{"as_of":"2026-08-11T10:27:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:18f521e2347e7f340e952cd775637bc6f14fe6284f66954e5a39f72e36ff65a6","coverage":[{"denominator":0,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":0,"source":"paper_references, paper_reference_links","source_observed_at":null,"state":"measured"},{"denominator":37,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":37,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-11T06:34:44.6726+00:00","state":"measured"},{"denominator":37,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":37,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-11T00:00:02.153079Z","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":"2026-07-04T12:19:49.361463Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2109.03824","last_updated":"2021-10-04T15:23:18Z","snapshot_observed_at":"2026-08-11T02:50:45.407187Z","submitted_at":"2021-09-08T18:00:00Z","title":"Geometry of Krylov Complexity","version":2},"cited_work":{"arxiv_id":"2109.03824","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2109.03824","snapshot_observed_at":"2026-07-04T12:19:49.361463Z","title":"Caputa, J","venue":null,"work_id":"b040d2fd-f970-40ae-bedb-e32a210db1de","year":2022},"citing_paper":{"arxiv_id":"2412.08925","last_updated":"2026-05-21T00:24:08Z","snapshot_observed_at":"2026-07-06T20:05:41.350080Z","submitted_at":"2024-12-12T04:23:29Z","title":"Generalized CV Conjecture and Krylov Complexity in Two-Mode Hermitian Systems via Information Geometry","version":3},"reference_index":52,"source":"pdf_text","source_observed_at":"2026-05-23T07:16:44.979654Z"},"links":{"cited_paper":"/paper/2109.03824","citing_paper":"/paper/2412.08925"},"observation_digest":"sha256:fc3e385a55d0baab385b217d02a6c590568b47d445a7277b4cf5d8064cdb7852","observation_id":"1879e15b-aedb-4511-9f08-798fd890528d","resolution":{"observed_at":"2026-05-23T07:17:42.467684Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2109.03824","last_updated":"2021-10-04T15:23:18Z","snapshot_observed_at":"2026-08-11T02:50:45.407187Z","submitted_at":"2021-09-08T18:00:00Z","title":"Geometry of Krylov Complexity","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2109.03824","snapshot_observed_at":"2026-08-11T00:00:02.153079Z","title":"Caputa, J","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2412.19797","last_updated":"2025-05-06T22:53:09Z","snapshot_observed_at":"2026-08-11T05:27:48.978624Z","submitted_at":"2024-12-27T18:56:27Z","title":"Streamlined Krylov construction and classification of ergodic Floquet systems","version":3},"reference_index":40,"source":"pdf_text","source_observed_at":"2026-08-11T00:00:02.153079Z"},"links":{"cited_paper":"/paper/2109.03824","citing_paper":"/paper/2412.19797"},"observation_digest":"sha256:8ecc662770c7b180b7757904fc5fd87475c7bc5aabfba82322ac3c3a9ecd5169","observation_id":"b128095c-e736-4588-969c-17b377dbbe3d","resolution":{"observed_at":"2026-08-11T00:00:02.153079Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2109.03824","last_updated":"2021-10-04T15:23:18Z","snapshot_observed_at":"2026-08-11T02:50:45.407187Z","submitted_at":"2021-09-08T18:00:00Z","title":"Geometry of Krylov Complexity","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2109.03824","snapshot_observed_at":"2026-08-10T21:31:07.215770Z","title":"Caputa, J","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2501.04795","last_updated":"2025-01-08T19:20:03Z","snapshot_observed_at":"2026-08-11T02:51:19.860936Z","submitted_at":"2025-01-08T19:20:03Z","title":"Phase Transitions in Quasi-Periodically Driven Quantum Critical Systems: Analytical Results","version":1},"reference_index":71,"source":"pdf_text","source_observed_at":"2026-08-10T21:31:07.215770Z"},"links":{"cited_paper":"/paper/2109.03824","citing_paper":"/paper/2501.04795"},"observation_digest":"sha256:4fea6ee8462b9e034cf15c142b55f05f6cbd1e148a35803ef87c3f19c5de0f56","observation_id":"9010e9da-7efd-48bc-a1a3-c91c93f5ff75","resolution":{"observed_at":"2026-08-10T21:31:07.215770Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2109.03824","last_updated":"2021-10-04T15:23:18Z","snapshot_observed_at":"2026-08-11T02:50:45.407187Z","submitted_at":"2021-09-08T18:00:00Z","title":"Geometry of Krylov Complexity","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2109.03824","snapshot_observed_at":"2026-08-09T04:50:16.781302Z","title":"Caputa, J.M","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2502.03434","last_updated":"2025-07-18T07:43:22Z","snapshot_observed_at":"2026-08-09T09:22:51.719813Z","submitted_at":"2025-02-05T18:29:03Z","title":"Dynamics of monitored SSH Model in Krylov Space: From Complexity to Quantum Fisher Information","version":3},"reference_index":64,"source":"pdf_text","source_observed_at":"2026-08-09T04:50:16.781302Z"},"links":{"cited_paper":"/paper/2109.03824","citing_paper":"/paper/2502.03434"},"observation_digest":"sha256:58b588c0f267f065f030cd9b9cdc7bd77377a8ddb8664b0be5349051d5c2f349","observation_id":"86b63d91-5cb7-4805-aa58-bef8d90a7b31","resolution":{"observed_at":"2026-08-09T04:50:16.781302Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2109.03824","last_updated":"2021-10-04T15:23:18Z","snapshot_observed_at":"2026-08-11T02:50:45.407187Z","submitted_at":"2021-09-08T18:00:00Z","title":"Geometry