:12:37.586183Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T20:12:37.598318Z","title":"A parameter-free hedging algorithm","venue":null,"work_id":null,"year":2009},"citing_paper":{"arxiv_id":"2509.08911","last_updated":"2025-09-10T18:15:41Z","snapshot_observed_at":"2026-08-08T00:35:55.880889Z","submitted_at":"2025-09-10T18:15:41Z","title":"Instance-Optimal Matrix Multiplicative Weight Update and Its Quantum Applications","version":1},"reference_index":26,"source":"arxiv_source","source_observed_at":"2026-08-04T20:12:37.598318Z"},"links":{"citing_paper":"/paper/2509.08911"},"observation_digest":"sha256:6b0955f1672a0dec8daa439f49ddb09cb87607ca1d66142fe8112919b7d96757","observation_id":"3f9154ce-1ea1-478f-b804-8ff3ce4bf3ce","resolution":{"observed_at":"2026-08-04T20:12:37.598318Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T20:12:37.607381Z","title":"Quantum G ibbs Sampling","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2509.08911","last_updated":"2025-09-10T18:15:41Z","snapshot_observed_at":"2026-08-08T00:35:55.880889Z","submitted_at":"2025-09-10T18:15:41Z","title":"Instance-Optimal Matrix Multiplicative Weight Update and Its Quantum Applications","version":1},"reference_index":27,"source":"arxiv_source","source_observed_at":"2026-08-04T20:12:37.607381Z"},"links":{"citing_paper":"/paper/2509.08911"},"observation_digest":"sha256:b5b6056e49266cdab495330788c5907abdcfb9a175aff2768e3e5dc1593b5caf","observation_id":"0aa7a98e-0be0-46f9-9645-b8051bd80ec8","resolution":{"observed_at":"2026-08-04T20:12:37.607381Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T20:12:37.617915Z","title":"Dalzell, Mario Berta, Fernando GSL Brand \\ a o, and Joel A","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2509.08911","last_updated":"2025-09-10T18:15:41Z","snapshot_observed_at":"2026-08-08T00:35:55.880889Z","submitted_at":"2025-09-10T18:15:41Z","title":"Instance-Optimal Matrix Multiplicative Weight Update and Its Quantum Applications","version":1},"reference_index":28,"source":"arxiv_source","source_observed_at":"2026-08-04T20:12:37.617915Z"},"links":{"citing_paper":"/paper/2509.08911"},"observation_digest":"sha256:e92a80657017ebfbf7844b06876704801d442fe85cc32570e0dad3d2e9693bd4","observation_id":"1cb986d3-6127-487d-8349-7fe6451f01ea","resolution":{"observed_at":"2026-08-04T20:12:37.617915Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T20:12:37.628141Z","title":"Impossible tuning made possible: A new expert algorithm and its applications","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2509.08911","last_updated":"2025-09-10T18:15:41Z","snapshot_observed_at":"2026-08-08T00:35:55.880889Z","submitted_at":"2025-09-10T18:15:41Z","title":"Instance-Optimal Matrix Multiplicative Weight Update and Its Quantum Applications","version":1},"reference_index":29,"source":"arxiv_source","source_observed_at":"2026-08-04T20:12:37.628141Z"},"links":{"citing_paper":"/paper/2509.08911"},"observation_digest":"sha256:544e3ac3a07f577daf1389b6b2318ccafda2082f638b6746cc7213f11cc794f1","observation_id":"996135d8-4101-4125-a6a8-9091e2879067","resolution":{"observed_at":"2026-08-04T20:12:37.628141Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T20:12:37.639349Z","title":"Efficient P auli channel estimation with logarithmic quantum memory","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2509.08911","last_updated":"2025-09-10T18:15:41Z","snapshot_observed_at":"2026-08-08T00:35:55.880889Z","submitted_at":"2025-09-10T18:15:41Z","title":"Instance-Optimal Matrix Multiplicative Weight Update and Its Quantum Applications","version":1},"reference_index":30,"source":"arxiv_source","source_observed_at":"2026-08-04T20:12:37.639349Z"},"links":{"citing_paper":"/paper/2509.08911"},"observation_digest":"sha256:d02c7da393f531f2efafe6e94776798e60d60433e913e7f9d5f1d21b108d9b1a","observation_id":"4ae03834-2619-4014-ad6c-49a1d0a611fe","resolution":{"observed_at":"2026-08-04T20:12:37.639349Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2505.22743","last_updated":"2025-06-17T05:24:14Z","snapshot_observed_at":"2026-08-09T05:12:45.044052Z","submitted_at":"2025-05-28T18:04:10Z","title":"Information-Computation Gaps in Quantum Learning via Low-Degree Likelihood","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2505.22743","snapshot_observed_at":"2026-08-04T20:12:37.658116Z","title":"Information-computation gaps in quantum learning via low-degree likelihood","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2509.08911","last_updated":"2025-09-10T18:15:41Z","snapshot_observed_at":"2026-08-08T00:35:55.880889Z","submitted_at":"2025-09-10T18:15:41Z","title":"Instance-Optimal Matrix Multiplicative Weight Update and Its Quantum Applications","version":1},"reference_index":31,"source":"arxiv_source","source_observed_at":"2026-08-04T20:12:37.658116Z"},"links":{"cited_paper":"/paper/2505.22743","citing_paper":"/paper/2509.08911"},"observation_digest":"sha256:dd9a6e5903d174b79b80ad82f6b3a8b91cd6dd1f6e28cfd66b4853b39fe923da","observation_id":"a3f88c2c-a7f8-4ecd-b145-d8523fa2194d","resolution":{"observed_at":"2026-08-04T20:12:37.658116Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T20:12:37.664563Z","title":"Adaptive online learning of quantum states","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2509.08911","last_updated":"2025-09-10T18:15:41Z","snapshot_observed_at":"2026-08-08T00:35:55.880889Z","submitted_at":"2025-09-10T18:15:41Z","title":"Instance-Optimal Matrix Multiplicative Weight Update and Its Quantum Applications","version":1},"reference_index":32,"source":"arxiv_source","source_observed_at":"2026-08-04T20:12:37.664563Z"},"links":{"citing_paper":"/paper/2509.08911"},"observation_digest":"sha256:e3a5b291351127c969b0c3542752ee780b8ab29c16a607f3089ed812e1417f13","observation_id":"29fb8a0f-b2a5-4af8-b9f1-d89d94a3212f","resolution":{"observed_at":"2026-08-04T20:12:37.664563Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2006.01013","last_updated":"2020-06-01T15:17:55Z","snapshot_observed_at":"2026-08-09T13:50:05.982789Z","submitted_at":"2020-06-01T15:17:55Z","title":"More Practical and Adaptive Algorithms for Online Quantum State Learning","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2006.01013","snapshot_observed_at":"2026-08-04T20:12:37.675667Z","title":"More practical and adaptive algorithms for online quantum state learning","venue":null,"work_id":null,"year":2006},"citing_paper":{"arxiv_id":"2509.08911","last_updated":"2025-09-10T18:15:41Z","snapshot_observed_at":"2026-08-08T00:35:55.880889Z","submitted_at":"2025-09-10T18:15:41Z","title":"Instance-Optimal Matrix Multiplicative Weight Update and Its Quantum Applications","version":1},"reference_index":33,"source":"arxiv_source","source_observed_at":"2026-08-04T20:12:37.675667Z"},"links":{"cited_paper":"/paper/2006.01013","citing_paper":"/paper/2509.08911"},"observation_digest":"sha256:7669a781629a7e188c34f6cc0e7ad8d0e6b08a84a87ce25420609edaaeac18d5","observation_id":"5782c61b-8e4a-4a85-9d97-f38dbaf24d8a","resolution":{"observed_at":"2026-08-04T20:12:37.675667Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T20:12:37.690479Z","title":"Prediction with advice of unknown number of experts","venue":null,"work_id":null,"year":2010},"citing_paper":{"arxiv_id":"2509.08911","last_updated":"2025-09-10T18:15:41Z","snapshot_observed_at":"2026-08-08T00:35:55.880889Z","submitted_at":"2025-09-10T18:15:41Z","title":"Instance-Optimal Matrix Multiplicative Weight Update and Its Quantum Applications","version":1},"reference_index":34,"source":"arxiv_source","source_observed_at":"2026-08-04T20:12:37.690479Z"},"links":{"citing_paper":"/paper/2509.08911"},"observation_digest":"sha256:d08e59debb1417ccacf6ea4424a4034fb91b0ede6165fbb3edd7cf1c7492b922","observation_id":"1ab6860d-3eb6-4e2a-8cf7-54135968cd0c","resolution":{"observed_at":"2026-08-04T20:12:37.690479Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T20:12:37.705882Z","title":"Quantum