{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:F3J4DHMN2RT35KNJCJKKOZU7YF","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":"324440c023fc6d3a5d6a8c2e34b06ed64a1ca91897526c54dba2b828e9b936aa","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SY","submitted_at":"2012-11-25T11:52:38Z","title_canon_sha256":"d213b69c009a394255322c7d44354be34ec7ea85204aad39fdd22f29b72ab87a"},"schema_version":"1.0","source":{"id":"1211.5758","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1211.5758","created_at":"2026-05-18T03:40:02Z"},{"alias_kind":"arxiv_version","alias_value":"1211.5758v1","created_at":"2026-05-18T03:40:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.5758","created_at":"2026-05-18T03:40:02Z"},{"alias_kind":"pith_short_12","alias_value":"F3J4DHMN2RT3","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_16","alias_value":"F3J4DHMN2RT35KNJ","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_8","alias_value":"F3J4DHMN","created_at":"2026-05-18T12:27:04Z"}],"graph_snapshots":[{"event_id":"sha256:ba61da4bcd93ba9d6c0d386fce0e5a56b0587873469f300a2ef0e9231f800564","target":"graph","created_at":"2026-05-18T03:40:02Z","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":"The problem of inverting a system in presence of a series-defined output is analyzed. Inverse models are derived that consist of a set of algebraic equations. The inversion is performed explicitly for an output trajectory functional, which is a linear combination of some basis functions with arbitrarily free coefficients. The observer canonical form is exploited, and the input-output representation is solved using a series method. It is shown that the only required system characteristic is observability, which implies that there is no need for output redefinition. An exact inverse model is fou","authors_text":"Jean-Francois Stumper, Ralph Kennel","cross_cats":["math.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SY","submitted_at":"2012-11-25T11:52:38Z","title":"Inversion of Linear and Nonlinear Observable Systems with Series-defined Output Trajectories"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.5758","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":"sha256:255c10af8908410d2bfff8a811e98eda435328e350152ea1630461f3d9bf1425","target":"record","created_at":"2026-05-18T03:40:02Z","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":"324440c023fc6d3a5d6a8c2e34b06ed64a1ca91897526c54dba2b828e9b936aa","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SY","submitted_at":"2012-11-25T11:52:38Z","title_canon_sha256":"d213b69c009a394255322c7d44354be34ec7ea85204aad39fdd22f29b72ab87a"},"schema_version":"1.0","source":{"id":"1211.5758","kind":"arxiv","version":1}},"canonical_sha256":"2ed3c19d8dd467bea9a91254a7669fc14fcb8bf78ed8eda633221f56ce2fd593","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2ed3c19d8dd467bea9a91254a7669fc14fcb8bf78ed8eda633221f56ce2fd593","first_computed_at":"2026-05-18T03:40:02.014506Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:40:02.014506Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ewhJTtptGK1WgyuDAbETFl4MKaXIwtWIz/nfRMUBmKiR3W9CSEDLhOOIwEV4mQ/THM+MEfFERFIfMTqQhVTeDg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:40:02.015226Z","signed_message":"canonical_sha256_bytes"},"source_id":"1211.5758","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:255c10af8908410d2bfff8a811e98eda435328e350152ea1630461f3d9bf1425","sha256:ba61da4bcd93ba9d6c0d386fce0e5a56b0587873469f300a2ef0e9231f800564"],"state_sha256":"3271424a0d944d31c740c6323c38db435f0cecd3c4ad08dce97f552041199d5d"}