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We establish a direct link between dynamics in the time-dependent Krylov subspace and the underlying Lie-algebraic structure of the Hamiltonian. We develop a general framework in which the dynamics in the time-dependent Krylov subspace is generated by ladder operators of the associated Lie algebra. In particular, we identify the minimal conditions under which the exact time-dependent Krylov dynamics is naturally determined by the interaction-picture Hamil","authors_text":"Adolfo del Campo, Andr\\'as Grabarits, E. 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Remarkably, saturation of this bound is strongly affected by temporal driving and persists only when the Hamiltonian commutes with itself at different times.","weakest_assumption":"The Hamiltonian possesses an underlying Lie-algebraic structure that permits an embedded sl(2,C) subalgebra or equivalent ladder-operator generation of the Krylov dynamics, as stated in the identification of 'minimal conditions under which the exact time-dependent Krylov dynamics is naturally determined by the interaction-picture Hamiltonian and governed by an embedded sl(2,C) subalgebra.'"}},"verdict_id":"7fc08046-3b08-4bc9-ae1d-9a1afbc37e0f"}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:cdd674a62c29078839e063a93e8b7f9c48af950600c1eef27a87dbab1b73a4f7","target":"record","created_at":"2026-05-20T00:00:40Z","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":"1e7e73d615222e168999ae1463feeff316dd4a94028308bd61ad756e8b47ea6d","cross_cats_sorted":["hep-th"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"quant-ph","submitted_at":"2026-05-06T18:00:00Z","title_canon_sha256":"60907d5c45207e012f8ea72536dfa9faf2970cfb8ce2926723d14de2befbc843"},"schema_version":"1.0","source":{"id":"2605.05290","kind":"arxiv","version":2}},"canonical_sha256":"a6e268de72810ab710524f7bf2b510de3e4e8eaf10102f928d88aefdcbf28273","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a6e268de72810ab710524f7bf2b510de3e4e8eaf10102f928d88aefdcbf28273","first_computed_at":"2026-05-20T00:00:40.899663Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-20T00:00:40.899663Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"oCvzjFrog4BLlWxgWau7QdAqjAx43A5g8Qnh77L86vmu+MEUcAmQkjt4YzQ7nGeRvHe52e0YFaK1f9mFrHrQAg==","signature_status":"signed_v1","signed_at":"2026-05-20T00:00:40.900466Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.05290","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cdd674a62c29078839e063a93e8b7f9c48af950600c1eef27a87dbab1b73a4f7","sha256:3fce8fb77c43683a1cea1ed461522dd04d885553829c7a0f09aa16cdaacc019d"],"state_sha256":"3534eff61e381301dce41e76718e4e244c1a61ab3f89e6dfc2a0af265c82ac7e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/oU4Z/sgINIOGKHZmQmN+mlS6y5fDdHUPZi3nh458pHjI0pZdtzcEr6aNW6g8qjgPjlVfgGSbmq49GJmMh57CA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T18:43:40.806834Z","bundle_sha256":"6e6df32128a10497a8e8aab66b166706d81624132e42d6b5c525d3ddba350397"}}