algorithms for gibbs sampling and hitting-time estimation","venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2509.08911","last_updated":"2025-09-10T18:15:41Z","snapshot_observed_at":"2026-08-08T00:35:55.880889Z","submitted_at":"2025-09-10T18:15:41Z","title":"Instance-Optimal Matrix Multiplicative Weight Update and Its Quantum Applications","version":1},"reference_index":35,"source":"arxiv_source","source_observed_at":"2026-08-04T20:12:37.705882Z"},"links":{"citing_paper":"/paper/2509.08911"},"observation_digest":"sha256:eafb1ed3105a66940e9ebc7f62c1799ba58327c1f4eae6563c3a5d8fb862ce95","observation_id":"819cc1a2-87bd-438f-89e8-4f4f2585210b","resolution":{"observed_at":"2026-08-04T20:12:37.705882Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T20:12:37.716921Z","title":"Eric Tai, Matthew Rispoli, Robert Schittko, Philipp M","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2509.08911","last_updated":"2025-09-10T18:15:41Z","snapshot_observed_at":"2026-08-08T00:35:55.880889Z","submitted_at":"2025-09-10T18:15:41Z","title":"Instance-Optimal Matrix Multiplicative Weight Update and Its Quantum Applications","version":1},"reference_index":36,"source":"arxiv_source","source_observed_at":"2026-08-04T20:12:37.716921Z"},"links":{"citing_paper":"/paper/2509.08911"},"observation_digest":"sha256:4cb6fe7c10630e7f4398aaa2ed5ec8e340b6eb3081e26057d4533c8b55143770","observation_id":"7ff1ab3f-9c9e-4871-96d0-b83787c98c10","resolution":{"observed_at":"2026-08-04T20:12:37.716921Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T20:12:37.729375Z","title":"Fully unconstrained online learning","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2509.08911","last_updated":"2025-09-10T18:15:41Z","snapshot_observed_at":"2026-08-08T00:35:55.880889Z","submitted_at":"2025-09-10T18:15:41Z","title":"Instance-Optimal Matrix Multiplicative Weight Update and Its Quantum Applications","version":1},"reference_index":37,"source":"arxiv_source","source_observed_at":"2026-08-04T20:12:37.729375Z"},"links":{"citing_paper":"/paper/2509.08911"},"observation_digest":"sha256:3e678c7cfd673ce44c12d007cb1ca31226a8d2d1b11c0b0f2eeb338793d7229b","observation_id":"c691f72d-4681-4518-8c19-7545ad2a993b","resolution":{"observed_at":"2026-08-04T20:12:37.729375Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T20:12:37.736706Z","title":"Black-box reductions for parameter-free online learning in B anach spaces","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2509.08911","last_updated":"2025-09-10T18:15:41Z","snapshot_observed_at":"2026-08-08T00:35:55.880889Z","submitted_at":"2025-09-10T18:15:41Z","title":"Instance-Optimal Matrix Multiplicative Weight Update and Its Quantum Applications","version":1},"reference_index":38,"source":"arxiv_source","source_observed_at":"2026-08-04T20:12:37.736706Z"},"links":{"citing_paper":"/paper/2509.08911"},"observation_digest":"sha256:44cb2699ea1466cddd379c9ab2e3e206a37c3b679d73aa418582bfea17bfaaf7","observation_id":"62ef7ba7-f528-401e-b7a2-ed7cb8728453","resolution":{"observed_at":"2026-08-04T20:12:37.736706Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T20:12:37.753331Z","title":"Order statistics","venue":null,"work_id":null,"year":2004},"citing_paper":{"arxiv_id":"2509.08911","last_updated":"2025-09-10T18:15:41Z","snapshot_observed_at":"2026-08-08T00:35:55.880889Z","submitted_at":"2025-09-10T18:15:41Z","title":"Instance-Optimal Matrix Multiplicative Weight Update and Its Quantum Applications","version":1},"reference_index":39,"source":"arxiv_source","source_observed_at":"2026-08-04T20:12:37.753331Z"},"links":{"citing_paper":"/paper/2509.08911"},"observation_digest":"sha256:90e95ef39ec605d31ec640b29b993f04d58b8a0cd805f159e17cb2b16905815f","observation_id":"da3e89a9-5a5d-42d1-a645-d9ef4e1250d4","resolution":{"observed_at":"2026-08-04T20:12:37.753331Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T20:12:37.759749Z","title":"Quantum certification and benchmarking","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2509.08911","last_updated":"2025-09-10T18:15:41Z","snapshot_observed_at":"2026-08-08T00:35:55.880889Z","submitted_at":"2025-09-10T18:15:41Z","title":"Instance-Optimal Matrix Multiplicative Weight Update and Its Quantum Applications","version":1},"reference_index":40,"source":"arxiv_source","source_observed_at":"2026-08-04T20:12:37.759749Z"},"links":{"citing_paper":"/paper/2509.08911"},"observation_digest":"sha256:f542b793766bacaf022851a1a461412a30ce9b96cabd6da82de74dbd84801397","observation_id":"8f723d14-586d-4f9c-b44c-0955d519274c","resolution":{"observed_at":"2026-08-04T20:12:37.759749Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T20:12:37.772257Z","title":"Flammia, Hsin-Yuan Huang, Richard Kueng, John Preskill, Beno \\^ t Vermersch, and Peter Zoller","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2509.08911","last_updated":"2025-09-10T18:15:41Z","snapshot_observed_at":"2026-08-08T00:35:55.880889Z","submitted_at":"2025-09-10T18:15:41Z","title":"Instance-Optimal Matrix Multiplicative Weight Update and Its Quantum Applications","version":1},"reference_index":41,"source":"arxiv_source","source_observed_at":"2026-08-04T20:12:37.772257Z"},"links":{"citing_paper":"/paper/2509.08911"},"observation_digest":"sha256:82c253e53e5a04fb08d3f0700e6070ad4dcdb7a064d25763b423ac147824780b","observation_id":"f9b200e5-4879-45b6-bc9f-da6c783d6e2a","resolution":{"observed_at":"2026-08-04T20:12:37.772257Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T20:12:37.781404Z","title":"Foster, Satyen Kale, Mehryar Mohri, and Karthik Sridharan","venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2509.08911","last_updated":"2025-09-10T18:15:41Z","snapshot_observed_at":"2026-08-08T00:35:55.880889Z","submitted_at":"2025-09-10T18:15:41Z","title":"Instance-Optimal Matrix Multiplicative Weight Update and Its Quantum Applications","version":1},"reference_index":42,"source":"arxiv_source","source_observed_at":"2026-08-04T20:12:37.781404Z"},"links":{"citing_paper":"/paper/2509.08911"},"observation_digest":"sha256:16526044bee2dbeb3b8fadbc996af94f15b5fdf2df62873a623f989793e13fd5","observation_id":"f3a810b9-cd44-47f5-8a7a-761358c69628","resolution":{"observed_at":"2026-08-04T20:12:37.781404Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T20:12:37.790802Z","title":"Foster, Alexander Rakhlin, and Karthik Sridharan","venue":null,"work_id":null,"year":2015},"citing_paper":{"arxiv_id":"2509.08911","last_updated":"2025-09-10T18:15:41Z","snapshot_observed_at":"2026-08-08T00:35:55.880889Z","submitted_at":"2025-09-10T18:15:41Z","title":"Instance-Optimal Matrix Multiplicative Weight Update and Its Quantum Applications","version":1},"reference_index":43,"source":"arxiv_source","source_observed_at":"2026-08-04T20:12:37.790802Z"},"links":{"citing_paper":"/paper/2509.08911"},"observation_digest":"sha256:02f4522f99e2007f67889a2f496f9e517622db8abc4e23c4cc678f7f8564a9ca","observation_id":"8fb9ea5d-9156-4b95-9f40-0e19a0b6bfde","resolution":{"observed_at":"2026-08-04T20:12:37.790802Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T20:12:37.799697Z","title":"Online learning: Sufficient statistics and the B urkholder method","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2509.08911","last_updated":"2025-09-10T18:15:41Z","snapshot_observed_at":"2026-08-08T00:35:55.880889Z","submitted_at":"2025-09-10T18:15:41Z","title":"Instance-Optimal Matrix Multiplicative Weight Update and Its Quantum Applications","version":1},"reference_index":44,"source":"arxiv_source","source_observed_at":"2026-08-04T20:12:37.799697Z"},"links":{"citing_paper":"/paper/2509.08911"},"observation_digest":"sha256:75e2a6213b1d2a8599d3687504c2fa27293b1ce90df077dd163d20aae664cac7","observation_id":"37ab4341-2f48-4cb8-94ab-fea96bb38927","resolution":{"observed_at":"2026-08-04T20:12:37.799697Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T20:12:37.807914Z","title":"Advances