{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:G3I7XMHMNZ5EJGI6HFPIQ4S4Z3","short_pith_number":"pith:G3I7XMHM","canonical_record":{"source":{"id":"1207.3120","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2012-07-12T23:26:57Z","cross_cats_sorted":[],"title_canon_sha256":"cd4fcf708785a06d471732a08ddea1cf863d6f8c6f6162c61c5e43a0bd646bee","abstract_canon_sha256":"82161b4af0722cedbf6ce6364c8cef1a249c4e4360395e23e570929dbf6a7d65"},"schema_version":"1.0"},"canonical_sha256":"36d1fbb0ec6e7a44991e395e88725ccec42007373d5a38b258968dd879aea61f","source":{"kind":"arxiv","id":"1207.3120","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1207.3120","created_at":"2026-05-18T03:51:12Z"},{"alias_kind":"arxiv_version","alias_value":"1207.3120v1","created_at":"2026-05-18T03:51:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.3120","created_at":"2026-05-18T03:51:12Z"},{"alias_kind":"pith_short_12","alias_value":"G3I7XMHMNZ5E","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_16","alias_value":"G3I7XMHMNZ5EJGI6","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_8","alias_value":"G3I7XMHM","created_at":"2026-05-18T12:27:06Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:G3I7XMHMNZ5EJGI6HFPIQ4S4Z3","target":"record","payload":{"canonical_record":{"source":{"id":"1207.3120","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2012-07-12T23:26:57Z","cross_cats_sorted":[],"title_canon_sha256":"cd4fcf708785a06d471732a08ddea1cf863d6f8c6f6162c61c5e43a0bd646bee","abstract_canon_sha256":"82161b4af0722cedbf6ce6364c8cef1a249c4e4360395e23e570929dbf6a7d65"},"schema_version":"1.0"},"canonical_sha256":"36d1fbb0ec6e7a44991e395e88725ccec42007373d5a38b258968dd879aea61f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:51:12.420164Z","signature_b64":"ofCROlV1azR98cWXpIcstb9GbMDwsYTwPDyX1+UJdZWQBBrndmCGZmrjZ8OLsURGpjBHVEQ57h+fGHIn5qXzCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"36d1fbb0ec6e7a44991e395e88725ccec42007373d5a38b258968dd879aea61f","last_reissued_at":"2026-05-18T03:51:12.419605Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:51:12.419605Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1207.3120","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:51:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5De1xN17xSCS26o+nirAt+qX7vAYz60Ifq6LcT/u+EekufFZOjNvIwtR/P1mZkwMs4mnJkhf2LGih2hdjN6TBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T21:09:43.571867Z"},"content_sha256":"22ddaf33cd6be15089cd6c6186108b8534df46fb70e3bb36743450caeb55818c","schema_version":"1.0","event_id":"sha256:22ddaf33cd6be15089cd6c6186108b8534df46fb70e3bb36743450caeb55818c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:G3I7XMHMNZ5EJGI6HFPIQ4S4Z3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Optimal Disturbance Rejection and Robustness for Infinite Dimensional LTV Systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Seddik M. Djouadi","submitted_at":"2012-07-12T23:26:57Z","abstract_excerpt":"In this paper, we consider the optimal disturbance rejection problem for possibly infinite dimensional linear time-varying (LTV) systems using a framework based on operator algebras of classes of bounded linear operators. This approach does not assume any state space representation and views LTV systems as causal operators. After reducing the problem to a shortest distance minimization in a space of bounded linear operators, duality theory is applied to show existence of optimal solutions, which satisfy a \"time-varying\" allpass or flatness condition. Under mild assumptions the optimal TV contr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.3120","kind":"arxiv","version":1},"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":"2026-05-18T03:51:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JZrx0rXGBOVdiv+RsLz1d4It7IlpmpiXaWDd7sfNmVacb4MYCfK3LaSMRG9pYfptB7a8CTzmA39IoK1yIWTFAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T21:09:43.572228Z"},"content_sha256":"2f44edf6aeb6b47b71ca443c26efdf5a63a8661373761b9593dd7045fc1af047","schema_version":"1.0","event_id":"sha256:2f44edf6aeb6b47b71ca443c26efdf5a63a8661373761b9593dd7045fc1af047"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/G3I7XMHMNZ5EJGI6HFPIQ4S4Z3/bundle.json","state_url":"https://pith.science