{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2008:NGUJG2TSEPQGHUJFAU3JBTAGSU","short_pith_number":"pith:NGUJG2TS","canonical_record":{"source":{"id":"0801.0702","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"quant-ph","submitted_at":"2008-01-04T17:26:59Z","cross_cats_sorted":[],"title_canon_sha256":"32f7208b85e990682eea552d8550890e38414784fc886256946f027c6c73848b","abstract_canon_sha256":"78ddbfb1eed1258a148338180d6e026a6e9e2a8b0d24ae855a4341e7cfef7398"},"schema_version":"1.0"},"canonical_sha256":"69a8936a7223e063d125053690cc0695294552ce3fe0aafa483d2242ad6a4a63","source":{"kind":"arxiv","id":"0801.0702","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0801.0702","created_at":"2026-05-18T04:02:36Z"},{"alias_kind":"arxiv_version","alias_value":"0801.0702v2","created_at":"2026-05-18T04:02:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0801.0702","created_at":"2026-05-18T04:02:36Z"},{"alias_kind":"pith_short_12","alias_value":"NGUJG2TSEPQG","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_16","alias_value":"NGUJG2TSEPQGHUJF","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_8","alias_value":"NGUJG2TS","created_at":"2026-05-18T12:25:57Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2008:NGUJG2TSEPQGHUJFAU3JBTAGSU","target":"record","payload":{"canonical_record":{"source":{"id":"0801.0702","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"quant-ph","submitted_at":"2008-01-04T17:26:59Z","cross_cats_sorted":[],"title_canon_sha256":"32f7208b85e990682eea552d8550890e38414784fc886256946f027c6c73848b","abstract_canon_sha256":"78ddbfb1eed1258a148338180d6e026a6e9e2a8b0d24ae855a4341e7cfef7398"},"schema_version":"1.0"},"canonical_sha256":"69a8936a7223e063d125053690cc0695294552ce3fe0aafa483d2242ad6a4a63","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:02:36.485426Z","signature_b64":"G0VpnMJ9S7QC+5bRbXf/8NSc2/2OTcI+OYezTSQIfOtU6yz3aY2mAulMpMUf+IijLIbda6Zpe43+A5K+LgKEAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"69a8936a7223e063d125053690cc0695294552ce3fe0aafa483d2242ad6a4a63","last_reissued_at":"2026-05-18T04:02:36.484730Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:02:36.484730Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0801.0702","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:02:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2GiU4DlA0rjBEqxqzDrA0Mru2nLCni8hbNbfWaWcqUCKqW+ezgdWOixrILnPyWRHipPjNIPz20wyaXmrY4rdBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T22:06:00.916761Z"},"content_sha256":"3cacb6f27f2177befa59cf9ad2c5a757016b1781474da8dde0d143dcaaa1ec90","schema_version":"1.0","event_id":"sha256:3cacb6f27f2177befa59cf9ad2c5a757016b1781474da8dde0d143dcaaa1ec90"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2008:NGUJG2TSEPQGHUJFAU3JBTAGSU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Analysis of Lyapunov Method for Control of Quantum Systems","license":"","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Sonia G. Schirmer, Xiaoting Wang","submitted_at":"2008-01-04T17:26:59Z","abstract_excerpt":"We present a detailed analysis of the convergence properties of Lyapunov control for finite-dimensional quantum systems based on the application of the LaSalle invariance principle and stability analysis from dynamical systems and control theory. For a certain class of ideal Hamiltonians, convergence results are derived both pure-state and mixed-state control, and the effectiveness of the method for more realistic Hamiltonians is discussed."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0801.0702","kind":"arxiv","version":2},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:02:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WSA2u65Ag8s/+gIMl/1dOvVW+19WNGqTTTtkSULW86z77XxgoFSbkeOptm2bFjFWiLoVS3+gIS+Its17tkeEBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T22:06:00.917489Z"},"content_sha256":"096050c8b9b40e4a3c6a10aab08dd64a91751a547bf955ef121fbbd696ea6f8f","schema_version":"1.0","event_id":"sha256:096050c8b9b40e4a3c6a10aab08dd64a91751a547bf955ef121fbbd696ea6f8f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NGUJG2TSEPQGHUJFAU3JBTAGSU/bundle.json","state_url":"https://pith.science