{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:EJVV2ZJTWRZ37KMS342MFPY7TV","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":"8275cfb1b6a2bd8b8fc26dc3d78565170635ed969882480a1d3e012070ae6529","cross_cats_sorted":["math.MP","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2008-12-02T18:07:39Z","title_canon_sha256":"ac34ffa9833973fddb6b90ac3101a211a9a9fca298b1333711efab6d7190e669"},"schema_version":"1.0","source":{"id":"0812.0562","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0812.0562","created_at":"2026-07-04T17:22:51Z"},{"alias_kind":"arxiv_version","alias_value":"0812.0562v3","created_at":"2026-07-04T17:22:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0812.0562","created_at":"2026-07-04T17:22:51Z"},{"alias_kind":"pith_short_12","alias_value":"EJVV2ZJTWRZ3","created_at":"2026-07-04T17:22:51Z"},{"alias_kind":"pith_short_16","alias_value":"EJVV2ZJTWRZ37KMS","created_at":"2026-07-04T17:22:51Z"},{"alias_kind":"pith_short_8","alias_value":"EJVV2ZJT","created_at":"2026-07-04T17:22:51Z"}],"graph_snapshots":[{"event_id":"sha256:efa714355622989bfad8c9c39cefef93430f9f638dee1a2d1df93d46ef5b408b","target":"graph","created_at":"2026-07-04T17:22:51Z","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/0812.0562/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We present a decomposition scheme based on Lie-Trotter-Suzuki product formulae to represent an ordered operator exponential as a product of ordinary operator exponentials. We provide a rigorous proof that does not use a time-displacement superoperator, and can be applied to non-analytic functions. Our proof provides explicit bounds on the error and includes cases where the functions are not infinitely differentiable. We show that Lie-Trotter-Suzuki product formulae can still be used for functions that are not infinitely differentiable, but that arbitrary order scaling may not be achieved.","authors_text":"Barry C. Sanders (U Calgary), Dominic W. Berry (Macquarie University), Nathan Wiebe (U Calgary), Peter Hoyer (U Calgary)","cross_cats":["math.MP","quant-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2008-12-02T18:07:39Z","title":"Higher Order Decompositions of Ordered Operator Exponentials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0812.0562","kind":"arxiv","version":3},"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":"sha256:4f7ff1177f1b63f31b63318e511c9393c9fa79189a7a44159977a1b93630b96c","target":"record","created_at":"2026-07-04T17:22:51Z","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":"8275cfb1b6a2bd8b8fc26dc3d78565170635ed969882480a1d3e012070ae6529","cross_cats_sorted":["math.MP","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2008-12-02T18:07:39Z","title_canon_sha256":"ac34ffa9833973fddb6b90ac3101a211a9a9fca298b1333711efab6d7190e669"},"schema_version":"1.0","source":{"id":"0812.0562","kind":"arxiv","version":3}},"canonical_sha256":"226b5d6533b473bfa992df34c2bf1f9d4cde50c8b920117409e302f5dc34b585","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"226b5d6533b473bfa992df34c2bf1f9d4cde50c8b920117409e302f5dc34b585","first_computed_at":"2026-07-04T17:22:51.534433Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T17:22:51.534433Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bkM2bsBMvmiX/ZlhTI82bz39KQgGQ5HoAwGgSm+/MzI1mXlK3bq840Co4b2nbE5UIGk6GyCtg8ZIknqgOhQaDA==","signature_status":"signed_v1","signed_at":"2026-07-04T17:22:51.534775Z","signed_message":"canonical_sha256_bytes"},"source_id":"0812.0562","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4f7ff1177f1b63f31b63318e511c9393c9fa79189a7a44159977a1b93630b96c","sha256:efa714355622989bfad8c9c39cefef93430f9f638dee1a2d1df93d46ef5b408b"],"state_sha256":"b0c9c6fb92e3493b318d07bc55aa382380f9097cb4b945467829c8cc04da905e"}