of Krylov Complexity","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2109.03824","snapshot_observed_at":"2026-08-06T22:39:59.936981Z","title":"Caputa, J.M","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2506.21156","last_updated":"2025-06-26T11:25:44Z","snapshot_observed_at":"2026-08-07T15:59:29.654745Z","submitted_at":"2025-06-26T11:25:44Z","title":"Complexity of PXP scars revisited","version":1},"reference_index":42,"source":"pdf_text","source_observed_at":"2026-08-06T22:39:59.936981Z"},"links":{"cited_paper":"/paper/2109.03824","citing_paper":"/paper/2506.21156"},"observation_digest":"sha256:9bea52565c407f714a81524af6930b5434af6542b54455d0b3f36e4970f0b73c","observation_id":"f5da651e-c67f-47ca-8371-0892c76cb7f0","resolution":{"observed_at":"2026-08-06T22:39:59.936981Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2109.03824","last_updated":"2021-10-04T15:23:18Z","snapshot_observed_at":"2026-08-11T02:50:45.407187Z","submitted_at":"2021-09-08T18:00:00Z","title":"Geometry of Krylov Complexity","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2109.03824","snapshot_observed_at":"2026-08-06T21:56:08.788157Z","title":"Caputa, J","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2506.23345","last_updated":"2025-06-29T17:39:54Z","snapshot_observed_at":"2026-08-11T05:22:24.700384Z","submitted_at":"2025-06-29T17:39:54Z","title":"Trotterization, Operator Scrambling, and Entanglement","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-06T21:56:08.788157Z"},"links":{"cited_paper":"/paper/2109.03824","citing_paper":"/paper/2506.23345"},"observation_digest":"sha256:2654b85cce8029210c117c37f40c6c0695168ecee0827ae86e850039355eb3f6","observation_id":"a2070759-9902-41b9-8a4f-827ff8c821a6","resolution":{"observed_at":"2026-08-06T21:56:08.788157Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2109.03824","last_updated":"2021-10-04T15:23:18Z","snapshot_observed_at":"2026-08-11T02:50:45.407187Z","submitted_at":"2021-09-08T18:00:00Z","title":"Geometry of Krylov Complexity","version":2},"cited_work":{"arxiv_id":"2109.03824","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2109.03824","snapshot_observed_at":"2026-07-04T12:19:49.361463Z","title":"Caputa, J","venue":null,"work_id":"b040d2fd-f970-40ae-bedb-e32a210db1de","year":2022},"citing_paper":{"arxiv_id":"2507.23667","last_updated":"2026-04-20T14:35:05Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2025-07-31T15:47:34Z","title":"Universal Time Evolution of Holographic and Quantum Complexity","version":2},"reference_index":49,"source":"pdf_text","source_observed_at":"2026-05-19T02:18:35.187658Z"},"links":{"cited_paper":"/paper/2109.03824","citing_paper":"/paper/2507.23667"},"observation_digest":"sha256:8118c58d65eac8a00ecad52d64a60675043b510b3f10c73887c395f2bd737279","observation_id":"34edcbc1-3246-45ab-b7f8-9aea1d2c42c5","resolution":{"observed_at":"2026-05-19T02:21:59.507452Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2109.03824","last_updated":"2021-10-04T15:23:18Z","snapshot_observed_at":"2026-08-11T02:50:45.407187Z","submitted_at":"2021-09-08T18:00:00Z","title":"Geometry of Krylov Complexity","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2109.03824","snapshot_observed_at":"2026-08-03T21:05:58.946772Z","title":"Caputa, J","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2511.17711","last_updated":"2026-06-21T19:56:43Z","snapshot_observed_at":"2026-08-08T11:07:59.466073Z","submitted_at":"2025-11-21T19:02:44Z","title":"Quantum Cosmology in Krylov Space: Complexity and Entropy","version":2},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-03T21:05:58.946772Z"},"links":{"cited_paper":"/paper/2109.03824","citing_paper":"/paper/2511.17711"},"observation_digest":"sha256:399c50e5e67c7ed26adf9c6204f5f858fc860e055887c783cc321131e5fed577","observation_id":"1f5a3123-7716-4e4c-99d9-e8199a139085","resolution":{"observed_at":"2026-08-03T21:05:58.946772Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2109.03824","last_updated":"2021-10-04T15:23:18Z","snapshot_observed_at":"2026-08-11T02:50:45.407187Z","submitted_at":"2021-09-08T18:00:00Z","title":"Geometry of Krylov Complexity","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2109.03824","snapshot_observed_at":"2026-08-03T20:15:03.330302Z","title":"Magan, and Dimitrios Patramanis","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2511.20769","last_updated":"2026-06-23T14:34:45Z","snapshot_observed_at":"2026-08-06T10:48:49.561286Z","submitted_at":"2025-11-25T19:03:19Z","title":"Krylov Complexity of Supersymmetric SYK Models","version":3},"reference_index":51,"source":"pdf_text","source_observed_at":"2026-08-03T20:15:03.330302Z"},"links":{"cited_paper":"/paper/2109.03824","citing_paper":"/paper/2511.20769"},"observation_digest":"sha256:9ee12de1ed801181fa45bac88055088d79e87c0a7161265569427d621553e00b","observation_id":"d188c409-b9db-49c9-ad2d-f07eac4dfccc","resolution":{"observed_at":"2026-08-03T20:15:03.330302Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2109.03824","last_updated":"2021-10-04T15:23:18Z","snapshot_observed_at":"2026-08-11T02:50:45.407187Z","submitted_at":"2021-09-08T18:00:00Z","title":"Geometry