in quantum metrology","venue":null,"work_id":null,"year":2011},"citing_paper":{"arxiv_id":"2509.08911","last_updated":"2025-09-10T18:15:41Z","snapshot_observed_at":"2026-08-08T00:35:55.880889Z","submitted_at":"2025-09-10T18:15:41Z","title":"Instance-Optimal Matrix Multiplicative Weight Update and Its Quantum Applications","version":1},"reference_index":45,"source":"arxiv_source","source_observed_at":"2026-08-04T20:12:37.807914Z"},"links":{"citing_paper":"/paper/2509.08911"},"observation_digest":"sha256:f85c1ae7ac8836481ce65aad9b5a1783b85b22a6456dd07ae7a3b57b7bff7c2a","observation_id":"7016dff0-b4b0-4ddd-b6d8-63de5c8e6ff1","resolution":{"observed_at":"2026-08-04T20:12:37.807914Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T20:12:37.822377Z","title":"Lower bounds for the H elmholtz function","venue":null,"work_id":null,"year":1965},"citing_paper":{"arxiv_id":"2509.08911","last_updated":"2025-09-10T18:15:41Z","snapshot_observed_at":"2026-08-08T00:35:55.880889Z","submitted_at":"2025-09-10T18:15:41Z","title":"Instance-Optimal Matrix Multiplicative Weight Update and Its Quantum Applications","version":1},"reference_index":46,"source":"arxiv_source","source_observed_at":"2026-08-04T20:12:37.822377Z"},"links":{"citing_paper":"/paper/2509.08911"},"observation_digest":"sha256:1c20fd5bdbd98251e90ba99da5731c88cca305749ae466bd06cc06802d965ce8","observation_id":"399e1625-b3c4-4a9e-9f99-43ea10bbcf46","resolution":{"observed_at":"2026-08-04T20:12:37.822377Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T20:12:37.842470Z","title":"Learning distributions over quantum measurement outcomes","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2509.08911","last_updated":"2025-09-10T18:15:41Z","snapshot_observed_at":"2026-08-08T00:35:55.880889Z","submitted_at":"2025-09-10T18:15:41Z","title":"Instance-Optimal Matrix Multiplicative Weight Update and Its Quantum Applications","version":1},"reference_index":47,"source":"arxiv_source","source_observed_at":"2026-08-04T20:12:37.842470Z"},"links":{"citing_paper":"/paper/2509.08911"},"observation_digest":"sha256:6e8f16b5a62aad83d136c43fa2ba71d3570e6b00f503be880609af8bd756e3ce","observation_id":"9fc4bd84-2ed4-444e-9648-b863a2bfc311","resolution":{"observed_at":"2026-08-04T20:12:37.842470Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2410.12712","last_updated":"2024-10-16T16:17:21Z","snapshot_observed_at":"2026-07-06T19:34:41.712266Z","submitted_at":"2024-10-16T16:17:21Z","title":"On the sample complexity of purity and inner product estimation","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2410.12712","snapshot_observed_at":"2026-08-04T20:12:37.849426Z","title":"On the sample complexity of purity and inner product estimation","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2509.08911","last_updated":"2025-09-10T18:15:41Z","snapshot_observed_at":"2026-08-08T00:35:55.880889Z","submitted_at":"2025-09-10T18:15:41Z","title":"Instance-Optimal Matrix Multiplicative Weight Update and Its Quantum Applications","version":1},"reference_index":48,"source":"arxiv_source","source_observed_at":"2026-08-04T20:12:37.849426Z"},"links":{"cited_paper":"/paper/2410.12712","citing_paper":"/paper/2509.08911"},"observation_digest":"sha256:ca09cda7d21f2fb4c086dbf128b8c254fe079141f9d410a4cc342b7de9f72745","observation_id":"9fcc4564-2abb-4623-9fb4-3c80ac4ba60d","resolution":{"observed_at":"2026-08-04T20:12:37.849426Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T20:12:37.862987Z","title":null,"venue":null,"work_id":null,"year":1941},"citing_paper":{"arxiv_id":"2509.08911","last_updated":"2025-09-10T18:15:41Z","snapshot_observed_at":"2026-08-08T00:35:55.880889Z","submitted_at":"2025-09-10T18:15:41Z","title":"Instance-Optimal Matrix Multiplicative Weight Update and Its Quantum Applications","version":1},"reference_index":49,"source":"arxiv_source","source_observed_at":"2026-08-04T20:12:37.862987Z"},"links":{"citing_paper":"/paper/2509.08911"},"observation_digest":"sha256:d6af455e9f632377e17be0f800e31299e1b66ae82e04c1eedfbf06da69023a31","observation_id":"6806c4a7-e8b9-4b20-9734-ebf6b0586361","resolution":{"observed_at":"2026-08-04T20:12:37.862987Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T20:12:37.872911Z","title":"Harrow, Zhengfeng Ji, Xiaodi Wu, and Nengkun Yu","venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2509.08911","last_updated":"2025-09-10T18:15:41Z","snapshot_observed_at":"2026-08-08T00:35:55.880889Z","submitted_at":"2025-09-10T18:15:41Z","title":"Instance-Optimal Matrix Multiplicative Weight Update and Its Quantum Applications","version":1},"reference_index":50,"source":"arxiv_source","source_observed_at":"2026-08-04T20:12:37.872911Z"},"links":{"citing_paper":"/paper/2509.08911"},"observation_digest":"sha256:9c3fa24f324aca3d2d1654e20c793378604421cad1fc8170b9e1288a22f8654e","observation_id":"a8313b74-5387-44b3-a500-bfe9ca45c4e0","resolution":{"observed_at":"2026-08-04T20:12:37.872911Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T20:12:37.878783Z","title":"Pedersen","venue":null,"work_id":null,"year":2003},"citing_paper":{"arxiv_id":"2509.08911","last_updated":"2025-09-10T18:15:41Z","snapshot_observed_at":"2026-08-08T00:35:55.880889Z","submitted_at":"2025-09-10T18:15:41Z","title":"Instance-Optimal Matrix Multiplicative Weight Update and Its Quantum Applications","version":1},"reference_index":51,"source":"arxiv_source","source_observed_at":"2026-08-04T20:12:37.878783Z"},"links":{"citing_paper":"/paper/2509.08911"},"observation_digest":"sha256:e0b9cda8517938de76450df7c1570f1a6c34a4277d1bf830b40cc0731c345b92","observation_id":"013d3855-55d9-4be7-9455-a05cc9309b61","resolution":{"observed_at":"2026-08-04T20:12:37.878783Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T20:12:37.884158Z","title":"Optimal anytime regret with two experts","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2509.08911","last_updated":"2025-09-10T18:15:41Z","snapshot_observed_at":"2026-08-08T00:35:55.880889Z","submitted_at":"2025-09-10T18:15:41Z","title":"Instance-Optimal Matrix Multiplicative Weight Update and Its Quantum Applications","version":1},"reference_index":52,"source":"arxiv_source","source_observed_at":"2026-08-04T20:12:37.884158Z"},"links":{"citing_paper":"/paper/2509.08911"},"observation_digest":"sha256:93a6fbcd6d7bbaca6a79d14cedf8fa6ef213f7f87fe975473de0262a6e1429f8","observation_id":"92afa7ee-3adb-4789-9684-4ab4e49981e0","resolution":{"observed_at":"2026-08-04T20:12:37.884158Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T20:12:37.906359Z","title":"Optimal anytime regret for two experts","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2509.08911","last_updated":"2025-09-10T18:15:41Z","snapshot_observed_at":"2026-08-08T00:35:55.880889Z","submitted_at":"2025-09-10T18:15:41Z","title":"Instance-Optimal Matrix Multiplicative Weight Update and Its Quantum Applications","version":1},"reference_index":53,"source":"arxiv_source","source_observed_at":"2026-08-04T20:12:37.906359Z"},"links":{"citing_paper":"/paper/2509.08911"},"observation_digest":"sha256:99c24f920cbca33d7d59cde50ebae0f36f300d78ee014668f5e6d0d99d299888","observation_id":"e51abdf6-4823-40a2-a74a-9e9c0234a2ec","resolution":{"observed_at":"2026-08-04T20:12:37.906359Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T20:12:37.918907Z","title":"Continuous prediction with experts' advice","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2509.08911","last_updated":"2025-09-10T18:15:41Z","snapshot_observed_at":"2026-08-08T00:35:55.880889Z","submitted_at":"2025-09-10T18:15:41Z","title":"Instance-Optimal Matrix Multiplicative Weight Update and Its Quantum