{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:2GOORCYIABLF7RDXELCDS5ARYM","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":"99ec401481c282d7382f018be9e713972ddaa33b4df41dd7a058460f2671bbab","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2012-10-16T07:37:25Z","title_canon_sha256":"e390089fa4f2fab082c2ccbf70ca68fe28f609eb4679f9b65a1c9c098799c466"},"schema_version":"1.0","source":{"id":"1210.4281","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.4281","created_at":"2026-05-18T00:16:24Z"},{"alias_kind":"arxiv_version","alias_value":"1210.4281v2","created_at":"2026-05-18T00:16:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.4281","created_at":"2026-05-18T00:16:24Z"},{"alias_kind":"pith_short_12","alias_value":"2GOORCYIABLF","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_16","alias_value":"2GOORCYIABLF7RDX","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_8","alias_value":"2GOORCYI","created_at":"2026-05-18T12:26:50Z"}],"graph_snapshots":[{"event_id":"sha256:9beedeb50f4552ab1aac17042b1f1dc66aeabca3f6c1a7013e070f66aee3c3c1","target":"graph","created_at":"2026-05-18T00:16:24Z","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 consider a control problem where the state must reach asymptotically a target while paying an integral payoff with a non-negative Lagrangian. The dynamics is just continuous, and no assumptions are made on the zero level set of the Lagrangian. Through an inequality involving a positive number $\\bar p_0$ and a Minimum Restraint Function $U=U(x)$ --a special type of Control Lyapunov Function-- we provide a condition implying that (i) the control system is asymptotically controllable, and (ii) the value function is bounded above by $U/\\bar p_0$.","authors_text":"Franco Rampazzo, Monica Motta","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2012-10-16T07:37:25Z","title":"Asymptotic controllability and optimal control"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.4281","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:b7db63828123ca1141dcd548373f1b296bae150efea60d68b21352c124be1afa","target":"record","created_at":"2026-05-18T00:16:24Z","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":"99ec401481c282d7382f018be9e713972ddaa33b4df41dd7a058460f2671bbab","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2012-10-16T07:37:25Z","title_canon_sha256":"e390089fa4f2fab082c2ccbf70ca68fe28f609eb4679f9b65a1c9c098799c466"},"schema_version":"1.0","source":{"id":"1210.4281","kind":"arxiv","version":2}},"canonical_sha256":"d19ce88b0800565fc47722c4397411c32b0dbe18241b5e9540fdb0cf95c303d2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d19ce88b0800565fc47722c4397411c32b0dbe18241b5e9540fdb0cf95c303d2","first_computed_at":"2026-05-18T00:16:24.305027Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:16:24.305027Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mTOFqbevfHOd3Vdky/dNEpq7uRNpr8WRMYVSV7w+0GgtrAvvQVCIi0k5HQ1LyvJvm2tKV/2dXcWToClSCpg7DA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:16:24.305754Z","signed_message":"canonical_sha256_bytes"},"source_id":"1210.4281","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b7db63828123ca1141dcd548373f1b296bae150efea60d68b21352c124be1afa","sha256:9beedeb50f4552ab1aac17042b1f1dc66aeabca3f6c1a7013e070f66aee3c3c1"],"state_sha256":"e611ff1a4bdce75dff0fb8550986ff6cd035ace0c3e2439021302419dacc400b"}