/pith/NGUJG2TSEPQGHUJFAU3JBTAGSU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NGUJG2TSEPQGHUJFAU3JBTAGSU/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-06T22:06:00Z","links":{"resolver":"https://pith.science/pith/NGUJG2TSEPQGHUJFAU3JBTAGSU","bundle":"https://pith.science/pith/NGUJG2TSEPQGHUJFAU3JBTAGSU/bundle.json","state":"https://pith.science/pith/NGUJG2TSEPQGHUJFAU3JBTAGSU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NGUJG2TSEPQGHUJFAU3JBTAGSU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:NGUJG2TSEPQGHUJFAU3JBTAGSU","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":"78ddbfb1eed1258a148338180d6e026a6e9e2a8b0d24ae855a4341e7cfef7398","cross_cats_sorted":[],"license":"","primary_cat":"quant-ph","submitted_at":"2008-01-04T17:26:59Z","title_canon_sha256":"32f7208b85e990682eea552d8550890e38414784fc886256946f027c6c73848b"},"schema_version":"1.0","source":{"id":"0801.0702","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0801.0702","created_at":"2026-05-18T04:02:36Z"},{"alias_kind":"arxiv_version","alias_value":"0801.0702v2","created_at":"2026-05-18T04:02:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0801.0702","created_at":"2026-05-18T04:02:36Z"},{"alias_kind":"pith_short_12","alias_value":"NGUJG2TSEPQG","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_16","alias_value":"NGUJG2TSEPQGHUJF","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_8","alias_value":"NGUJG2TS","created_at":"2026-05-18T12:25:57Z"}],"graph_snapshots":[{"event_id":"sha256:096050c8b9b40e4a3c6a10aab08dd64a91751a547bf955ef121fbbd696ea6f8f","target":"graph","created_at":"2026-05-18T04:02:36Z","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":"We present a detailed analysis of the convergence properties of Lyapunov control for finite-dimensional quantum systems based on the application of the LaSalle invariance principle and stability analysis from dynamical systems and control theory. For a certain class of ideal Hamiltonians, convergence results are derived both pure-state and mixed-state control, and the effectiveness of the method for more realistic Hamiltonians is discussed.","authors_text":"Sonia G. Schirmer, Xiaoting Wang","cross_cats":[],"headline":"","license":"","primary_cat":"quant-ph","submitted_at":"2008-01-04T17:26:59Z","title":"Analysis of Lyapunov Method for Control of Quantum Systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0801.0702","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":"sha256:3cacb6f27f2177befa59cf9ad2c5a757016b1781474da8dde0d143dcaaa1ec90","target":"record","created_at":"2026-05-18T04:02:36Z","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":"78ddbfb1eed1258a148338180d6e026a6e9e2a8b0d24ae855a4341e7cfef7398","cross_cats_sorted":[],"license":"","primary_cat":"quant-ph","submitted_at":"2008-01-04T17:26:59Z","title_canon_sha256":"32f7208b85e990682eea552d8550890e38414784fc886256946f027c6c73848b"},"schema_version":"1.0","source":{"id":"0801.0702","kind":"arxiv","version":2}},"canonical_sha256":"69a8936a7223e063d125053690cc0695294552ce3fe0aafa483d2242ad6a4a63","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"69a8936a7223e063d125053690cc0695294552ce3fe0aafa483d2242ad6a4a63","first_computed_at":"2026-05-18T04:02:36.484730Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:02:36.484730Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"G0VpnMJ9S7QC+5bRbXf/8NSc2/2OTcI+OYezTSQIfOtU6yz3aY2mAulMpMUf+IijLIbda6Zpe43+A5K+LgKEAw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:02:36.485426Z","signed_message":"canonical_sha256_bytes"},"source_id":"0801.0702","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3cacb6f27f2177befa59cf9ad2c5a757016b1781474da8dde0d143dcaaa1ec90","sha256:096050c8b9b40e4a3c6a10aab08dd64a91751a547bf955ef121fbbd696ea6f8f"],"state_sha256":"457fe154d27df6ada7a28efdf16d698b81c2d8bf915142a2823a711ce00be591"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mU9egBsdIOC2CV0ZotliEqQqVKUCkfT69SNMqyvrLutpiHyROL8SJ2p76eTIN7kd7Yd4Ub+3hQvjOH8tjgceAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T22:06:00.921600Z","bundle_sha256":"c0194b02f66ac9dae6975db131892907baa6d7f30a44407d35db50fba7d818ce"}}