Applications","version":1},"reference_index":54,"source":"arxiv_source","source_observed_at":"2026-08-04T20:12:37.918907Z"},"links":{"citing_paper":"/paper/2509.08911"},"observation_digest":"sha256:47facf9b9814d626966eb93cab853a8139a16d62efbe01b3e1a05165b1625883","observation_id":"f7eb0946-87c8-4e52-9e8f-e5869c07f424","resolution":{"observed_at":"2026-08-04T20:12:37.918907Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1909.05207","last_updated":"2023-08-06T14:24:26Z","snapshot_observed_at":"2026-08-06T03:42:24.250183Z","submitted_at":"2019-09-07T19:06:23Z","title":"Introduction to Online Convex Optimization","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1909.05207","snapshot_observed_at":"2026-08-04T20:12:37.930775Z","title":"Introduction to online convex optimization","venue":null,"work_id":null,"year":1909},"citing_paper":{"arxiv_id":"2509.08911","last_updated":"2025-09-10T18:15:41Z","snapshot_observed_at":"2026-08-08T00:35:55.880889Z","submitted_at":"2025-09-10T18:15:41Z","title":"Instance-Optimal Matrix Multiplicative Weight Update and Its Quantum Applications","version":1},"reference_index":55,"source":"arxiv_source","source_observed_at":"2026-08-04T20:12:37.930775Z"},"links":{"cited_paper":"/paper/1909.05207","citing_paper":"/paper/2509.08911"},"observation_digest":"sha256:0e06d398e775163302db7cb1ffc8c152f36c478164958b7f8c06d0a56b5a9d18","observation_id":"cdf543cd-6be4-44f0-b08b-244df8b784ab","resolution":{"observed_at":"2026-08-04T20:12:37.930775Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T20:12:37.938095Z","title":"On contraction coefficients, partial orders and approximation of capacities for quantum channels","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2509.08911","last_updated":"2025-09-10T18:15:41Z","snapshot_observed_at":"2026-08-08T00:35:55.880889Z","submitted_at":"2025-09-10T18:15:41Z","title":"Instance-Optimal Matrix Multiplicative Weight Update and Its Quantum Applications","version":1},"reference_index":56,"source":"arxiv_source","source_observed_at":"2026-08-04T20:12:37.938095Z"},"links":{"citing_paper":"/paper/2509.08911"},"observation_digest":"sha256:8424bf88fbb8395d1b571517ab98c7942479ae50f789db11c56e1e4682613b7f","observation_id":"0d6950d8-c7fe-4e59-9483-6c72dc5ce2fe","resolution":{"observed_at":"2026-08-04T20:12:37.938095Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T20:12:37.944787Z","title":null,"venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2509.08911","last_updated":"2025-09-10T18:15:41Z","snapshot_observed_at":"2026-08-08T00:35:55.880889Z","submitted_at":"2025-09-10T18:15:41Z","title":"Instance-Optimal Matrix Multiplicative Weight Update and Its Quantum Applications","version":1},"reference_index":57,"source":"arxiv_source","source_observed_at":"2026-08-04T20:12:37.944787Z"},"links":{"citing_paper":"/paper/2509.08911"},"observation_digest":"sha256:4f98518d76b532ad81e5e6e358670fdda9c883626573fb0015c375013f81ffd4","observation_id":"382b0f48-b1b4-4ce3-afa7-057280b7e910","resolution":{"observed_at":"2026-08-04T20:12:37.944787Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T20:12:37.953453Z","title":"Predicting many properties of a quantum system from very few measurements","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2509.08911","last_updated":"2025-09-10T18:15:41Z","snapshot_observed_at":"2026-08-08T00:35:55.880889Z","submitted_at":"2025-09-10T18:15:41Z","title":"Instance-Optimal Matrix Multiplicative Weight Update and Its Quantum Applications","version":1},"reference_index":58,"source":"arxiv_source","source_observed_at":"2026-08-04T20:12:37.953453Z"},"links":{"citing_paper":"/paper/2509.08911"},"observation_digest":"sha256:6b64d62d0f31e3ae54c96fbf0b14cee9d9029080b68a0dc9bf050748b1507e43","observation_id":"2b32d424-7141-401a-8a0f-262b65b13a8a","resolution":{"observed_at":"2026-08-04T20:12:37.953453Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T20:12:37.963229Z","title":"Huggins, Sam McArdle, Thomas E","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2509.08911","last_updated":"2025-09-10T18:15:41Z","snapshot_observed_at":"2026-08-08T00:35:55.880889Z","submitted_at":"2025-09-10T18:15:41Z","title":"Instance-Optimal Matrix Multiplicative Weight Update and Its Quantum Applications","version":1},"reference_index":59,"source":"arxiv_source","source_observed_at":"2026-08-04T20:12:37.963229Z"},"links":{"citing_paper":"/paper/2509.08911"},"observation_digest":"sha256:8493abdc3a04ff53f5b3f69788e50a5c39e91440edb57f59835bff95994deccf","observation_id":"405919bf-f4f2-4739-8093-abb525fa7066","resolution":{"observed_at":"2026-08-04T20:12:37.963229Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T20:12:37.970530Z","title":"Preiss, M","venue":null,"work_id":null,"year":2015},"citing_paper":{"arxiv_id":"2509.08911","last_updated":"2025-09-10T18:15:41Z","snapshot_observed_at":"2026-08-08T00:35:55.880889Z","submitted_at":"2025-09-10T18:15:41Z","title":"Instance-Optimal Matrix Multiplicative Weight Update and Its Quantum Applications","version":1},"reference_index":60,"source":"arxiv_source","source_observed_at":"2026-08-04T20:12:37.970530Z"},"links":{"citing_paper":"/paper/2509.08911"},"observation_digest":"sha256:0b31072b14fcac82f7a60f380b2464fb3325d032f08393ae5f9401d048426350","observation_id":"24692085-6919-4783-81c6-b1675c773b4e","resolution":{"observed_at":"2026-08-04T20:12:37.970530Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T20:12:37.983961Z","title":"Pseudorandom quantum states","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2509.08911","last_updated":"2025-09-10T18:15:41Z","snapshot_observed_at":"2026-08-08T00:35:55.880889Z","submitted_at":"2025-09-10T18:15:41Z","title":"Instance-Optimal Matrix Multiplicative Weight Update and Its Quantum Applications","version":1},"reference_index":61,"source":"arxiv_source","source_observed_at":"2026-08-04T20:12:37.983961Z"},"links":{"citing_paper":"/paper/2509.08911"},"observation_digest":"sha256:b8ac0091fac81843af43b884ed9f638051bf06b9bfcd071ff862fbea2a62ead4","observation_id":"0ebe64dd-c713-4ba1-948b-49f102b26eb7","resolution":{"observed_at":"2026-08-04T20:12:37.983961Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T20:12:37.990431Z","title":"Kastoryano and Fernando G.S.L","venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2509.08911","last_updated":"2025-09-10T18:15:41Z","snapshot_observed_at":"2026-08-08T00:35:55.880889Z","submitted_at":"2025-09-10T18:15:41Z","title":"Instance-Optimal Matrix Multiplicative Weight Update and Its Quantum Applications","version":1},"reference_index":62,"source":"arxiv_source","source_observed_at":"2026-08-04T20:12:37.990431Z"},"links":{"citing_paper":"/paper/2509.08911"},"observation_digest":"sha256:a87db528c8fdaaeb349f62f537bffd05f2b36bb40850de4e11a53920cd4d8dd5","observation_id":"19b4eaf0-100a-4b49-8d31-96f0494cca53","resolution":{"observed_at":"2026-08-04T20:12:37.990431Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T20:12:37.997663Z","title":"Eric Tai, Alexander Lukin, Matthew Rispoli, Robert Schittko, Philipp M","venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2509.08911","last_updated":"2025-09-10T18:15:41Z","snapshot_observed_at":"2026-08-08T00:35:55.880889Z","submitted_at":"2025-09-10T18:15:41Z","title":"Instance-Optimal Matrix Multiplicative Weight Update and Its Quantum Applications","version":1},"reference_index":63,"source":"arxiv_source","source_observed_at":"2026-08-04T20:12:37.997663Z"},"links":{"citing_paper":"/paper/2509.08911"},"observation_digest":"sha256:e02110ae238cee10c07571c4ce8e46d38488f4db4affc4d41dc34cafd6b55ff5","observation_id":"10e5b5ed-c602-4f43-a440-59900d6236a1","resolution":{"observed_at":"2026-08-04T20:12:37.997663Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T20:12:38.007195Z","title":"Exponential error suppression for near-term quantum