{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2022:JVXXRUJVAMFBAE36CVOE6LXR3T","short_pith_number":"pith:JVXXRUJV","schema_version":"1.0","canonical_sha256":"4d6f78d135030a10137e155c4f2ef1dcd9debae421ff341a8ea74203eb8bad89","source":{"kind":"arxiv","id":"2205.12815","version":1},"attestation_state":"computed","paper":{"title":"Krylov complexity and orthogonal polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","quant-ph"],"primary_cat":"hep-th","authors_text":"Wolfgang M\\\"uck, Yi Yang","submitted_at":"2022-05-25T14:40:54Z","abstract_excerpt":"Krylov complexity measures operator growth with respect to a basis, which is adapted to the Heisenberg time evolution. The construction of that basis relies on the Lanczos algorithm, also known as the recursion method. The mathematics of Krylov complexity can be described in terms of orthogonal polynomials. We provide a pedagogical introduction to the subject and work out analytically a number of examples involving the classical orthogonal polynomials, polynomials of the Hahn class, and the Tricomi-Carlitz polynomials."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2205.12815","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2022-05-25T14:40:54Z","cross_cats_sorted":["cond-mat.stat-mech","quant-ph"],"title_canon_sha256":"8e3d790c7136a84555dc4280736c54183e0f7201892b66fcb3e7e22dd374dab7","abstract_canon_sha256":"d5e4ad8d79d7a10250ddbc3a3f9059d306aa7950c10957bc31d6a3cbf2124f3e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:56:18.006999Z","signature_b64":"sBlozk+KoECRIl+0zPqIqUu0PihZEPXR5nc/9hlIeaok346Rt45T5jS93yLwm59X+CpvsGnU6HFYdpti1sGyAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4d6f78d135030a10137e155c4f2ef1dcd9debae421ff341a8ea74203eb8bad89","last_reissued_at":"2026-07-05T04:56:18.006508Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:56:18.006508Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Krylov complexity and orthogonal polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","quant-ph"],"primary_cat":"hep-th","authors_text":"Wolfgang M\\\"uck, Yi Yang","submitted_at":"2022-05-25T14:40:54Z","abstract_excerpt":"Krylov complexity measures operator growth with respect to a basis, which is adapted to the Heisenberg time evolution. The construction of that basis relies on the Lanczos algorithm, also known as the recursion method. The mathematics of Krylov complexity can be described in terms of orthogonal polynomials. We provide a pedagogical introduction to the subject and work out analytically a number of examples involving the classical orthogonal polynomials, polynomials of the Hahn class, and the Tricomi-Carlitz polynomials."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2205.12815","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2205.12815/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"2205.12815","created_at":"2026-07-05T04:56:18.006571+00:00"},{"alias_kind":"arxiv_version","alias_value":"2205.12815v1","created_at":"2026-07-05T04:56:18.006571+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2205.12815","created_at":"2026-07-05T04:56:18.006571+00:00"},{"alias_kind":"pith_short_12","alias_value":"JVXXRUJVAMFB","created_at":"2026-07-05T04:56:18.006571+00:00"},{"alias_kind":"pith_short_16","alias_value":"JVXXRUJVAMFBAE36","created_at":"2026-07-05T04:56:18.006571+00:00"},{"alias_kind":"pith_short_8","alias_value":"JVXXRUJV","created_at":"2026-07-05T04:56:18.006571+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":8,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2607.05294","citing_title":"Polynomial Initial-State Jumps and Christoffel Transforms in Krylov Complexity","ref_index":7,"is_internal_anchor":true},{"citing_arxiv_id":"2606.21662","citing_title":"On the Universality of Probe Complexity in $\\mathcal{N}=4$ SYM","ref_index":19,"is_internal_anchor":false},{"citing_arxiv_id":"2607.01351","citing_title":"Wigner negativity in Krylov space and emergent semiclassicality","ref_index":48,"is_internal_anchor":false},{"citing_arxiv_id":"2605.13956","citing_title":"q-Askey Deformations of Double-Scaled SYK","ref_index":137,"is_internal_anchor":false},{"citing_arxiv_id":"2606.20220","citing_title":"Higher-loop wormhole length in sine-dilaton gravity from DSSYK Krylov complexity","ref_index":41,"is_internal_anchor":false},{"citing_arxiv_id":"2605.28681","citing_title":"Krylov complexity has it all","ref_index":14,"is_internal_anchor":false},{"citing_arxiv_id":"2601.09801","citing_title":"Probing the Chaos to Integrability Transition in Double-Scaled SYK","ref_index":98,"is_internal_anchor":false},{"citing_arxiv_id":"2605.13956","citing_title":"q-Askey Deformations of Double-Scaled SYK","ref_index":137,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/JVXXRUJVAMFBAE36CVOE6LXR3T","json":"https://pith.science/pith/JVXXRUJVAMFBAE36CVOE6LXR3T.json","graph_json":"https://pith.science/api/pith-number/JVXXRUJVAMFBAE36CVOE6LXR3T/graph.json","events_json":"https://pith.science/api/pith-number/JVXXRUJVAMFBAE36CVOE6LXR3T/events.json","paper":"https://pith.science/paper/JVXXRUJV"},"agent_actions":{"view_html":"https://pith.science/pith/JVXXRUJVAMFBAE36CVOE6LXR3T","download_json":"https://pith.science/pith/JVXXRUJVAMFBAE36CVOE6LXR3T.json","view_paper":"https://pith.science/paper/JVXXRUJV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2205.12815&json=true","fetch_graph":"https://pith.science/api/pith-number/JVXXRUJVAMFBAE36CVOE6LXR3T/graph.json","fetch_events":"https://pith.science/api/pith-number/JVXXRUJVAMFBAE36CVOE6LXR3T/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JVXXRUJVAMFBAE36CVOE6LXR3T/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JVXXRUJVAMFBAE36CVOE6LXR3T/action/storage_attestation","attest_author":"https://pith.science/pith/JVXXRUJVAMFBAE36CVOE6LXR3T/action/author_attestation","sign_citation":"https://pith.science/pith/JVXXRUJVAMFBAE36CVOE6LXR3T/action/citation_signature","submit_replication":"https://pith.science/pith/JVXXRUJVAMFBAE36CVOE6LXR3T/action/replication_record"}},"created_at":"2026-07-05T04:56:18.006571+00:00","updated_at":"2026-07-05T04:56:18.006571+00:00"}