{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:RU7IHXQ4VMXC3WBD2XIECT6XHE","short_pith_number":"pith:RU7IHXQ4","schema_version":"1.0","canonical_sha256":"8d3e83de1cab2e2dd823d5d0414fd739225245dc8aac9675322ca0f5c974d6f1","source":{"kind":"arxiv","id":"2602.04949","version":3},"attestation_state":"computed","paper":{"title":"Emergence of Krylov complexity through quantum walks: An exploration of the quantum origins of complexity","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cond-mat.str-el","quant-ph"],"primary_cat":"hep-th","authors_text":"Dimitrios Patramanis, Watse Sybesma","submitted_at":"2026-02-04T19:00:00Z","abstract_excerpt":"In this work we study the relationship between quantum random walks on graphs and Krylov/spread complexity. We show that the latter's definition naturally emerges through a canonical method of reducing a graph to a chain, on which we can identify the usual Krylov structure. We use this identification to construct families of graphs corresponding to special classes of systems with known complexity features and conversely, to compute Krylov complexity for graphs of physical interest. The two main outcomes are the analytic computation of the Lanczos coefficients for the SYK model for an arbitrary"},"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":"2602.04949","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2026-02-04T19:00:00Z","cross_cats_sorted":["cond-mat.str-el","quant-ph"],"title_canon_sha256":"a40eb78c31da1099c37fbfc41225c4b48ec797f6fdae88faff5051fa438ac46f","abstract_canon_sha256":"41338e423dce42b5883d2c1ecc7eed41506f724f98ae125ee41c303cc52daf96"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-09T02:07:19.373777Z","signature_b64":"l9NDBl5b91FY3V6IAL2kUjBgEjkWInTDvqF/9dKQIUDSUjywlFAIM1D/6mXQz02a1bIRY0tuXKNEkln0rbmQDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8d3e83de1cab2e2dd823d5d0414fd739225245dc8aac9675322ca0f5c974d6f1","last_reissued_at":"2026-06-09T02:07:19.372715Z","signature_status":"signed_v1","first_computed_at":"2026-06-09T02:07:19.372715Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Emergence of Krylov complexity through quantum walks: An exploration of the quantum origins of complexity","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cond-mat.str-el","quant-ph"],"primary_cat":"hep-th","authors_text":"Dimitrios Patramanis, Watse Sybesma","submitted_at":"2026-02-04T19:00:00Z","abstract_excerpt":"In this work we study the relationship between quantum random walks on graphs and Krylov/spread complexity. We show that the latter's definition naturally emerges through a canonical method of reducing a graph to a chain, on which we can identify the usual Krylov structure. We use this identification to construct families of graphs corresponding to special classes of systems with known complexity features and conversely, to compute Krylov complexity for graphs of physical interest. The two main outcomes are the analytic computation of the Lanczos coefficients for the SYK model for an arbitrary"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2602.04949","kind":"arxiv","version":3},"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/2602.04949/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":"2602.04949","created_at":"2026-06-09T02:07:19.372854+00:00"},{"alias_kind":"arxiv_version","alias_value":"2602.04949v3","created_at":"2026-06-09T02:07:19.372854+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2602.04949","created_at":"2026-06-09T02:07:19.372854+00:00"},{"alias_kind":"pith_short_12","alias_value":"RU7IHXQ4VMXC","created_at":"2026-06-09T02:07:19.372854+00:00"},{"alias_kind":"pith_short_16","alias_value":"RU7IHXQ4VMXC3WBD","created_at":"2026-06-09T02:07:19.372854+00:00"},{"alias_kind":"pith_short_8","alias_value":"RU7IHXQ4","created_at":"2026-06-09T02:07:19.372854+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2603.19359","citing_title":"Towards a Refinement of Krylov Complexity: Scrambling, Classical Operator Growth and Replicas","ref_index":84,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/RU7IHXQ4VMXC3WBD2XIECT6XHE","json":"https://pith.science/pith/RU7IHXQ4VMXC3WBD2XIECT6XHE.json","graph_json":"https://pith.science/api/pith-number/RU7IHXQ4VMXC3WBD2XIECT6XHE/graph.json","events_json":"https://pith.science/api/pith-number/RU7IHXQ4VMXC3WBD2XIECT6XHE/events.json","paper":"https://pith.science/paper/RU7IHXQ4"},"agent_actions":{"view_html":"https://pith.science/pith/RU7IHXQ4VMXC3WBD2XIECT6XHE","download_json":"https://pith.science/pith/RU7IHXQ4VMXC3WBD2XIECT6XHE.json","view_paper":"https://pith.science/paper/RU7IHXQ4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2602.04949&json=true","fetch_graph":"https://pith.science/api/pith-number/RU7IHXQ4VMXC3WBD2XIECT6XHE/graph.json","fetch_events":"https://pith.science/api/pith-number/RU7IHXQ4VMXC3WBD2XIECT6XHE/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/RU7IHXQ4VMXC3WBD2XIECT6XHE/action/timestamp_anchor","attest_storage":"https://pith.science/pith/RU7IHXQ4VMXC3WBD2XIECT6XHE/action/storage_attestation","attest_author":"https://pith.science/pith/RU7IHXQ4VMXC3WBD2XIECT6XHE/action/author_attestation","sign_citation":"https://pith.science/pith/RU7IHXQ4VMXC3WBD2XIECT6XHE/action/citation_signature","submit_replication":"https://pith.science/pith/RU7IHXQ4VMXC3WBD2XIECT6XHE/action/replication_record"}},"created_at":"2026-06-09T02:07:19.372854+00:00","updated_at":"2026-06-09T02:07:19.372854+00:00"}