devices","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2509.08911","last_updated":"2025-09-10T18:15:41Z","snapshot_observed_at":"2026-08-08T00:35:55.880889Z","submitted_at":"2025-09-10T18:15:41Z","title":"Instance-Optimal Matrix Multiplicative Weight Update and Its Quantum Applications","version":1},"reference_index":64,"source":"arxiv_source","source_observed_at":"2026-08-04T20:12:38.007195Z"},"links":{"citing_paper":"/paper/2509.08911"},"observation_digest":"sha256:3d0167d8bfea72728edef39e24785d9ec39ec18e6398de29eae8f907da05e11f","observation_id":"c5d64d59-5be1-4126-a627-e7027c5c76fb","resolution":{"observed_at":"2026-08-04T20:12:38.007195Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T20:12:38.017352Z","title":"Koolen and Tim Van Erven","venue":null,"work_id":null,"year":2015},"citing_paper":{"arxiv_id":"2509.08911","last_updated":"2025-09-10T18:15:41Z","snapshot_observed_at":"2026-08-08T00:35:55.880889Z","submitted_at":"2025-09-10T18:15:41Z","title":"Instance-Optimal Matrix Multiplicative Weight Update and Its Quantum Applications","version":1},"reference_index":65,"source":"arxiv_source","source_observed_at":"2026-08-04T20:12:38.017352Z"},"links":{"citing_paper":"/paper/2509.08911"},"observation_digest":"sha256:e7e94e10a5eb3a5f49bb0ff9c78cef8a599d3f1e3050cb84d6096d331198fe5d","observation_id":"2712056b-83b7-4eca-aa5d-cc69cc06d1b8","resolution":{"observed_at":"2026-08-04T20:12:38.017352Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T20:12:38.024536Z","title":null,"venue":null,"work_id":null,"year":2007},"citing_paper":{"arxiv_id":"2509.08911","last_updated":"2025-09-10T18:15:41Z","snapshot_observed_at":"2026-08-08T00:35:55.880889Z","submitted_at":"2025-09-10T18:15:41Z","title":"Instance-Optimal Matrix Multiplicative Weight Update and Its Quantum Applications","version":1},"reference_index":66,"source":"arxiv_source","source_observed_at":"2026-08-04T20:12:38.024536Z"},"links":{"citing_paper":"/paper/2509.08911"},"observation_digest":"sha256:a526e11fc8aabf798de9f64a5b2e0bbff4b1171df353162d1904c15e693b714f","observation_id":"1cfab5b2-8e74-4ad6-bb5a-c7dca157f417","resolution":{"observed_at":"2026-08-04T20:12:38.024536Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T20:12:38.038016Z","title":"Lecture 3: Golden-thompson and the frobenius inner product","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2509.08911","last_updated":"2025-09-10T18:15:41Z","snapshot_observed_at":"2026-08-08T00:35:55.880889Z","submitted_at":"2025-09-10T18:15:41Z","title":"Instance-Optimal Matrix Multiplicative Weight Update and Its Quantum Applications","version":1},"reference_index":67,"source":"arxiv_source","source_observed_at":"2026-08-04T20:12:38.038016Z"},"links":{"citing_paper":"/paper/2509.08911"},"observation_digest":"sha256:21d7f178a0bc7ffc7b5b8ba81b02b1353e4b028eb9eb694ea3563ae49545b906","observation_id":"2b55344a-367a-4efc-9ef3-5b1189f7d2aa","resolution":{"observed_at":"2026-08-04T20:12:38.038016Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T20:12:38.053649Z","title":"Lessa, Ruochen Ma, Jian-Hao Zhang, Zhen Bi, Meng Cheng, and Chong Wang","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2509.08911","last_updated":"2025-09-10T18:15:41Z","snapshot_observed_at":"2026-08-08T00:35:55.880889Z","submitted_at":"2025-09-10T18:15:41Z","title":"Instance-Optimal Matrix Multiplicative Weight Update and Its Quantum Applications","version":1},"reference_index":68,"source":"arxiv_source","source_observed_at":"2026-08-04T20:12:38.053649Z"},"links":{"citing_paper":"/paper/2509.08911"},"observation_digest":"sha256:1e32de41c9f9203e0fa6825764766ae9b39cd36dee343e98527ffeb96ca776fd","observation_id":"5cb8125d-8a3a-468a-ad7b-430d8a47248e","resolution":{"observed_at":"2026-08-04T20:12:38.053649Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T20:12:38.059090Z","title":null,"venue":null,"work_id":null,"year":1994},"citing_paper":{"arxiv_id":"2509.08911","last_updated":"2025-09-10T18:15:41Z","snapshot_observed_at":"2026-08-08T00:35:55.880889Z","submitted_at":"2025-09-10T18:15:41Z","title":"Instance-Optimal Matrix Multiplicative Weight Update and Its Quantum Applications","version":1},"reference_index":69,"source":"arxiv_source","source_observed_at":"2026-08-04T20:12:38.059090Z"},"links":{"citing_paper":"/paper/2509.08911"},"observation_digest":"sha256:bf2fe3d0ff014eb333bd40919a337713a785bd29f7bf25700d78a98ce7f1753b","observation_id":"dd3ef367-fe07-4694-a1f8-6f6b4f73c363","resolution":{"observed_at":"2026-08-04T20:12:38.059090Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2410.17718","last_updated":"2025-04-24T11:32:19Z","snapshot_observed_at":"2026-08-07T12:30:35.437359Z","submitted_at":"2024-10-23T09:47:43Z","title":"Exponential Separations between Quantum Learning with and without Purification","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2410.17718","snapshot_observed_at":"2026-08-04T20:12:38.065557Z","title":"Exponential separations between quantum learning with and without purification","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2509.08911","last_updated":"2025-09-10T18:15:41Z","snapshot_observed_at":"2026-08-08T00:35:55.880889Z","submitted_at":"2025-09-10T18:15:41Z","title":"Instance-Optimal Matrix Multiplicative Weight Update and Its Quantum Applications","version":1},"reference_index":70,"source":"arxiv_source","source_observed_at":"2026-08-04T20:12:38.065557Z"},"links":{"cited_paper":"/paper/2410.17718","citing_paper":"/paper/2509.08911"},"observation_digest":"sha256:97968384c72f7d2b49c7cf18497f1b5ec0e0558f2f23612ca82b97b664fe396d","observation_id":"dee9e701-f6de-45b3-8086-1d640b021b71","resolution":{"observed_at":"2026-08-04T20:12:38.065557Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T20:12:38.072067Z","title":"Quantum principal component analysis","venue":null,"work_id":null,"year":2014},"citing_paper":{"arxiv_id":"2509.08911","last_updated":"2025-09-10T18:15:41Z","snapshot_observed_at":"2026-08-08T00:35:55.880889Z","submitted_at":"2025-09-10T18:15:41Z","title":"Instance-Optimal Matrix Multiplicative Weight Update and Its Quantum Applications","version":1},"reference_index":71,"source":"arxiv_source","source_observed_at":"2026-08-04T20:12:38.072067Z"},"links":{"citing_paper":"/paper/2509.08911"},"observation_digest":"sha256:bf72948c7c98071e97e415856be0782e86fdcbd7411f93696277978f413adb1f","observation_id":"d3023a9f-3de4-46ef-8890-097b67dc8879","resolution":{"observed_at":"2026-08-04T20:12:38.072067Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T20:12:38.082926Z","title":"Multi-armed quantum bandits: Exploration versus exploitation when learning properties of quantum states","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2509.08911","last_updated":"2025-09-10T18:15:41Z","snapshot_observed_at":"2026-08-08T00:35:55.880889Z","submitted_at":"2025-09-10T18:15:41Z","title":"Instance-Optimal Matrix Multiplicative Weight Update and Its Quantum Applications","version":1},"reference_index":72,"source":"arxiv_source","source_observed_at":"2026-08-04T20:12:38.082926Z"},"links":{"citing_paper":"/paper/2509.08911"},"observation_digest":"sha256:0a5921a4750a27aebc013d12cc20739cd3e3f869a41a4a9540ca1e941711e477","observation_id":"0b674842-9075-4163-b7a3-09222ff8b853","resolution":{"observed_at":"2026-08-04T20:12:38.082926Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T20:12:38.098389Z","title":"Schapire","venue":null,"work_id":null,"year":2015},"citing_paper":{"arxiv_id":"2509.08911","last_updated":"2025-09-10T18:15:41Z","snapshot_observed_at":"2026-08-08T00:35:55.880889Z","submitted_at":"2025-09-10T18:15:41Z","title":"Instance-Optimal Matrix Multiplicative Weight Update and Its Quantum Applications","version":1},"reference_index":73,"source":"arxiv_source","source_observed_at":"2026-08-04T20:12:38.098389Z"},"links":{"citing_paper":"/paper/2509.08911"},"observation_digest":"sha256:5b72a0ac5f8797ffdf39b7d0b02eb6be44f748972f67d0e3e933e9fe2b5c46ad","observation_id":"58b677f0-b4ac-4139-b54f-42026a9e1940","resolution":{"observed_at":"2026-08-04T20:12:38.098389Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T20:12:38.109210Z","title":"Minimax