{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:VP2K5SJHTPKHNAU4LWQPPCUIZN","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":"b5d0cc2e61c16dd601c0b40d46e1deccdbb22bb95331c575eeb3868376bd893a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-04-18T14:36:49Z","title_canon_sha256":"c5cafe129501a70b8d87685014b22c826ebd1b19973b434b646a71cf4ba76f3a"},"schema_version":"1.0","source":{"id":"1804.06765","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.06765","created_at":"2026-05-18T00:18:05Z"},{"alias_kind":"arxiv_version","alias_value":"1804.06765v1","created_at":"2026-05-18T00:18:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.06765","created_at":"2026-05-18T00:18:05Z"},{"alias_kind":"pith_short_12","alias_value":"VP2K5SJHTPKH","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_16","alias_value":"VP2K5SJHTPKHNAU4","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_8","alias_value":"VP2K5SJH","created_at":"2026-05-18T12:32:59Z"}],"graph_snapshots":[{"event_id":"sha256:c57f340c6b1a71453538b1ce66ddc56a928632d90f129f6ed685ec98528e7199","target":"graph","created_at":"2026-05-18T00:18:05Z","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 article is concerned with the asymptotic behavior of a 2D overhead crane. Taking into account the presence of a delay in the boundary, and assuming that no displacement term appears in the system, a distributed (interior) damping feedback law is proposed in order to compensate the effect of the delay. Then, invoking the frequency domain method, the solutions of the closed-loop system are proved to converge exponentially to a stationary position. This improves the recent result obtained by Al-Musallam-Ammari-Chentouf, where the rate of convergence is at most of polynomial type.","authors_text":"Boumedi\\`ene Chentouf, Ka\\\"is Ammari","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-04-18T14:36:49Z","title":"Further results on the asymptotic behavior of a 2D overhead crane with input delays: Exponential convergence"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.06765","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":"sha256:2ff58dbea0d61dab3224982ac510aff60100b290b87c9544746f0b1963c3e1ca","target":"record","created_at":"2026-05-18T00:18:05Z","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":"b5d0cc2e61c16dd601c0b40d46e1deccdbb22bb95331c575eeb3868376bd893a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-04-18T14:36:49Z","title_canon_sha256":"c5cafe129501a70b8d87685014b22c826ebd1b19973b434b646a71cf4ba76f3a"},"schema_version":"1.0","source":{"id":"1804.06765","kind":"arxiv","version":1}},"canonical_sha256":"abf4aec9279bd476829c5da0f78a88cb40bc3a8162d63a6b13429f340ce85747","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"abf4aec9279bd476829c5da0f78a88cb40bc3a8162d63a6b13429f340ce85747","first_computed_at":"2026-05-18T00:18:05.791830Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:18:05.791830Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"pWrX1QxOdSzsMbvvTiQebHBhhMGYs2xTyN35W5sEj/DPnc3z3QeOEXiyF9fn42/1dQXuJ+lxNvtde/wThKpUDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:18:05.792427Z","signed_message":"canonical_sha256_bytes"},"source_id":"1804.06765","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2ff58dbea0d61dab3224982ac510aff60100b290b87c9544746f0b1963c3e1ca","sha256:c57f340c6b1a71453538b1ce66ddc56a928632d90f129f6ed685ec98528e7199"],"state_sha256":"3c429519260f8e6f9dfb5a9f46a7241e5b2478be3d2464e623d08b5b5dfbff24"}