{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:F6IGZRSGTBRLFM2ZFFK5OO4CTT","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":"c298eca84485782b39885f2bc5331d0233049198332c82e706dac70d20306295","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2014-05-26T14:39:51Z","title_canon_sha256":"195c2c415aa97d38a121b9fd9c9f4c6d2aff2da0113e018a91746f6e003ff579"},"schema_version":"1.0","source":{"id":"1405.6591","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1405.6591","created_at":"2026-05-18T02:49:19Z"},{"alias_kind":"arxiv_version","alias_value":"1405.6591v1","created_at":"2026-05-18T02:49:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.6591","created_at":"2026-05-18T02:49:19Z"},{"alias_kind":"pith_short_12","alias_value":"F6IGZRSGTBRL","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_16","alias_value":"F6IGZRSGTBRLFM2Z","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_8","alias_value":"F6IGZRSG","created_at":"2026-05-18T12:28:28Z"}],"graph_snapshots":[{"event_id":"sha256:06f2435ba70b8ab270a42fbc720a615b0bee4b2b3b7c926d4b8da05f1ba903af","target":"graph","created_at":"2026-05-18T02:49:19Z","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 introduce a nonlocal control condition and the notion of approximate controllability for fractional order quasilinear control inclusions. Approximate controllability of a fractional control nonlocal delay quasilinear functional differential inclusion in a Hilbert space is studied. The results are obtained by using the fractional power of operators, multi-valued analysis, and Sadovskii's fixed point theorem. Main result gives an appropriate set of sufficient conditions for the considered system to be approximately controllable. As an example, a fractional partial nonlocal control functional ","authors_text":"Amar Debbouche, Delfim F. M. Torres","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2014-05-26T14:39:51Z","title":"Approximate Controllability of Fractional Delay Dynamic Inclusions with Nonlocal Control Conditions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.6591","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":"sha256:2c0ccfdb92aea1814329cdccc56fe711c2bc48fd846f015798d8f32a2427884f","target":"record","created_at":"2026-05-18T02:49:19Z","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":"c298eca84485782b39885f2bc5331d0233049198332c82e706dac70d20306295","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2014-05-26T14:39:51Z","title_canon_sha256":"195c2c415aa97d38a121b9fd9c9f4c6d2aff2da0113e018a91746f6e003ff579"},"schema_version":"1.0","source":{"id":"1405.6591","kind":"arxiv","version":1}},"canonical_sha256":"2f906cc6469862b2b3592955d73b829cc648906323bf162e8b92d6337a48be3a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2f906cc6469862b2b3592955d73b829cc648906323bf162e8b92d6337a48be3a","first_computed_at":"2026-05-18T02:49:19.831467Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:49:19.831467Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yNFZagkD087yXVBcivfwQR3vHJ5bzzLNUsDO7LbpW8llUXqVXgDv6FQueyupXM3bbIjecC6DOMne5ueXYzTMBw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:49:19.832056Z","signed_message":"canonical_sha256_bytes"},"source_id":"1405.6591","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2c0ccfdb92aea1814329cdccc56fe711c2bc48fd846f015798d8f32a2427884f","sha256:06f2435ba70b8ab270a42fbc720a615b0bee4b2b3b7c926d4b8da05f1ba903af"],"state_sha256":"c90ed32f96dca77eb96ce084218947483efe12b931e6d956346e4bbc7baf5a9b"}