optimal algorithms for unconstrained linear optimization","venue":null,"work_id":null,"year":2013},"citing_paper":{"arxiv_id":"2509.08911","last_updated":"2025-09-10T18:15:41Z","snapshot_observed_at":"2026-08-08T00:35:55.880889Z","submitted_at":"2025-09-10T18:15:41Z","title":"Instance-Optimal Matrix Multiplicative Weight Update and Its Quantum Applications","version":1},"reference_index":74,"source":"arxiv_source","source_observed_at":"2026-08-04T20:12:38.109210Z"},"links":{"citing_paper":"/paper/2509.08911"},"observation_digest":"sha256:93fe426310dc2ae3f68a88429266e6701304b3b16d47a2976f6e798cb6a1d4d4","observation_id":"6bb62eb5-8d88-4549-affb-0250179e2a42","resolution":{"observed_at":"2026-08-04T20:12:38.109210Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T20:12:38.116240Z","title":"Unconstrained online linear learning in H ilbert spaces: Minimax algorithms and normal approximations","venue":null,"work_id":null,"year":2014},"citing_paper":{"arxiv_id":"2509.08911","last_updated":"2025-09-10T18:15:41Z","snapshot_observed_at":"2026-08-08T00:35:55.880889Z","submitted_at":"2025-09-10T18:15:41Z","title":"Instance-Optimal Matrix Multiplicative Weight Update and Its Quantum Applications","version":1},"reference_index":75,"source":"arxiv_source","source_observed_at":"2026-08-04T20:12:38.116240Z"},"links":{"citing_paper":"/paper/2509.08911"},"observation_digest":"sha256:d71566924721a99f902fe4f5ea64fe186b6ccc84a81f7574c04517ce5528e99f","observation_id":"e5b32c17-1f14-4495-928e-b2650960e7d0","resolution":{"observed_at":"2026-08-04T20:12:38.116240Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T20:12:38.127945Z","title":"Introduction to H aar measure tools in quantum information: A beginner's tutorial","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2509.08911","last_updated":"2025-09-10T18:15:41Z","snapshot_observed_at":"2026-08-08T00:35:55.880889Z","submitted_at":"2025-09-10T18:15:41Z","title":"Instance-Optimal Matrix Multiplicative Weight Update and Its Quantum Applications","version":1},"reference_index":76,"source":"arxiv_source","source_observed_at":"2026-08-04T20:12:38.127945Z"},"links":{"citing_paper":"/paper/2509.08911"},"observation_digest":"sha256:2efc18414fde33fdb40805654eafc16e6c1cb0bb6be850c06d03761e0d81c713","observation_id":"9e583263-88ef-4cc8-86d2-f6b33bd5ef33","resolution":{"observed_at":"2026-08-04T20:12:38.127945Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T20:12:38.138017Z","title":null,"venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2509.08911","last_updated":"2025-09-10T18:15:41Z","snapshot_observed_at":"2026-08-08T00:35:55.880889Z","submitted_at":"2025-09-10T18:15:41Z","title":"Instance-Optimal Matrix Multiplicative Weight Update and Its Quantum Applications","version":1},"reference_index":77,"source":"arxiv_source","source_observed_at":"2026-08-04T20:12:38.138017Z"},"links":{"citing_paper":"/paper/2509.08911"},"observation_digest":"sha256:c8e553cc03dcfda9d1c53c3cadd5050e00194cb98c669167846bbe7f487a7235","observation_id":"deb2a650-c7ca-4a08-b67f-e579115d9f1d","resolution":{"observed_at":"2026-08-04T20:12:38.138017Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T20:12:38.147318Z","title":"A trace inequality of J ohn von N eumann","venue":null,"work_id":null,"year":1975},"citing_paper":{"arxiv_id":"2509.08911","last_updated":"2025-09-10T18:15:41Z","snapshot_observed_at":"2026-08-08T00:35:55.880889Z","submitted_at":"2025-09-10T18:15:41Z","title":"Instance-Optimal Matrix Multiplicative Weight Update and Its Quantum Applications","version":1},"reference_index":78,"source":"arxiv_source","source_observed_at":"2026-08-04T20:12:38.147318Z"},"links":{"citing_paper":"/paper/2509.08911"},"observation_digest":"sha256:031099e0e3bd6f3918667b85a80f0f2b82844c67690e335fe25f4958edd0a474","observation_id":"4150750b-c163-446b-82cc-c24c9db1e898","resolution":{"observed_at":"2026-08-04T20:12:38.147318Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T20:12:38.159085Z","title":"Quantum speedup of Monte Carlo methods","venue":null,"work_id":null,"year":2015},"citing_paper":{"arxiv_id":"2509.08911","last_updated":"2025-09-10T18:15:41Z","snapshot_observed_at":"2026-08-08T00:35:55.880889Z","submitted_at":"2025-09-10T18:15:41Z","title":"Instance-Optimal Matrix Multiplicative Weight Update and Its Quantum Applications","version":1},"reference_index":79,"source":"arxiv_source","source_observed_at":"2026-08-04T20:12:38.159085Z"},"links":{"citing_paper":"/paper/2509.08911"},"observation_digest":"sha256:59948aca6362e002c5d1d130359d8f10fa87bc187120d7e75ea3701e36b4b458","observation_id":"080316b3-b29a-488d-8a24-b3321ea5ad35","resolution":{"observed_at":"2026-08-04T20:12:38.159085Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T20:12:38.168736Z","title":"Tan, Matthew J","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2509.08911","last_updated":"2025-09-10T18:15:41Z","snapshot_observed_at":"2026-08-08T00:35:55.880889Z","submitted_at":"2025-09-10T18:15:41Z","title":"Instance-Optimal Matrix Multiplicative Weight Update and Its Quantum Applications","version":1},"reference_index":80,"source":"arxiv_source","source_observed_at":"2026-08-04T20:12:38.168736Z"},"links":{"citing_paper":"/paper/2509.08911"},"observation_digest":"sha256:8e39830ee2f8a70c492ae04ecb0aba6de33b937f62c9ef8d169dce9334886d53","observation_id":"828e8180-ed1f-4747-b11d-10c8cbe2fb76","resolution":{"observed_at":"2026-08-04T20:12:38.168736Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T20:12:38.178432Z","title":"Minimax optimal quantile and semi-adversarial regret via root-logarithmic regularizers","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2509.08911","last_updated":"2025-09-10T18:15:41Z","snapshot_observed_at":"2026-08-08T00:35:55.880889Z","submitted_at":"2025-09-10T18:15:41Z","title":"Instance-Optimal Matrix Multiplicative Weight Update and Its Quantum Applications","version":1},"reference_index":81,"source":"arxiv_source","source_observed_at":"2026-08-04T20:12:38.178432Z"},"links":{"citing_paper":"/paper/2509.08911"},"observation_digest":"sha256:36157291340cdbf77e8ac49b05c28f94b71797562bcd5ca1529778e95de48341","observation_id":"017f2005-8417-4a00-8771-e3f375acc731","resolution":{"observed_at":"2026-08-04T20:12:38.178432Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T20:12:38.188556Z","title":"Nielsen and Isaac L","venue":null,"work_id":null,"year":2010},"citing_paper":{"arxiv_id":"2509.08911","last_updated":"2025-09-10T18:15:41Z","snapshot_observed_at":"2026-08-08T00:35:55.880889Z","submitted_at":"2025-09-10T18:15:41Z","title":"Instance-Optimal Matrix Multiplicative Weight Update and Its Quantum Applications","version":1},"reference_index":82,"source":"arxiv_source","source_observed_at":"2026-08-04T20:12:38.188556Z"},"links":{"citing_paper":"/paper/2509.08911"},"observation_digest":"sha256:c7a7eb6c478f403af0631d2057d8662b1d9b46dcb01c591ec6f5f4738c9b730b","observation_id":"3357c55f-e34e-463c-8067-009faa181797","resolution":{"observed_at":"2026-08-04T20:12:38.188556Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T20:12:38.208057Z","title":"Efficient quantum tomography","venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2509.08911","last_updated":"2025-09-10T18:15:41Z","snapshot_observed_at":"2026-08-08T00:35:55.880889Z","submitted_at":"2025-09-10T18:15:41Z","title":"Instance-Optimal Matrix Multiplicative Weight Update and Its Quantum Applications","version":1},"reference_index":83,"source":"arxiv_source","source_observed_at":"2026-08-04T20:12:38.208057Z"},"links":{"citing_paper":"/paper/2509.08911"},"observation_digest":"sha256:887d54dea985333978aac8b5167d41d521963168b630101cc16404e4410ab5c1","observation_id":"da45b624-2f31-456b-8c49-b7f05f0f1cc7","resolution":{"observed_at":"2026-08-04T20:12:38.208057Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T20:12:38.220409Z","title":"Dimension-free