of Krylov Complexity","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2109.03824","snapshot_observed_at":"2026-08-03T17:58:41.697256Z","title":"Geometry of Krylov complexity,","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2512.07715","last_updated":"2026-07-24T08:59:56Z","snapshot_observed_at":"2026-08-09T00:39:41.038052Z","submitted_at":"2025-12-08T17:05:15Z","title":"Grand Canonical vs Canonical Krylov Complexity in Double-Scaled Complex SYK Model","version":2},"reference_index":40,"source":"pdf_text","source_observed_at":"2026-08-03T17:58:41.697256Z"},"links":{"cited_paper":"/paper/2109.03824","citing_paper":"/paper/2512.07715"},"observation_digest":"sha256:f87648a7cc81070f4434f5a01bcf09f963f19a357fa34901091ae2295bccb826","observation_id":"771ddbc9-ea98-482b-adc2-0095c02dc329","resolution":{"observed_at":"2026-08-03T17:58:41.697256Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2109.03824","last_updated":"2021-10-04T15:23:18Z","snapshot_observed_at":"2026-08-11T02:50:45.407187Z","submitted_at":"2021-09-08T18:00:00Z","title":"Geometry of Krylov Complexity","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2109.03824","snapshot_observed_at":"2026-08-03T11:03:36.208190Z","title":"Caputa, J","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2601.07937","last_updated":"2026-07-31T01:25:00Z","snapshot_observed_at":"2026-08-10T00:14:55.770998Z","submitted_at":"2026-01-12T19:07:22Z","title":"Attention in Krylov Space: Transformer-Based Extrapolation of Lanczos Coefficients","version":2},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-03T11:03:36.208190Z"},"links":{"cited_paper":"/paper/2109.03824","citing_paper":"/paper/2601.07937"},"observation_digest":"sha256:916707f07d84b6b911a1646326bdfa1b67fec08df27d9ac66a0ea9dab49319eb","observation_id":"901d13ee-739a-4509-a9ba-f52fbb346533","resolution":{"observed_at":"2026-08-03T11:03:36.208190Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2109.03824","last_updated":"2021-10-04T15:23:18Z","snapshot_observed_at":"2026-08-11T02:50:45.407187Z","submitted_at":"2021-09-08T18:00:00Z","title":"Geometry of Krylov Complexity","version":2},"cited_work":{"arxiv_id":"2109.03824","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2109.03824","snapshot_observed_at":"2026-07-04T12:19:49.361463Z","title":"Caputa, J","venue":null,"work_id":"b040d2fd-f970-40ae-bedb-e32a210db1de","year":2022},"citing_paper":{"arxiv_id":"2601.09801","last_updated":"2026-04-28T13:42:45Z","snapshot_observed_at":"2026-07-06T22:41:43.594456Z","submitted_at":"2026-01-14T19:08:01Z","title":"Probing the Chaos to Integrability Transition in Double-Scaled SYK","version":2},"reference_index":99,"source":"pdf_text","source_observed_at":"2026-05-16T14:15:15.772460Z"},"links":{"cited_paper":"/paper/2109.03824","citing_paper":"/paper/2601.09801"},"observation_digest":"sha256:7ade4255ce7d44f7c9de3d1d2699d6001cc87d0a253ea57bfebf2cf8974204c6","observation_id":"62435d6f-f5e7-44e3-82f7-dc664f41a762","resolution":{"observed_at":"2026-05-16T14:17:59.409470Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2109.03824","last_updated":"2021-10-04T15:23:18Z","snapshot_observed_at":"2026-08-11T02:50:45.407187Z","submitted_at":"2021-09-08T18:00:00Z","title":"Geometry of Krylov Complexity","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2109.03824","snapshot_observed_at":"2026-08-03T04:36:18.840182Z","title":"Caputa, J.M","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2602.04949","last_updated":"2026-07-14T06:12:37Z","snapshot_observed_at":"2026-08-08T11:20:02.917864Z","submitted_at":"2026-02-04T19:00:00Z","title":"Emergence of Krylov complexity through quantum walks: An exploration of the quantum origins of complexity","version":5},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-08-03T04:36:18.840182Z"},"links":{"cited_paper":"/paper/2109.03824","citing_paper":"/paper/2602.04949"},"observation_digest":"sha256:31ce6985d1b11d5873b3062f6f9e6bb828f52760e72a8e569d55a3791b4901e3","observation_id":"a233b6e9-f479-4ab8-b88a-a98e12ff8c09","resolution":{"observed_at":"2026-08-03T04:36:18.840182Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2109.03824","last_updated":"2021-10-04T15:23:18Z","snapshot_observed_at":"2026-08-11T02:50:45.407187Z","submitted_at":"2021-09-08T18:00:00Z","title":"Geometry of Krylov Complexity","version":2},"cited_work":{"arxiv_id":"2109.03824","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2109.03824","snapshot_observed_at":"2026-07-04T12:19:49.361463Z","title":"Caputa, J","venue":null,"work_id":"b040d2fd-f970-40ae-bedb-e32a210db1de","year":2022},"citing_paper":{"arxiv_id":"2602.11627","last_updated":"2026-04-21T12:16:15Z","snapshot_observed_at":"2026-08-04T20:25:32.939260Z","submitted_at":"2026-02-12T06:23:37Z","title":"Krylov Subspace Dynamics as Near-Horizon AdS$_2$ Holography","version":2},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-05-16T06:06:44.386970Z"},"links":{"cited_paper":"/paper/2109.03824","citing_paper":"/paper/2602.11627"},"observation_digest":"sha256:3d2dffe76eca757c3aa457872d5924d4f9230da69f5362ddcbbd3f7153e68002","observation_id":"ddf1d1b7-1b18-4e54-8f95-9f33a74e013d","resolution":{"observed_at":"2026-05-16T06:07:25.639729Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2109.03824","last_updated":"2021-10-04T15:23:18Z","snapshot_observed_at":"2026-08-11T02:50:45.407187Z","submitted_at":"2021-09-08T18:00:00Z","title":"Geometry