{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:ENFXI2NOMD6TTW2T2QNDZHWONX","short_pith_number":"pith:ENFXI2NO","schema_version":"1.0","canonical_sha256":"234b7469ae60fd39db53d41a3c9ece6ddfe1cd5e0be93fb103e5066b1b84726f","source":{"kind":"arxiv","id":"1204.2318","version":3},"attestation_state":"computed","paper":{"title":"A note on the switching adiabatic theorem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","quant-ph"],"primary_cat":"math-ph","authors_text":"Alexander Elgart, George A. Hagedorn","submitted_at":"2012-04-11T02:08:20Z","abstract_excerpt":"We derive a nearly optimal upper bound on the running time in the adiabatic theorem for a switching family of Hamiltonians. We assume the switching Hamiltonian is in the Gevrey class $G^\\alpha$ as a function of time, and we show that the error in adiabatic approximation remains small for running times of order $g^{-2}\\,|\\ln\\,g\\,|^{6\\alpha}$. Here $g$ denotes the minimal spectral gap between the eigenvalue(s) of interest and the rest of the spectrum of the instantaneous Hamiltonian."},"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":"1204.2318","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-04-11T02:08:20Z","cross_cats_sorted":["math.MP","quant-ph"],"title_canon_sha256":"8f03a8df58ba5e5985005954573637d955d8743c91eb7b6c94671eac3269ca32","abstract_canon_sha256":"027456e99a2ced93a98cf583374952d562e79ee4fa2d48ad155f5621081c3b62"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:57:53.765283Z","signature_b64":"AEe9k+5rqnMO8RAAratgCrshSvS20s8etCHNqsxI6Gney810CfCoqicpqo3jABVL2DoE32I7DQ2tB0bU4hj3Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"234b7469ae60fd39db53d41a3c9ece6ddfe1cd5e0be93fb103e5066b1b84726f","last_reissued_at":"2026-05-18T01:57:53.764793Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:57:53.764793Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A note on the switching adiabatic theorem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","quant-ph"],"primary_cat":"math-ph","authors_text":"Alexander Elgart, George A. Hagedorn","submitted_at":"2012-04-11T02:08:20Z","abstract_excerpt":"We derive a nearly optimal upper bound on the running time in the adiabatic theorem for a switching family of Hamiltonians. We assume the switching Hamiltonian is in the Gevrey class $G^\\alpha$ as a function of time, and we show that the error in adiabatic approximation remains small for running times of order $g^{-2}\\,|\\ln\\,g\\,|^{6\\alpha}$. Here $g$ denotes the minimal spectral gap between the eigenvalue(s) of interest and the rest of the spectrum of the instantaneous Hamiltonian."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.2318","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":""},"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":"1204.2318","created_at":"2026-05-18T01:57:53.764879+00:00"},{"alias_kind":"arxiv_version","alias_value":"1204.2318v3","created_at":"2026-05-18T01:57:53.764879+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.2318","created_at":"2026-05-18T01:57:53.764879+00:00"},{"alias_kind":"pith_short_12","alias_value":"ENFXI2NOMD6T","created_at":"2026-05-18T12:27:04.183437+00:00"},{"alias_kind":"pith_short_16","alias_value":"ENFXI2NOMD6TTW2T","created_at":"2026-05-18T12:27:04.183437+00:00"},{"alias_kind":"pith_short_8","alias_value":"ENFXI2NO","created_at":"2026-05-18T12:27:04.183437+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2605.22770","citing_title":"Adiabatic Quantum Phase Estimation","ref_index":29,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/ENFXI2NOMD6TTW2T2QNDZHWONX","json":"https://pith.science/pith/ENFXI2NOMD6TTW2T2QNDZHWONX.json","graph_json":"https://pith.science/api/pith-number/ENFXI2NOMD6TTW2T2QNDZHWONX/graph.json","events_json":"https://pith.science/api/pith-number/ENFXI2NOMD6TTW2T2QNDZHWONX/events.json","paper":"https://pith.science/paper/ENFXI2NO"},"agent_actions":{"view_html":"https://pith.science/pith/ENFXI2NOMD6TTW2T2QNDZHWONX","download_json":"https://pith.science/pith/ENFXI2NOMD6TTW2T2QNDZHWONX.json","view_paper":"https://pith.science/paper/ENFXI2NO","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1204.2318&json=true","fetch_graph":"https://pith.science/api/pith-number/ENFXI2NOMD6TTW2T2QNDZHWONX/graph.json","fetch_events":"https://pith.science/api/pith-number/ENFXI2NOMD6TTW2T2QNDZHWONX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ENFXI2NOMD6TTW2T2QNDZHWONX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ENFXI2NOMD6TTW2T2QNDZHWONX/action/storage_attestation","attest_author":"https://pith.science/pith/ENFXI2NOMD6TTW2T2QNDZHWONX/action/author_attestation","sign_citation":"https://pith.science/pith/ENFXI2NOMD6TTW2T2QNDZHWONX/action/citation_signature","submit_replication":"https://pith.science/pith/ENFXI2NOMD6TTW2T2QNDZHWONX/action/replication_record"}},"created_at":"2026-05-18T01:57:53.764879+00:00","updated_at":"2026-05-18T01:57:53.764879+00:00"}