exponentiated gradient","venue":null,"work_id":null,"year":2013},"citing_paper":{"arxiv_id":"2509.08911","last_updated":"2025-09-10T18:15:41Z","snapshot_observed_at":"2026-08-08T00:35:55.880889Z","submitted_at":"2025-09-10T18:15:41Z","title":"Instance-Optimal Matrix Multiplicative Weight Update and Its Quantum Applications","version":1},"reference_index":84,"source":"arxiv_source","source_observed_at":"2026-08-04T20:12:38.220409Z"},"links":{"citing_paper":"/paper/2509.08911"},"observation_digest":"sha256:734b06235fb8939a135f9161730324887b228898076de6bbcaa356c58453752f","observation_id":"8a0a352a-b1c4-41e7-9eaf-74549ff00d38","resolution":{"observed_at":"2026-08-04T20:12:38.220409Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1912.13213","last_updated":"2026-06-21T08:13:27Z","snapshot_observed_at":"2026-07-06T08:47:45.187408Z","submitted_at":"2019-12-31T08:16:31Z","title":"Online Learning: A Modern Introduction Using Convex Optimization","version":10},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1912.13213","snapshot_observed_at":"2026-08-04T20:12:38.228241Z","title":"A modern introduction to online learning","venue":null,"work_id":null,"year":1912},"citing_paper":{"arxiv_id":"2509.08911","last_updated":"2025-09-10T18:15:41Z","snapshot_observed_at":"2026-08-08T00:35:55.880889Z","submitted_at":"2025-09-10T18:15:41Z","title":"Instance-Optimal Matrix Multiplicative Weight Update and Its Quantum Applications","version":1},"reference_index":85,"source":"arxiv_source","source_observed_at":"2026-08-04T20:12:38.228241Z"},"links":{"cited_paper":"/paper/1912.13213","citing_paper":"/paper/2509.08911"},"observation_digest":"sha256:dc88836369cf7824b07ecb9f9b648a64bd25a3d810cc9d4bc3b56ba9060a5ef4","observation_id":"a27a5868-8d07-462d-b354-a35e96219f80","resolution":{"observed_at":"2026-08-04T20:12:38.228241Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1511.02176","last_updated":"2015-11-06T18:01:38Z","snapshot_observed_at":"2026-07-06T04:35:39.949579Z","submitted_at":"2015-11-06T18:01:38Z","title":"Optimal Non-Asymptotic Lower Bound on the Minimax Regret of Learning with Expert Advice","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1511.02176","snapshot_observed_at":"2026-08-04T20:12:38.234355Z","title":"Optimal non-asymptotic lower bound on the minimax regret of learning with expert advice","venue":null,"work_id":null,"year":2015},"citing_paper":{"arxiv_id":"2509.08911","last_updated":"2025-09-10T18:15:41Z","snapshot_observed_at":"2026-08-08T00:35:55.880889Z","submitted_at":"2025-09-10T18:15:41Z","title":"Instance-Optimal Matrix Multiplicative Weight Update and Its Quantum Applications","version":1},"reference_index":86,"source":"arxiv_source","source_observed_at":"2026-08-04T20:12:38.234355Z"},"links":{"cited_paper":"/paper/1511.02176","citing_paper":"/paper/2509.08911"},"observation_digest":"sha256:fb24f10f99cf4365b947d8ffd174da2fce9ea6fd1d9db7ef9854df82b365a46f","observation_id":"faeb484d-100f-4e8e-bdf9-964e8a2661b7","resolution":{"observed_at":"2026-08-04T20:12:38.234355Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T20:12:38.242265Z","title":"Coin betting and parameter-free online learning","venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2509.08911","last_updated":"2025-09-10T18:15:41Z","snapshot_observed_at":"2026-08-08T00:35:55.880889Z","submitted_at":"2025-09-10T18:15:41Z","title":"Instance-Optimal Matrix Multiplicative Weight Update and Its Quantum Applications","version":1},"reference_index":87,"source":"arxiv_source","source_observed_at":"2026-08-04T20:12:38.242265Z"},"links":{"citing_paper":"/paper/2509.08911"},"observation_digest":"sha256:d06c6c8ab2dfd07790bbb983a7953138bc3c8210ae6e7bc04fa9bb69d988e20a","observation_id":"df7e848b-905f-41c2-bc05-6e4e234aea85","resolution":{"observed_at":"2026-08-04T20:12:38.242265Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T20:12:38.249319Z","title":null,"venue":null,"work_id":null,"year":1993},"citing_paper":{"arxiv_id":"2509.08911","last_updated":"2025-09-10T18:15:41Z","snapshot_observed_at":"2026-08-08T00:35:55.880889Z","submitted_at":"2025-09-10T18:15:41Z","title":"Instance-Optimal Matrix Multiplicative Weight Update and Its Quantum Applications","version":1},"reference_index":88,"source":"arxiv_source","source_observed_at":"2026-08-04T20:12:38.249319Z"},"links":{"citing_paper":"/paper/2509.08911"},"observation_digest":"sha256:dab9b9a67ccae6bc95e3aca7d24575e4b2b2f60decf555c52a59be911dfd8756","observation_id":"4d883d16-f91e-4f98-9be8-3610363c41da","resolution":{"observed_at":"2026-08-04T20:12:38.249319Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T20:12:38.259346Z","title":"Near optimal memory-regret tradeoff for online learning","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2509.08911","last_updated":"2025-09-10T18:15:41Z","snapshot_observed_at":"2026-08-08T00:35:55.880889Z","submitted_at":"2025-09-10T18:15:41Z","title":"Instance-Optimal Matrix Multiplicative Weight Update and Its Quantum Applications","version":1},"reference_index":89,"source":"arxiv_source","source_observed_at":"2026-08-04T20:12:38.259346Z"},"links":{"citing_paper":"/paper/2509.08911"},"observation_digest":"sha256:0de0d1deb86a2c5537678554b131a78acbf2473c6953a40e555835ddb5db0199","observation_id":"33f03090-9179-411d-aa46-bade41bcff5c","resolution":{"observed_at":"2026-08-04T20:12:38.259346Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T20:12:38.268843Z","title":"Online prediction in sub-linear space","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2509.08911","last_updated":"2025-09-10T18:15:41Z","snapshot_observed_at":"2026-08-08T00:35:55.880889Z","submitted_at":"2025-09-10T18:15:41Z","title":"Instance-Optimal Matrix Multiplicative Weight Update and Its Quantum Applications","version":1},"reference_index":90,"source":"arxiv_source","source_observed_at":"2026-08-04T20:12:38.268843Z"},"links":{"citing_paper":"/paper/2509.08911"},"observation_digest":"sha256:13737c5ceac74f9c898d848f2eb61907f9e2c32445b5efb657d917508b5e09d1","observation_id":"795a34e0-2789-4a69-8c39-d0de364c259e","resolution":{"observed_at":"2026-08-04T20:12:38.268843Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T20:12:38.277613Z","title":"On a matrix trace inequality due to A ndo, H iai and O kubo","venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2509.08911","last_updated":"2025-09-10T18:15:41Z","snapshot_observed_at":"2026-08-08T00:35:55.880889Z","submitted_at":"2025-09-10T18:15:41Z","title":"Instance-Optimal Matrix Multiplicative Weight Update and Its Quantum Applications","version":1},"reference_index":91,"source":"arxiv_source","source_observed_at":"2026-08-04T20:12:38.277613Z"},"links":{"citing_paper":"/paper/2509.08911"},"observation_digest":"sha256:9d732a1a909520ebd7b9efca3fa46ad0f6017e91a66024d1b778167c5696d19a","observation_id":"ba90e5dd-41ec-471e-a1e1-fb84e346d4de","resolution":{"observed_at":"2026-08-04T20:12:38.277613Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T20:12:38.287329Z","title":"Quantum computing in the NISQ era and beyond","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2509.08911","last_updated":"2025-09-10T18:15:41Z","snapshot_observed_at":"2026-08-08T00:35:55.880889Z","submitted_at":"2025-09-10T18:15:41Z","title":"Instance-Optimal Matrix Multiplicative Weight Update and Its Quantum Applications","version":1},"reference_index":92,"source":"arxiv_source","source_observed_at":"2026-08-04T20:12:38.287329Z"},"links":{"citing_paper":"/paper/2509.08911"},"observation_digest":"sha256:73b1c07d2d48eb8c9aa12eec3a9deb46946c884452bc49aa42606d9f5c5de3bb","observation_id":"fdaf9ee7-ef9f-4265-91af-56eef9fa58a4","resolution":{"observed_at":"2026-08-04T20:12:38.287329Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2210.11505","last_updated":"2024-03-29T07:46:11Z","snapshot_observed_at":"2026-07-06T14:08:22.637175Z","submitted_at":"2022-10-20T18:12:42Z","title":"Exponentially