{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2006:DHIXJDBLO5563S3NSB6XY52GQB","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":"407c61e9d9e88e425225b38a8a275adca09035d806659930c081e354d17f44dd","cross_cats_sorted":["math-ph","math.MP"],"license":"","primary_cat":"quant-ph","submitted_at":"2006-04-17T01:11:10Z","title_canon_sha256":"3bb4803c0d4d0b1ce890a5acca90142845a719681eedd7ad9bb411e261ce26e6"},"schema_version":"1.0","source":{"id":"quant-ph/0604115","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"quant-ph/0604115","created_at":"2026-05-18T03:50:00Z"},{"alias_kind":"arxiv_version","alias_value":"quant-ph/0604115v1","created_at":"2026-05-18T03:50:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.quant-ph/0604115","created_at":"2026-05-18T03:50:00Z"},{"alias_kind":"pith_short_12","alias_value":"DHIXJDBLO556","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"DHIXJDBLO5563S3N","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"DHIXJDBL","created_at":"2026-05-18T12:25:53Z"}],"graph_snapshots":[{"event_id":"sha256:d206b7d90b87cb8555c12124a4530b8987187f8d12306d9b275063831024c4d8","target":"graph","created_at":"2026-05-18T03:50:00Z","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"},"paper":{"abstract_excerpt":"How to calculate the exponential of matrices in an explicit manner is one of fundamental problems in almost all subjects in Science.\n  Especially in Mathematical Physics or Quantum Optics many problems are reduced to this calculation by making use of some approximations whether they are appropriate or not. However, it is in general not easy.\n  In this paper we give a very useful formula which is both elementary and getting on with computer.","authors_text":"Hiroshi Oike, Kazuyuki Fujii","cross_cats":["math-ph","math.MP"],"headline":"","license":"","primary_cat":"quant-ph","submitted_at":"2006-04-17T01:11:10Z","title":"How to Calculate the Exponential of Matrices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"quant-ph/0604115","kind":"arxiv","version":1},"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:d7246ebf7267d5ee6011a1439cbae2e5c9e798d22c0d74fb50aae765fc041a62","target":"record","created_at":"2026-05-18T03:50:00Z","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":"407c61e9d9e88e425225b38a8a275adca09035d806659930c081e354d17f44dd","cross_cats_sorted":["math-ph","math.MP"],"license":"","primary_cat":"quant-ph","submitted_at":"2006-04-17T01:11:10Z","title_canon_sha256":"3bb4803c0d4d0b1ce890a5acca90142845a719681eedd7ad9bb411e261ce26e6"},"schema_version":"1.0","source":{"id":"quant-ph/0604115","kind":"arxiv","version":1}},"canonical_sha256":"19d1748c2b777bedcb6d907d7c7746807c9d420d8bbe22a5d67deeaa1d224637","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"19d1748c2b777bedcb6d907d7c7746807c9d420d8bbe22a5d67deeaa1d224637","first_computed_at":"2026-05-18T03:50:00.285264Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:50:00.285264Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RHxY34T7Od0PN3wpJ5tBM4D636NDdkDU8/qLts9awavZdGrafCL3crsXKR2ty3EvBL+1brwtLYx1gVx9IF34Cg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:50:00.285943Z","signed_message":"canonical_sha256_bytes"},"source_id":"quant-ph/0604115","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d7246ebf7267d5ee6011a1439cbae2e5c9e798d22c0d74fb50aae765fc041a62","sha256:d206b7d90b87cb8555c12124a4530b8987187f8d12306d9b275063831024c4d8"],"state_sha256":"bc0a1b567c2f35c8564283a643a776bfb7f34572731ba500bfbcac79f723b6c7"}