of Krylov Complexity","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2109.03824","snapshot_observed_at":"2026-08-02T22:14:10.161191Z","title":"Caputa, J","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2602.17757","last_updated":"2026-05-26T22:15:39Z","snapshot_observed_at":"2026-08-09T23:40:32.624214Z","submitted_at":"2026-02-19T19:00:00Z","title":"Krylov Complexity, Confinement and Universality","version":2},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-02T22:14:10.161191Z"},"links":{"cited_paper":"/paper/2109.03824","citing_paper":"/paper/2602.17757"},"observation_digest":"sha256:1f39576ae2bbe1bdd014cda440789dcad778070e2bf06d514f2fc485337b212d","observation_id":"81bd5ac9-0244-4413-9953-adf4f1d7c326","resolution":{"observed_at":"2026-08-02T22:14:10.161191Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2109.03824","last_updated":"2021-10-04T15:23:18Z","snapshot_observed_at":"2026-08-11T02:50:45.407187Z","submitted_at":"2021-09-08T18:00:00Z","title":"Geometry of Krylov Complexity","version":2},"cited_work":{"arxiv_id":"2109.03824","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2109.03824","snapshot_observed_at":"2026-07-04T12:19:49.361463Z","title":"Caputa, J","venue":null,"work_id":"b040d2fd-f970-40ae-bedb-e32a210db1de","year":2022},"citing_paper":{"arxiv_id":"2603.10106","last_updated":"2026-05-07T16:33:14Z","snapshot_observed_at":"2026-07-18T23:19:02.757164Z","submitted_at":"2026-03-10T18:00:00Z","title":"Complexity and Operator Growth in Holographic 6d SCFTs","version":2},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-05-15T13:10:04.376356Z"},"links":{"cited_paper":"/paper/2109.03824","citing_paper":"/paper/2603.10106"},"observation_digest":"sha256:aa5c6bab378665cf64b10e26afaff48a0b14dddd5af7afc77345bd11d9d1b2c6","observation_id":"fa100b3e-c058-4125-9ff7-c3879310a24d","resolution":{"observed_at":"2026-05-15T13:10:49.813996Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2109.03824","last_updated":"2021-10-04T15:23:18Z","snapshot_observed_at":"2026-08-11T02:50:45.407187Z","submitted_at":"2021-09-08T18:00:00Z","title":"Geometry of Krylov Complexity","version":2},"cited_work":{"arxiv_id":"2109.03824","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2109.03824","snapshot_observed_at":"2026-07-04T12:19:49.361463Z","title":"Caputa, J","venue":null,"work_id":"b040d2fd-f970-40ae-bedb-e32a210db1de","year":2022},"citing_paper":{"arxiv_id":"2603.19359","last_updated":"2026-04-06T12:17:02Z","snapshot_observed_at":"2026-07-06T22:49:47.366739Z","submitted_at":"2026-03-19T18:00:07Z","title":"Towards a Refinement of Krylov Complexity: Scrambling, Classical Operator Growth and Replicas","version":2},"reference_index":59,"source":"pdf_text","source_observed_at":"2026-05-15T08:20:09.796633Z"},"links":{"cited_paper":"/paper/2109.03824","citing_paper":"/paper/2603.19359"},"observation_digest":"sha256:34ef55d4f26afb4ca1235981580678e74ef58f721574d64f1ec3298b316d1834","observation_id":"29a21204-f2c3-4670-b80a-ee5ed13e3f6b","resolution":{"observed_at":"2026-05-15T08:20:17.406879Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2109.03824","last_updated":"2021-10-04T15:23:18Z","snapshot_observed_at":"2026-08-11T02:50:45.407187Z","submitted_at":"2021-09-08T18:00:00Z","title":"Geometry of Krylov Complexity","version":2},"cited_work":{"arxiv_id":"2109.03824","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2109.03824","snapshot_observed_at":"2026-07-04T12:19:49.361463Z","title":"Caputa, J","venue":null,"work_id":"b040d2fd-f970-40ae-bedb-e32a210db1de","year":2022},"citing_paper":{"arxiv_id":"2604.05630","last_updated":"2026-04-07T09:35:02Z","snapshot_observed_at":"2026-08-11T08:27:58.342830Z","submitted_at":"2026-04-07T09:35:02Z","title":"Symmetry-resolved Krylov Complexity and the Uncoloured Tensor Model","version":1},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-05-10T19:58:39.417247Z"},"links":{"cited_paper":"/paper/2109.03824","citing_paper":"/paper/2604.05630"},"observation_digest":"sha256:a752558461a747dae959ce1f7a2d28a3c4e73da163ba4b74197f310e6bde86a2","observation_id":"f3d4ac79-1850-46d5-bff8-3c86d1b0d440","resolution":{"observed_at":"2026-05-10T22:20:48.375046Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2109.03824","last_updated":"2021-10-04T15:23:18Z","snapshot_observed_at":"2026-08-11T02:50:45.407187Z","submitted_at":"2021-09-08T18:00:00Z","title":"Geometry of Krylov Complexity","version":2},"cited_work":{"arxiv_id":"2109.03824","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2109.03824","snapshot_observed_at":"2026-07-04T12:19:49.361463Z","title":"Caputa, J","venue":null,"work_id":"b040d2fd-f970-40ae-bedb-e32a210db1de","year":2022},"citing_paper":{"arxiv_id":"2604.07432","last_updated":"2026-04-08T18:00:00Z","snapshot_observed_at":"2026-07-31T07:44:25.524747Z","submitted_at":"2026-04-08T18:00:00Z","title":"Holographic Krylov Complexity for Charged, Composite and Extended