{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:34ZCT7TL7DH3JZGJU3HB557VO4","short_pith_number":"pith:34ZCT7TL","canonical_record":{"source":{"id":"1706.05828","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-06-19T08:40:15Z","cross_cats_sorted":[],"title_canon_sha256":"6e6d2b238430b81cd06da3a9e9eb01806db001a0cf845267e7f58dd84ce46131","abstract_canon_sha256":"dac5c60cc247efc95a18488b33f93629c816e20e79a4023553f9382bcf628df7"},"schema_version":"1.0"},"canonical_sha256":"df3229fe6bf8cfb4e4c9a6ce1ef7f5773a4eb04c54f27d27fdcc370108d00441","source":{"kind":"arxiv","id":"1706.05828","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.05828","created_at":"2026-05-18T00:42:08Z"},{"alias_kind":"arxiv_version","alias_value":"1706.05828v1","created_at":"2026-05-18T00:42:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.05828","created_at":"2026-05-18T00:42:08Z"},{"alias_kind":"pith_short_12","alias_value":"34ZCT7TL7DH3","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_16","alias_value":"34ZCT7TL7DH3JZGJ","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_8","alias_value":"34ZCT7TL","created_at":"2026-05-18T12:30:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:34ZCT7TL7DH3JZGJU3HB557VO4","target":"record","payload":{"canonical_record":{"source":{"id":"1706.05828","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-06-19T08:40:15Z","cross_cats_sorted":[],"title_canon_sha256":"6e6d2b238430b81cd06da3a9e9eb01806db001a0cf845267e7f58dd84ce46131","abstract_canon_sha256":"dac5c60cc247efc95a18488b33f93629c816e20e79a4023553f9382bcf628df7"},"schema_version":"1.0"},"canonical_sha256":"df3229fe6bf8cfb4e4c9a6ce1ef7f5773a4eb04c54f27d27fdcc370108d00441","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:42:08.762904Z","signature_b64":"RpSat5ZXdupGjiFWSvqa1cvpR4IJj84iPHVXehrAaZ1+ZJEOiw6RWaI1p0WmGnJK2h3ySY5FTCUcQPMA0ID9BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"df3229fe6bf8cfb4e4c9a6ce1ef7f5773a4eb04c54f27d27fdcc370108d00441","last_reissued_at":"2026-05-18T00:42:08.762426Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:42:08.762426Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1706.05828","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":"2026-05-18T00:42:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+4r5+HbJC42dq6hovHcQIj+JDquh2O0eajvH1xKVDyxGgqDdOLcvVcItnEH83p8y59WLf27vCHAWoKbMPmKvCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T21:31:05.018489Z"},"content_sha256":"d0418d25be88a3eaa8b7ccb9a083332a6b9e0928687294913a212db6dfceda09","schema_version":"1.0","event_id":"sha256:d0418d25be88a3eaa8b7ccb9a083332a6b9e0928687294913a212db6dfceda09"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:34ZCT7TL7DH3JZGJU3HB557VO4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The geometry of the generalized algebraic Riccati equation and of the singular Hamiltonian system","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Augusto Ferrante, Lorenzo Ntogramatzidis","submitted_at":"2017-06-19T08:40:15Z","abstract_excerpt":"This paper analyzes the properties of the solutions of the generalized continuous algebraic Riccati equation from a geometric perspective. This analysis reveals the presence of a subspace that may provide an appropriate degree of freedom to stabilize the system in the related optimal control problem even in cases where the Riccati equation does not admit a stabilizing solution."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.05828","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":"2026-05-18T00:42:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AC8+JH4YE8B6AF4KeFAEh4eBUixtq7Hy8a8iW99OXbzGHKEj/xPYCgZqITKN7OTHlEHKxpgqAkCkzonhw8DRDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T21:31:05.018842Z"},"content_sha256":"1eca4a1f7d255c2ad2f0cf3c3b10fe751233e3c9ecbc130e4f8ea06d92ec5a64","schema_version":"1.0","event_id":"sha256:1eca4a1f7d255c2ad2f0cf3c3b10fe751233e3c9ecbc130e4f8ea06d92ec5a64"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/34ZCT7TL7DH3JZGJU3HB557VO4/bundle.json","state_url":"https://pith.