{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:NWMEVC5KFRGXX2F6J42VIU3M7T","short_pith_number":"pith:NWMEVC5K","schema_version":"1.0","canonical_sha256":"6d984a8baa2c4d7be8be4f3554536cfcc2ab491ad2d4415ad244a590e2fc14c8","source":{"kind":"arxiv","id":"1404.2427","version":1},"attestation_state":"computed","paper":{"title":"Projection onto simplicial cones by a semi-smooth Newton method","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NA"],"primary_cat":"math.OC","authors_text":"O. P. Ferreira, S. Z. N\\'emeth","submitted_at":"2014-04-09T10:40:05Z","abstract_excerpt":"By using Moreau's decomposition theorem for projecting onto cones, the problem of projecting onto a simplicial cone is reduced to finding the unique solution of a nonsmooth system of equations. It is shown that a semi-smooth Newton method applied to the system of equations associated to the problem of projecting onto a simplicial cone is always well defined, and the generated sequence is bounded for any starting point and under a somewhat restrictive assumption it is finite. Besides, under a mild assumption on the simplicial cone, the generated sequence converges linearly to the solution of th"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1404.2427","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2014-04-09T10:40:05Z","cross_cats_sorted":["math.NA"],"title_canon_sha256":"c6d15eab7320b2f5ad7ba9020bbb0d5cc12204a5394118956fb60e928480a7ad","abstract_canon_sha256":"cdf3aa8edda02f931897fc0bd4fa725cf3a7588434f4aa7c343e1a0bd2eef1d3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:54:31.540011Z","signature_b64":"nLLzndk6AiGyQf5y8vjZBQlZQF8MmzZEQvCl8h+K2a1kpvuGyvqFmbDUcJsD0eOPAHKGT3WQP+aOv8wxuMVKBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6d984a8baa2c4d7be8be4f3554536cfcc2ab491ad2d4415ad244a590e2fc14c8","last_reissued_at":"2026-05-18T02:54:31.539460Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:54:31.539460Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Projection onto simplicial cones by a semi-smooth Newton method","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NA"],"primary_cat":"math.OC","authors_text":"O. P. Ferreira, S. Z. N\\'emeth","submitted_at":"2014-04-09T10:40:05Z","abstract_excerpt":"By using Moreau's decomposition theorem for projecting onto cones, the problem of projecting onto a simplicial cone is reduced to finding the unique solution of a nonsmooth system of equations. It is shown that a semi-smooth Newton method applied to the system of equations associated to the problem of projecting onto a simplicial cone is always well defined, and the generated sequence is bounded for any starting point and under a somewhat restrictive assumption it is finite. Besides, under a mild assumption on the simplicial cone, the generated sequence converges linearly to the solution of th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.2427","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1404.2427","created_at":"2026-05-18T02:54:31.539540+00:00"},{"alias_kind":"arxiv_version","alias_value":"1404.2427v1","created_at":"2026-05-18T02:54:31.539540+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.2427","created_at":"2026-05-18T02:54:31.539540+00:00"},{"alias_kind":"pith_short_12","alias_value":"NWMEVC5KFRGX","created_at":"2026-05-18T12:28:41.024544+00:00"},{"alias_kind":"pith_short_16","alias_value":"NWMEVC5KFRGXX2F6","created_at":"2026-05-18T12:28:41.024544+00:00"},{"alias_kind":"pith_short_8","alias_value":"NWMEVC5K","created_at":"2026-05-18T12:28:41.024544+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/NWMEVC5KFRGXX2F6J42VIU3M7T","json":"https://pith.science/pith/NWMEVC5KFRGXX2F6J42VIU3M7T.json","graph_json":"https://pith.science/api/pith-number/NWMEVC5KFRGXX2F6J42VIU3M7T/graph.json","events_json":"https://pith.science/api/pith-number/NWMEVC5KFRGXX2F6J42VIU3M7T/events.json","paper":"https://pith.science/paper/NWMEVC5K"},"agent_actions":{"view_html":"https://pith.science/pith/NWMEVC5KFRGXX2F6J42VIU3M7T","download_json":"https://pith.science/pith/NWMEVC5KFRGXX2F6J42VIU3M7T.json","view_paper":"https://pith.science/paper/NWMEVC5K","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1404.2427&json=true","fetch_graph":"https://pith.science/api/pith-number/NWMEVC5KFRGXX2F6J42VIU3M7T/graph.json","fetch_events":"https://pith.science/api/pith-number/NWMEVC5KFRGXX2F6J42VIU3M7T/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NWMEVC5KFRGXX2F6J42VIU3M7T/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NWMEVC5KFRGXX2F6J42VIU3M7T/action/storage_attestation","attest_author":"https://pith.science/pith/NWMEVC5KFRGXX2F6J42VIU3M7T/action/author_attestation","sign_citation":"https://pith.science/pith/NWMEVC5KFRGXX2F6J42VIU3M7T/action/citation_signature","submit_replication":"https://pith.science/pith/NWMEVC5KFRGXX2F6J42VIU3M7T/action/replication_record"}},"created_at":"2026-05-18T02:54:31.539540+00:00","updated_at":"2026-05-18T02:54:31.539540+00:00"}