Probes","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-05-10T18:02:52.534128Z"},"links":{"cited_paper":"/paper/2109.03824","citing_paper":"/paper/2604.07432"},"observation_digest":"sha256:a510e4febb1c821d22e4bf216174c061e3665712f0c4eec586298e472127aa90","observation_id":"b6a61437-ea58-4b68-aaa0-2ff78bd8f5dc","resolution":{"observed_at":"2026-05-11T05:36:00.565410Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2109.03824","last_updated":"2021-10-04T15:23:18Z","snapshot_observed_at":"2026-08-11T02:50:45.407187Z","submitted_at":"2021-09-08T18:00:00Z","title":"Geometry of Krylov Complexity","version":2},"cited_work":{"arxiv_id":"2109.03824","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2109.03824","snapshot_observed_at":"2026-07-04T12:19:49.361463Z","title":"Caputa, J","venue":null,"work_id":"b040d2fd-f970-40ae-bedb-e32a210db1de","year":2022},"citing_paper":{"arxiv_id":"2605.07668","last_updated":"2026-05-08T12:39:43Z","snapshot_observed_at":"2026-07-06T23:20:01.856093Z","submitted_at":"2026-05-08T12:39:43Z","title":"Bridging Krylov Complexity and Universal Analog Quantum Simulator","version":1},"reference_index":82,"source":"pdf_text","source_observed_at":"2026-05-11T02:35:22.825362Z"},"links":{"cited_paper":"/paper/2109.03824","citing_paper":"/paper/2605.07668"},"observation_digest":"sha256:c597504b4bfa8c8cd1e440c854fbb79bde363c5f41afe47eb5fedd99ca10b961","observation_id":"7b27c4ad-a68c-4839-ace3-58d6cf084071","resolution":{"observed_at":"2026-05-11T03:15:55.524498Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2109.03824","last_updated":"2021-10-04T15:23:18Z","snapshot_observed_at":"2026-08-11T02:50:45.407187Z","submitted_at":"2021-09-08T18:00:00Z","title":"Geometry of Krylov Complexity","version":2},"cited_work":{"arxiv_id":"2109.03824","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2109.03824","snapshot_observed_at":"2026-07-04T12:19:49.361463Z","title":"Caputa, J","venue":null,"work_id":"b040d2fd-f970-40ae-bedb-e32a210db1de","year":2022},"citing_paper":{"arxiv_id":"2605.17550","last_updated":"2026-05-29T11:19:15Z","snapshot_observed_at":"2026-07-06T23:28:30.942078Z","submitted_at":"2026-05-17T17:21:31Z","title":"Krylov Correlators in $\\mathfrak{sl}(2,\\mathbb R)$ Models: Exact Results and Holographic Complexity","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-05-19T22:33:40.924339Z"},"links":{"cited_paper":"/paper/2109.03824","citing_paper":"/paper/2605.17550"},"observation_digest":"sha256:e94981bed245dfc325e435870e83d635308ac4c6763a4c9a1fee6cdaf1a31a44","observation_id":"57d4ac6d-6481-45bb-98dc-e819dd6202ae","resolution":{"observed_at":"2026-05-19T22:37:49.873634Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2109.03824","last_updated":"2021-10-04T15:23:18Z","snapshot_observed_at":"2026-08-11T02:50:45.407187Z","submitted_at":"2021-09-08T18:00:00Z","title":"Geometry of Krylov Complexity","version":2},"cited_work":{"arxiv_id":"2109.03824","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2109.03824","snapshot_observed_at":"2026-07-04T12:19:49.361463Z","title":"Caputa, J","venue":null,"work_id":"b040d2fd-f970-40ae-bedb-e32a210db1de","year":2022},"citing_paper":{"arxiv_id":"2605.17550","last_updated":"2026-05-29T11:19:15Z","snapshot_observed_at":"2026-07-06T23:28:30.942078Z","submitted_at":"2026-05-17T17:21:31Z","title":"Krylov Correlators in $\\mathfrak{sl}(2,\\mathbb R)$ Models: Exact Results and Holographic Complexity","version":2},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-05-25T05:47:12.013847Z"},"links":{"cited_paper":"/paper/2109.03824","citing_paper":"/paper/2605.17550"},"observation_digest":"sha256:2f0a42d6ab198751e3235c6cf477cb1d287143dfe53a760dded61e54815e34e8","observation_id":"055891c7-bea8-47b1-bdb4-cbdfd10ded34","resolution":{"observed_at":"2026-05-25T05:50:24.466247Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2109.03824","last_updated":"2021-10-04T15:23:18Z","snapshot_observed_at":"2026-08-11T02:50:45.407187Z","submitted_at":"2021-09-08T18:00:00Z","title":"Geometry of Krylov Complexity","version":2},"cited_work":{"arxiv_id":"2109.03824","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2109.03824","snapshot_observed_at":"2026-07-04T12:19:49.361463Z","title":"Caputa, J","venue":null,"work_id":"b040d2fd-f970-40ae-bedb-e32a210db1de","year":2022},"citing_paper":{"arxiv_id":"2605.17550","last_updated":"2026-05-29T11:19:15Z","snapshot_observed_at":"2026-07-06T23:28:30.942078Z","submitted_at":"2026-05-17T17:21:31Z","title":"Krylov Correlators in $\\mathfrak{sl}(2,\\mathbb R)$ Models: Exact Results and Holographic Complexity","version":4},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-06-30T19:11:39.162388Z"},"links":{"cited_paper":"/paper/2109.03824","citing_paper":"/paper/2605.17550"},"observation_digest":"sha256:17e7094ef78c4f101ea04715ff2b44ffcbd94106d3cdc8458f2762a4ed9bc76c","observation_id":"117737da-ddd0-49be-a00f-e75657b40736","resolution":{"observed_at":"2026-06-30T19:15:00.518827Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2109.03824","last_updated":"2021-10-04T15:23:18Z","snapshot_observed_at":"2026-08-11T02:50:45.407187Z","submitted_at":"2021-09-08T18:00:00Z","title":"Geometry of Krylov