science/pith/34ZCT7TL7DH3JZGJU3HB557VO4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/34ZCT7TL7DH3JZGJU3HB557VO4/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":"2026-06-24T21:31:05Z","links":{"resolver":"https://pith.science/pith/34ZCT7TL7DH3JZGJU3HB557VO4","bundle":"https://pith.science/pith/34ZCT7TL7DH3JZGJU3HB557VO4/bundle.json","state":"https://pith.science/pith/34ZCT7TL7DH3JZGJU3HB557VO4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/34ZCT7TL7DH3JZGJU3HB557VO4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:34ZCT7TL7DH3JZGJU3HB557VO4","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":"dac5c60cc247efc95a18488b33f93629c816e20e79a4023553f9382bcf628df7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-06-19T08:40:15Z","title_canon_sha256":"6e6d2b238430b81cd06da3a9e9eb01806db001a0cf845267e7f58dd84ce46131"},"schema_version":"1.0","source":{"id":"1706.05828","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.05828","created_at":"2026-05-18T00:42:08Z"},{"alias_kind":"arxiv_version","alias_value":"1706.05828v1","created_at":"2026-05-18T00:42:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.05828","created_at":"2026-05-18T00:42:08Z"},{"alias_kind":"pith_short_12","alias_value":"34ZCT7TL7DH3","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_16","alias_value":"34ZCT7TL7DH3JZGJ","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_8","alias_value":"34ZCT7TL","created_at":"2026-05-18T12:30:58Z"}],"graph_snapshots":[{"event_id":"sha256:1eca4a1f7d255c2ad2f0cf3c3b10fe751233e3c9ecbc130e4f8ea06d92ec5a64","target":"graph","created_at":"2026-05-18T00:42:08Z","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":"This paper analyzes the properties of the solutions of the generalized continuous algebraic Riccati equation from a geometric perspective. This analysis reveals the presence of a subspace that may provide an appropriate degree of freedom to stabilize the system in the related optimal control problem even in cases where the Riccati equation does not admit a stabilizing solution.","authors_text":"Augusto Ferrante, Lorenzo Ntogramatzidis","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-06-19T08:40:15Z","title":"The geometry of the generalized algebraic Riccati equation and of the singular Hamiltonian system"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.05828","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:d0418d25be88a3eaa8b7ccb9a083332a6b9e0928687294913a212db6dfceda09","target":"record","created_at":"2026-05-18T00:42:08Z","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":"dac5c60cc247efc95a18488b33f93629c816e20e79a4023553f9382bcf628df7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-06-19T08:40:15Z","title_canon_sha256":"6e6d2b238430b81cd06da3a9e9eb01806db001a0cf845267e7f58dd84ce46131"},"schema_version":"1.0","source":{"id":"1706.05828","kind":"arxiv","version":1}},"canonical_sha256":"df3229fe6bf8cfb4e4c9a6ce1ef7f5773a4eb04c54f27d27fdcc370108d00441","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"df3229fe6bf8cfb4e4c9a6ce1ef7f5773a4eb04c54f27d27fdcc370108d00441","first_computed_at":"2026-05-18T00:42:08.762426Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:42:08.762426Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RpSat5ZXdupGjiFWSvqa1cvpR4IJj84iPHVXehrAaZ1+ZJEOiw6RWaI1p0WmGnJK2h3ySY5FTCUcQPMA0ID9BA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:42:08.762904Z","signed_message":"canonical_sha256_bytes"},"source_id":"1706.05828","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d0418d25be88a3eaa8b7ccb9a083332a6b9e0928687294913a212db6dfceda09","sha256:1eca4a1f7d255c2ad2f0cf3c3b10fe751233e3c9ecbc130e4f8ea06d92ec5a64"],"state_sha256":"43384ed568d3bf582c50274c7782bfa74de5d2eec9f6f5b14406cbdb28cf56c3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9nWoPcDlsEYd5VLym/65bbbO7hbmZKv57Yms2yW82u/E1lkSvKTsIEaqNMKit5w8AwMJVEFkZQ1gIFYVQkzaAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T21:31:05.020791Z","bundle_sha256":"49f89a5ca6fe75236cb4590b75ca5d0f21eb32eef232f88af8ec8c18952af076"}}