tighter bounds on limitations of quantum error mitigation","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2210.11505","snapshot_observed_at":"2026-08-04T20:12:38.298012Z","title":"Exponentially tighter bounds on limitations of quantum error mitigation","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2509.08911","last_updated":"2025-09-10T18:15:41Z","snapshot_observed_at":"2026-08-08T00:35:55.880889Z","submitted_at":"2025-09-10T18:15:41Z","title":"Instance-Optimal Matrix Multiplicative Weight Update and Its Quantum Applications","version":1},"reference_index":93,"source":"arxiv_source","source_observed_at":"2026-08-04T20:12:38.298012Z"},"links":{"cited_paper":"/paper/2210.11505","citing_paper":"/paper/2509.08911"},"observation_digest":"sha256:9c794c9d7ab8bbec8b0eb7e80b5d7b7a2ec19b788c6de1c333d7598550d47f3e","observation_id":"3bc296ee-21b0-4846-824c-a00241a6ea35","resolution":{"observed_at":"2026-08-04T20:12:38.298012Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2406.04250","last_updated":"2024-06-06T16:54:20Z","snapshot_observed_at":"2026-08-08T13:26:03.824851Z","submitted_at":"2024-06-06T16:54:20Z","title":"Online learning of quantum processes","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2406.04250","snapshot_observed_at":"2026-08-04T20:12:38.316416Z","title":"Caro, Jens Eisert, and Sumeet Khatri","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2509.08911","last_updated":"2025-09-10T18:15:41Z","snapshot_observed_at":"2026-08-08T00:35:55.880889Z","submitted_at":"2025-09-10T18:15:41Z","title":"Instance-Optimal Matrix Multiplicative Weight Update and Its Quantum Applications","version":1},"reference_index":94,"source":"arxiv_source","source_observed_at":"2026-08-04T20:12:38.316416Z"},"links":{"cited_paper":"/paper/2406.04250","citing_paper":"/paper/2509.08911"},"observation_digest":"sha256:112c4c9fb66ca97241427a251f3137c4844241abd1759ccf401b7d7ab6eee834","observation_id":"4fa7509f-f015-4f1b-a04b-4e37dce4d605","resolution":{"observed_at":"2026-08-04T20:12:38.316416Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T20:12:38.336521Z","title":"Hermitian diagonalization in linear precision","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2509.08911","last_updated":"2025-09-10T18:15:41Z","snapshot_observed_at":"2026-08-08T00:35:55.880889Z","submitted_at":"2025-09-10T18:15:41Z","title":"Instance-Optimal Matrix Multiplicative Weight Update and Its Quantum Applications","version":1},"reference_index":95,"source":"arxiv_source","source_observed_at":"2026-08-04T20:12:38.336521Z"},"links":{"citing_paper":"/paper/2509.08911"},"observation_digest":"sha256:ccada32f0dc1f930f7b67f3de52dd1f3b8bb618f1886c47c53f2138d9ef9b722","observation_id":"4ecd053a-a9b4-451e-9456-08309816ef70","resolution":{"observed_at":"2026-08-04T20:12:38.336521Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T20:12:38.345969Z","title":"Shaw, Zhuo Chen, Joonhee Choi, Daniel K","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2509.08911","last_updated":"2025-09-10T18:15:41Z","snapshot_observed_at":"2026-08-08T00:35:55.880889Z","submitted_at":"2025-09-10T18:15:41Z","title":"Instance-Optimal Matrix Multiplicative Weight Update and Its Quantum Applications","version":1},"reference_index":96,"source":"arxiv_source","source_observed_at":"2026-08-04T20:12:38.345969Z"},"links":{"citing_paper":"/paper/2509.08911"},"observation_digest":"sha256:c2ebef9852b0fbc56ad533f1da7a36276305b85ab5d6549ab375c3c9ca35ab85","observation_id":"0b515ce2-b5d8-4f16-9832-7bc774db4087","resolution":{"observed_at":"2026-08-04T20:12:38.345969Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T20:12:38.358055Z","title":"Deterministic complexity analysis of hermitian eigenproblems","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2509.08911","last_updated":"2025-09-10T18:15:41Z","snapshot_observed_at":"2026-08-08T00:35:55.880889Z","submitted_at":"2025-09-10T18:15:41Z","title":"Instance-Optimal Matrix Multiplicative Weight Update and Its Quantum Applications","version":1},"reference_index":97,"source":"arxiv_source","source_observed_at":"2026-08-04T20:12:38.358055Z"},"links":{"citing_paper":"/paper/2509.08911"},"observation_digest":"sha256:84d28090398efb5771578f3b5833d9d0e9909b6a47bdbc3abdf9a8e7f79ec3c5","observation_id":"064f93df-7606-4eb9-afa8-2af7f9ffb188","resolution":{"observed_at":"2026-08-04T20:12:38.358055Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T20:12:38.367059Z","title":"Woodruff, Ziyu Xu, and Samson Zhou","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2509.08911","last_updated":"2025-09-10T18:15:41Z","snapshot_observed_at":"2026-08-08T00:35:55.880889Z","submitted_at":"2025-09-10T18:15:41Z","title":"Instance-Optimal Matrix Multiplicative Weight Update and Its Quantum Applications","version":1},"reference_index":98,"source":"arxiv_source","source_observed_at":"2026-08-04T20:12:38.367059Z"},"links":{"citing_paper":"/paper/2509.08911"},"observation_digest":"sha256:353332524974df8c65d7a68b25243ddfaedc4c10baf277c3226ffb2add97eee1","observation_id":"c8f73602-d0a7-443d-80c4-894eb6f070ea","resolution":{"observed_at":"2026-08-04T20:12:38.367059Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T20:12:38.374997Z","title":"No-regret algorithms for unconstrained online convex optimization","venue":null,"work_id":null,"year":2012},"citing_paper":{"arxiv_id":"2509.08911","last_updated":"2025-09-10T18:15:41Z","snapshot_observed_at":"2026-08-08T00:35:55.880889Z","submitted_at":"2025-09-10T18:15:41Z","title":"Instance-Optimal Matrix Multiplicative Weight Update and Its Quantum Applications","version":1},"reference_index":99,"source":"arxiv_source","source_observed_at":"2026-08-04T20:12:38.374997Z"},"links":{"citing_paper":"/paper/2509.08911"},"observation_digest":"sha256:8583d78ee5c223212a72340af4b7bcd558d486fa065ca0092dd17dd64cf3296f","observation_id":"8a36c24f-9eeb-4784-95ac-1a57b08cda4a","resolution":{"observed_at":"2026-08-04T20:12:38.374997Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T20:12:38.382792Z","title":"Thompson","venue":null,"work_id":null,"year":1965},"citing_paper":{"arxiv_id":"2509.08911","last_updated":"2025-09-10T18:15:41Z","snapshot_observed_at":"2026-08-08T00:35:55.880889Z","submitted_at":"2025-09-10T18:15:41Z","title":"Instance-Optimal Matrix Multiplicative Weight Update and Its Quantum Applications","version":1},"reference_index":100,"source":"arxiv_source","source_observed_at":"2026-08-04T20:12:38.382792Z"},"links":{"citing_paper":"/paper/2509.08911"},"observation_digest":"sha256:d0c8d60e6f08f3b040be8d8625a06d0916f8d566cd02619ecf4cad9e617f72e1","observation_id":"81b8c6fe-da4d-4d4a-9c47-110484a0f627","resolution":{"observed_at":"2026-08-04T20:12:38.382792Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2509.08911","last_updated":"2025-09-10T18:15:41Z","latest_version":1,"primary_category":"cs.LG","snapshot_observed_at":"2026-08-08T00:35:55.880889Z","submitted_at":"2025-09-10T18:15:41Z","title":"Instance-Optimal Matrix Multiplicative Weight Update and Its Quantum Applications"},"reference_resolution":{"displayed":100,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":100,"verified_exact":0,"verified_fuzzy":0},"total_outbound_references":119},"refusal":"A citation records a reference. It does not transfer a finding from one paper to another.","schema":"pith.paper-citation-record.v1","standing_sources":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"thesis":"As of 9 August 2026, this Paper Citation Record lists 100 of 119 outbound references and 1 inbound Pith citation observation for arXiv:2509.08911."}