Complexity","version":2},"cited_work":{"arxiv_id":"2109.03824","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2109.03824","snapshot_observed_at":"2026-07-04T12:19:49.361463Z","title":"Caputa, J","venue":null,"work_id":"b040d2fd-f970-40ae-bedb-e32a210db1de","year":2022},"citing_paper":{"arxiv_id":"2605.18594","last_updated":"2026-05-18T16:07:09Z","snapshot_observed_at":"2026-08-01T17:55:30.248859Z","submitted_at":"2026-05-18T16:07:09Z","title":"Krylov complexity and fidelity susceptibility in two-band Hamiltonians","version":1},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-05-20T10:20:27.767281Z"},"links":{"cited_paper":"/paper/2109.03824","citing_paper":"/paper/2605.18594"},"observation_digest":"sha256:1a2fadb9d7d73d815e74dc85878892b4696c2393359e3785e22c070154250dcd","observation_id":"9bde5ab8-6f85-446c-9793-52908dbfdf2f","resolution":{"observed_at":"2026-05-20T10:23:12.120703Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2109.03824","last_updated":"2021-10-04T15:23:18Z","snapshot_observed_at":"2026-08-11T02:50:45.407187Z","submitted_at":"2021-09-08T18:00:00Z","title":"Geometry of Krylov Complexity","version":2},"cited_work":{"arxiv_id":"2109.03824","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2109.03824","snapshot_observed_at":"2026-07-04T12:19:49.361463Z","title":"Caputa, J","venue":null,"work_id":"b040d2fd-f970-40ae-bedb-e32a210db1de","year":2022},"citing_paper":{"arxiv_id":"2605.28681","last_updated":"2026-07-21T06:54:52Z","snapshot_observed_at":"2026-08-07T11:11:19.951590Z","submitted_at":"2026-05-27T16:13:52Z","title":"Krylov complexity has it all","version":2},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-06-29T11:13:49.715091Z"},"links":{"cited_paper":"/paper/2109.03824","citing_paper":"/paper/2605.28681"},"observation_digest":"sha256:9bebff63e6a2d5902ab6bea1358b1fc51cd7bcaff4bd6b207af6f9f0b9db9f92","observation_id":"ffd4e251-07b8-4043-8a60-cc539875fdb4","resolution":{"observed_at":"2026-06-29T13:13:28.107343Z","resolver_source":"arxiv_id","status":"metadata_mismatch"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2109.03824","last_updated":"2021-10-04T15:23:18Z","snapshot_observed_at":"2026-08-11T02:50:45.407187Z","submitted_at":"2021-09-08T18:00:00Z","title":"Geometry of Krylov Complexity","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2109.03824","snapshot_observed_at":"2026-08-02T13:01:50.681294Z","title":"Geometry of Krylov complexity,","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2605.28681","last_updated":"2026-07-21T06:54:52Z","snapshot_observed_at":"2026-08-07T11:11:19.951590Z","submitted_at":"2026-05-27T16:13:52Z","title":"Krylov complexity has it all","version":3},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-02T13:01:50.681294Z"},"links":{"cited_paper":"/paper/2109.03824","citing_paper":"/paper/2605.28681"},"observation_digest":"sha256:7055f0b0553013eb480ddb677e4067f2f6cc2d22b5202a10e8d13ed4854625c7","observation_id":"33c0daf8-af01-4c65-b4fd-418bca11691f","resolution":{"observed_at":"2026-08-02T13:01:50.681294Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2109.03824","last_updated":"2021-10-04T15:23:18Z","snapshot_observed_at":"2026-08-11T02:50:45.407187Z","submitted_at":"2021-09-08T18:00:00Z","title":"Geometry of Krylov Complexity","version":2},"cited_work":{"arxiv_id":"2109.03824","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2109.03824","snapshot_observed_at":"2026-07-04T12:19:49.361463Z","title":"Caputa, J","venue":null,"work_id":"b040d2fd-f970-40ae-bedb-e32a210db1de","year":2022},"citing_paper":{"arxiv_id":"2606.20790","last_updated":"2026-06-30T17:34:25Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2026-06-18T18:00:00Z","title":"Complexity Inequalities for Quantum Subsystems","version":1},"reference_index":59,"source":"pdf_text","source_observed_at":"2026-06-26T15:49:11.884191Z"},"links":{"cited_paper":"/paper/2109.03824","citing_paper":"/paper/2606.20790"},"observation_digest":"sha256:41a0611cc9630f995a62da1699615b697bae77db37991cd0d5d7a52283a0691e","observation_id":"94781d47-b10f-4299-b472-4040ba5e0932","resolution":{"observed_at":"2026-07-04T05:39:39.971675Z","resolver_source":"arxiv_id","status":"metadata_mismatch"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2109.03824","last_updated":"2021-10-04T15:23:18Z","snapshot_observed_at":"2026-08-11T02:50:45.407187Z","submitted_at":"2021-09-08T18:00:00Z","title":"Geometry of Krylov Complexity","version":2},"cited_work":{"arxiv_id":"2109.03824","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2109.03824","snapshot_observed_at":"2026-07-04T12:19:49.361463Z","title":"Caputa, J","venue":null,"work_id":"b040d2fd-f970-40ae-bedb-e32a210db1de","year":2022},"citing_paper":{"arxiv_id":"2606.20790","last_updated":"2026-06-30T17:34:25Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2026-06-18T18:00:00Z","title":"Complexity Inequalities for Quantum Subsystems","version":2},"reference_index":62,"source":"pdf_text","source_observed_at":"2026-07-01T07:01:18.198749Z"},"links":{"cited_paper":"/paper/2109.03824","citing_paper":"/paper/2606.20790"},"observation_digest":"sha256:ff17df3cde93211430ee6a4924580b491544b8fa0dff95f20988a7e868e9000c","observation_id":"0e07815a-468c-420c-9e99-13069e9777aa","resolution":{"observed_at":"2026-07-01T07:05:28.840911Z","resolver_source":"arxiv_id","status":"metadata_mismatch"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2109.03824","last_updated":"2021-10-04T15:23:18Z","snapshot_observed_at":"2026-08-11T02:50:45.407187Z","submitted_at":"2021-09-08T18:00:00Z","title":"Geometry