/pith/G3I7XMHMNZ5EJGI6HFPIQ4S4Z3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/G3I7XMHMNZ5EJGI6HFPIQ4S4Z3/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":"2026-06-04T21:09:43Z","links":{"resolver":"https://pith.science/pith/G3I7XMHMNZ5EJGI6HFPIQ4S4Z3","bundle":"https://pith.science/pith/G3I7XMHMNZ5EJGI6HFPIQ4S4Z3/bundle.json","state":"https://pith.science/pith/G3I7XMHMNZ5EJGI6HFPIQ4S4Z3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/G3I7XMHMNZ5EJGI6HFPIQ4S4Z3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:G3I7XMHMNZ5EJGI6HFPIQ4S4Z3","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":"82161b4af0722cedbf6ce6364c8cef1a249c4e4360395e23e570929dbf6a7d65","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2012-07-12T23:26:57Z","title_canon_sha256":"cd4fcf708785a06d471732a08ddea1cf863d6f8c6f6162c61c5e43a0bd646bee"},"schema_version":"1.0","source":{"id":"1207.3120","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1207.3120","created_at":"2026-05-18T03:51:12Z"},{"alias_kind":"arxiv_version","alias_value":"1207.3120v1","created_at":"2026-05-18T03:51:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.3120","created_at":"2026-05-18T03:51:12Z"},{"alias_kind":"pith_short_12","alias_value":"G3I7XMHMNZ5E","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_16","alias_value":"G3I7XMHMNZ5EJGI6","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_8","alias_value":"G3I7XMHM","created_at":"2026-05-18T12:27:06Z"}],"graph_snapshots":[{"event_id":"sha256:2f44edf6aeb6b47b71ca443c26efdf5a63a8661373761b9593dd7045fc1af047","target":"graph","created_at":"2026-05-18T03:51:12Z","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":"In this paper, we consider the optimal disturbance rejection problem for possibly infinite dimensional linear time-varying (LTV) systems using a framework based on operator algebras of classes of bounded linear operators. This approach does not assume any state space representation and views LTV systems as causal operators. After reducing the problem to a shortest distance minimization in a space of bounded linear operators, duality theory is applied to show existence of optimal solutions, which satisfy a \"time-varying\" allpass or flatness condition. Under mild assumptions the optimal TV contr","authors_text":"Seddik M. Djouadi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2012-07-12T23:26:57Z","title":"Optimal Disturbance Rejection and Robustness for Infinite Dimensional LTV Systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.3120","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":"sha256:22ddaf33cd6be15089cd6c6186108b8534df46fb70e3bb36743450caeb55818c","target":"record","created_at":"2026-05-18T03:51:12Z","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":"82161b4af0722cedbf6ce6364c8cef1a249c4e4360395e23e570929dbf6a7d65","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2012-07-12T23:26:57Z","title_canon_sha256":"cd4fcf708785a06d471732a08ddea1cf863d6f8c6f6162c61c5e43a0bd646bee"},"schema_version":"1.0","source":{"id":"1207.3120","kind":"arxiv","version":1}},"canonical_sha256":"36d1fbb0ec6e7a44991e395e88725ccec42007373d5a38b258968dd879aea61f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"36d1fbb0ec6e7a44991e395e88725ccec42007373d5a38b258968dd879aea61f","first_computed_at":"2026-05-18T03:51:12.419605Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:51:12.419605Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ofCROlV1azR98cWXpIcstb9GbMDwsYTwPDyX1+UJdZWQBBrndmCGZmrjZ8OLsURGpjBHVEQ57h+fGHIn5qXzCg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:51:12.420164Z","signed_message":"canonical_sha256_bytes"},"source_id":"1207.3120","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:22ddaf33cd6be15089cd6c6186108b8534df46fb70e3bb36743450caeb55818c","sha256:2f44edf6aeb6b47b71ca443c26efdf5a63a8661373761b9593dd7045fc1af047"],"state_sha256":"31f671a82ccd186241681f80d599ae07e74b08b63eab1a33a475782e3b5e82a0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DjEub6e0yiKpm8fAWWQPvByS67lKDXzGYZWNqbM2mFq1iMRR196EolmRbhzTusZ3wuwWBtg6u97NRkb0omgvCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T21:09:43.574349Z","bundle_sha256":"40a879c60a53c13de501f5c62460c36ed84965d150526808b2fb83f764f8ef02"}}