{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:REJI65IYY6L7QYDMF36GZ2F2VD","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"934042daefd0c1c3ae1d4aef13bfbf7d1e4a4a90b58e498fb83efde142e68e6b","cross_cats_sorted":["cond-mat.stat-mech","cond-mat.str-el","quant-ph"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2021-09-08T18:00:00Z","title_canon_sha256":"f5ccea1f7cc9c8078ad8930bb2f6f6d3b5f62d41754a06790acd3f08f2e27578"},"schema_version":"1.0","source":{"id":"2109.03824","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2109.03824","created_at":"2026-07-05T03:19:45Z"},{"alias_kind":"arxiv_version","alias_value":"2109.03824v2","created_at":"2026-07-05T03:19:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2109.03824","created_at":"2026-07-05T03:19:45Z"},{"alias_kind":"pith_short_12","alias_value":"REJI65IYY6L7","created_at":"2026-07-05T03:19:45Z"},{"alias_kind":"pith_short_16","alias_value":"REJI65IYY6L7QYDM","created_at":"2026-07-05T03:19:45Z"},{"alias_kind":"pith_short_8","alias_value":"REJI65IY","created_at":"2026-07-05T03:19:45Z"}],"graph_snapshots":[{"event_id":"sha256:1f551309059c919e2302072490c14c2c81e77ea6fbbb9971b8c7787b5e29e0dd","target":"graph","created_at":"2026-07-05T03:19:45Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2109.03824/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We develop a geometric approach to operator growth and Krylov complexity in many-body quantum systems governed by symmetries. We start by showing a direct link between a unitary evolution with the Liouvillian and the displacement operator of appropriate generalized coherent states. This connection maps operator growth to a purely classical motion in phase space. The phase spaces are endowed with a natural information metric. We show that, in this geometry, operator growth is represented by geodesics and Krylov complexity is proportional to a volume. This geometric perspective also provides two","authors_text":"Dimitrios Patramanis, Javier M. Magan, Pawel Caputa","cross_cats":["cond-mat.stat-mech","cond-mat.str-el","quant-ph"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2021-09-08T18:00:00Z","title":"Geometry of Krylov Complexity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2109.03824","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:1c4181fa4f7083d5928779965fbc040de4bc896004a33841df647f5f173156fe","target":"record","created_at":"2026-07-05T03:19:45Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"934042daefd0c1c3ae1d4aef13bfbf7d1e4a4a90b58e498fb83efde142e68e6b","cross_cats_sorted":["cond-mat.stat-mech","cond-mat.str-el","quant-ph"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2021-09-08T18:00:00Z","title_canon_sha256":"f5ccea1f7cc9c8078ad8930bb2f6f6d3b5f62d41754a06790acd3f08f2e27578"},"schema_version":"1.0","source":{"id":"2109.03824","kind":"arxiv","version":2}},"canonical_sha256":"89128f7518c797f8606c2efc6ce8baa8c33f768a1f9e2863445bc200889e5823","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"89128f7518c797f8606c2efc6ce8baa8c33f768a1f9e2863445bc200889e5823","first_computed_at":"2026-07-05T03:19:45.758133Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T03:19:45.758133Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"W6ClR45+pGCOYpbj6XsXlQYpZGOnD7xT9DDd3zuCU799oLsap1bkh4o3Pz8BEnHFta+vwx2lSXVPRvIG+qzvBg==","signature_status":"signed_v1","signed_at":"2026-07-05T03:19:45.758635Z","signed_message":"canonical_sha256_bytes"},"source_id":"2109.03824","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1c4181fa4f7083d5928779965fbc040de4bc896004a33841df647f5f173156fe","sha256:1f551309059c919e2302072490c14c2c81e77ea6fbbb9971b8c7787b5e29e0dd"],"state_sha256":"15f3738ff00f32d509c8858be1b3c8f10f12d5d599fd2e750300e34cff16eec6"}