of Krylov Complexity","version":2},"cited_work":{"arxiv_id":"2109.03824","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2109.03824","snapshot_observed_at":"2026-07-04T12:19:49.361463Z","title":"Caputa, J","venue":null,"work_id":"b040d2fd-f970-40ae-bedb-e32a210db1de","year":2022},"citing_paper":{"arxiv_id":"2606.21662","last_updated":"2026-06-19T18:08:51Z","snapshot_observed_at":"2026-08-07T10:12:45.663710Z","submitted_at":"2026-06-19T18:08:51Z","title":"On the Universality of Probe Complexity in $\\mathcal{N}=4$ SYM","version":1},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-06-26T13:16:57.370342Z"},"links":{"cited_paper":"/paper/2109.03824","citing_paper":"/paper/2606.21662"},"observation_digest":"sha256:fbece5932995e5848328d1b403f491c6b095a0da193e25e08b637086d397099c","observation_id":"7c25ad36-30a6-4efe-99ff-3adeae98cba8","resolution":{"observed_at":"2026-07-04T07:39:38.660191Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2109.03824","last_updated":"2021-10-04T15:23:18Z","snapshot_observed_at":"2026-08-11T02:50:45.407187Z","submitted_at":"2021-09-08T18:00:00Z","title":"Geometry of Krylov Complexity","version":2},"cited_work":{"arxiv_id":"2109.03824","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2109.03824","snapshot_observed_at":"2026-07-04T12:19:49.361463Z","title":"Caputa, J","venue":null,"work_id":"b040d2fd-f970-40ae-bedb-e32a210db1de","year":2022},"citing_paper":{"arxiv_id":"2606.23785","last_updated":"2026-06-22T18:00:01Z","snapshot_observed_at":"2026-08-04T10:16:21.109108Z","submitted_at":"2026-06-22T18:00:01Z","title":"Controlled Chaos in 4D SCFTs","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-06-26T07:06:32.504627Z"},"links":{"cited_paper":"/paper/2109.03824","citing_paper":"/paper/2606.23785"},"observation_digest":"sha256:944228baa9e14a85bf4df736f322ecc2fd34be6b8690a5fc78f02d1ab6d3ad8f","observation_id":"1c4946b5-4430-40cf-aef1-ddecad1070e7","resolution":{"observed_at":"2026-07-04T12:19:49.363199Z","resolver_source":"arxiv_id","status":"metadata_mismatch"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2109.03824","last_updated":"2021-10-04T15:23:18Z","snapshot_observed_at":"2026-08-11T02:50:45.407187Z","submitted_at":"2021-09-08T18:00:00Z","title":"Geometry of Krylov Complexity","version":2},"cited_work":{"arxiv_id":"2109.03824","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2109.03824","snapshot_observed_at":"2026-07-04T12:19:49.361463Z","title":"Caputa, J","venue":null,"work_id":"b040d2fd-f970-40ae-bedb-e32a210db1de","year":2022},"citing_paper":{"arxiv_id":"2607.01351","last_updated":"2026-07-01T18:09:10Z","snapshot_observed_at":"2026-08-07T18:37:34.362404Z","submitted_at":"2026-07-01T18:09:10Z","title":"Wigner negativity in Krylov space and emergent semiclassicality","version":1},"reference_index":71,"source":"pdf_text","source_observed_at":"2026-07-03T19:27:01.063141Z"},"links":{"cited_paper":"/paper/2109.03824","citing_paper":"/paper/2607.01351"},"observation_digest":"sha256:844b0d06276527481df72caadddd58d81e3090e0dd282630ead9724a41c242eb","observation_id":"e1b16dc8-5a3c-467b-b905-a8559e86a136","resolution":{"observed_at":"2026-07-03T19:28:51.747342Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2109.03824","last_updated":"2021-10-04T15:23:18Z","snapshot_observed_at":"2026-08-11T02:50:45.407187Z","submitted_at":"2021-09-08T18:00:00Z","title":"Geometry of Krylov Complexity","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2109.03824","snapshot_observed_at":"2026-07-11T21:56:11.527892Z","title":"Caputa, J","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2607.04065","last_updated":"2026-07-19T04:36:16Z","snapshot_observed_at":"2026-08-03T21:02:08.683323Z","submitted_at":"2026-07-05T00:45:30Z","title":"The Normalised Wigner Negativity Rate as a Second-Moment Probe of Infall in AdS$_3$","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-07-11T21:56:11.527892Z"},"links":{"cited_paper":"/paper/2109.03824","citing_paper":"/paper/2607.04065"},"observation_digest":"sha256:ebffa0d14e0999ef6aefac9e47321ab06170160c4c9f1bdaed7fa6e4fdaac410","observation_id":"f7cce340-43fc-4cfd-b64d-5ddf25fededa","resolution":{"observed_at":"2026-07-11T21:56:11.527892Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2109.03824","last_updated":"2021-10-04T15:23:18Z","snapshot_observed_at":"2026-08-11T02:50:45.407187Z","submitted_at":"2021-09-08T18:00:00Z","title":"Geometry of Krylov Complexity","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2109.03824","snapshot_observed_at":"2026-08-02T08:52:51.745012Z","title":"Caputa, J.M","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2607.04065","last_updated":"2026-07-19T04:36:16Z","snapshot_observed_at":"2026-08-03T21:02:08.683323Z","submitted_at":"2026-07-05T00:45:30Z","title":"The Normalised Wigner Negativity Rate as a Second-Moment Probe of Infall in AdS$_3$","version":2},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-02T08:52:51.745012Z"},"links":{"cited_paper":"/paper/2109.03824","citing_paper":"/paper/2607.04065"},"observation_digest":"sha256:e4982f73d46619a08ed822cee1a4374be9fd78d502ef1e5a864f1edea884dd32","observation_id":"98fae156-a2ff-4509-961a-d883338b5b6c","resolution":{"observed_at":"2026-08-02T08:52:51.745012Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2109.03824","last_updated":"2021-10-04T15:23:18Z","snapshot_observed_at":"2026-08-11T02:50:45.407187Z","submitted_at":"2021-09-08T18:00:00Z","title":"Geometry of Krylov Complexity","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2109.03824","snapshot_observed_at":"2026-07-14T08:17:10.162534Z","title":"Caputa, J","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2607.10921","last_updated":"2026-07-12T20:55:21Z","snapshot_observed_at":"2026-08-06T19:12:39.129599Z","submitted_at":"2026-07-12T20:55:21Z","title":"Krylov Complexity from Loschmidt Amplitude","version":1},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-07-14T08:17:10.162534Z"},"links":{"cited_paper":"/paper/2109.03824","citing_paper":"/paper/2607.10921"},"observation_digest":"sha256:43ff84c7d10f5d377852eec373df06af81c6e5b571d091b8fc36ed7ad0d24c60","observation_id":"3f20d3ed-8b3f-497c-ae0e-616b7330c530","resolution":{"observed_at":"2026-07-14T08:17:10.162534Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2109.03824","last_updated":"2021-10-04T15:23:18Z","snapshot_observed_at":"2026-08-11T02:50:45.407187Z","submitted_at":"2021-09-08T18:00:00Z","title":"Geometry of Krylov Complexity","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2109.03824","snapshot_observed_at":"2026-08-01T18:19:15.482571Z","title":"Caputa, J.M","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2607.17346","last_updated":"2026-07-19T17:17:21Z","snapshot_observed_at":"2026-08-07T18:22:34.237628Z","submitted_at":"2026-07-19T17:17:21Z","title":"The Information Content of Krylov Observables: A Machine Learning Approach","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-01T18:19:15.482571Z"},"links":{"cited_paper":"/paper/2109.03824","citing_paper":"/paper/2607.17346"},"observation_digest":"sha256:80a9832b8e9e7d219ddc0c4c28a290d7230a4c84831974ab63e4b7ef5a887487","observation_id":"039579c9-342f-421c-b6ee-d857f99a67db","resolution":{"observed_at":"2026-08-01T18:19:15.482571Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2109.03824","last_updated":"2021-10-04T15:23:18Z","snapshot_observed_at":"2026-08-11T02:50:45.407187Z","submitted_at":"2021-09-08T18:00:00Z","title":"Geometry of Krylov Complexity","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2109.03824","snapshot_observed_at":"2026-08-01T00:56:36.004678Z","title":"Caputa, J","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2607.26011","last_updated":"2026-07-28T17:24:30Z","snapshot_observed_at":"2026-08-10T18:34:13.026467Z","submitted_at":"2026-07-28T17:24:30Z","title":"Krylov-Space Memory Cores","version":1},"reference_index":82,"source":"pdf_text","source_observed_at":"2026-08-01T00:56:36.004678Z"},"links":{"cited_paper":"/paper/2109.03824","citing_paper":"/paper/2607.26011"},"observation_digest":"sha256:7c73610b290c5e185035b8c74591c4eee72f24654937659ea24605c8e64a131e","observation_id":"9e4236a8-94f9-4c8f-bac7-aadfa7b8d067","resolution":{"observed_at":"2026-08-01T00:56:36.004678Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2109.03824","last_updated":"2021-10-04T15:23:18Z","snapshot_observed_at":"2026-08-11T02:50:45.407187Z","submitted_at":"2021-09-08T18:00:00Z","title":"Geometry of Krylov Complexity","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2109.03824","snapshot_observed_at":"2026-08-07T00:15:39.209012Z","title":"Caputa, J","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2608.02715","last_updated":"2026-08-03T18:00:00Z","snapshot_observed_at":"2026-08-07T23:09:56.513026Z","submitted_at":"2026-08-03T18:00:00Z","title":"Krylov Complexity and $c$-function along RG Flows","version":1},"reference_index":91,"source":"pdf_text","source_observed_at":"2026-08-07T00:15:39.209012Z"},"links":{"cited_paper":"/paper/2109.03824","citing_paper":"/paper/2608.02715"},"observation_digest":"sha256:7a38856368d372d4915d5c167048ea59c1a5ccd83e46985aea8b5a30283d62e9","observation_id":"f84fdb0b-8193-4ccf-accf-04c5ee6b222f","resolution":{"observed_at":"2026-08-07T00:15:39.209012Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"links":{"evidence":"/evidence","html":"/paper/2109.03824/citation-record","integrity":"/paper/2109.03824/integrity","json":"/paper/2109.03824/citation-record.json","paper":"/paper/2109.03824"},"outbound":[],"paper":{"arxiv_id":"2109.03824","last_updated":"2021-10-04T15:23:18Z","latest_version":2,"primary_category":"hep-th","snapshot_observed_at":"2026-08-11T02:50:45.407187Z","submitted_at":"2021-09-08T18:00:00Z","title":"Geometry of Krylov Complexity"},"reference_resolution":{"displayed":0,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":0,"verified_exact":0,"verified_fuzzy":0},"total_outbound_references":0},"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":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"thesis":"As of 11 August 2026, this Paper Citation Record lists 0 of 0 outbound references and 37 inbound Pith citation observations for arXiv:2109.03824."}