{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:HDHCFCG7I6HWOG4J7R2HLIR2HJ","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":"b0e01492ad7013b00715b3ce7bd7fce0b594e5f68227fd1caafbb1ec39acdd18","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-03-12T01:05:04Z","title_canon_sha256":"715d78db32973fc94415bac4cf8c19112202f58c2f4fc29f173d4f66bf8fc2a7"},"schema_version":"1.0","source":{"id":"1503.03543","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.03543","created_at":"2026-05-18T02:24:58Z"},{"alias_kind":"arxiv_version","alias_value":"1503.03543v1","created_at":"2026-05-18T02:24:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.03543","created_at":"2026-05-18T02:24:58Z"},{"alias_kind":"pith_short_12","alias_value":"HDHCFCG7I6HW","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_16","alias_value":"HDHCFCG7I6HWOG4J","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_8","alias_value":"HDHCFCG7","created_at":"2026-05-18T12:29:22Z"}],"graph_snapshots":[{"event_id":"sha256:1a117c3ef2fc264b0b85d11fba231e63a5bcffebaa3785d5e612544f1c4fc7ec","target":"graph","created_at":"2026-05-18T02:24:58Z","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":"In the framework of the majorization technique, an improved condition is proposed for the semilocal convergence of the Newton method under the mild assumption that the derivative of the involved operator F(x) is continuous. Our starting point is the Argyros representation of the optimal upper bound for the distance between the adjacent members of the Newton sequence. The major novel element of our proposal is the optimally reconstructed 'first integral' approximation to the recurrence relation defining the scalar majorizing sequence. Compared to the previous results of Argyros, it enables one ","authors_text":"Andrei Dubin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-03-12T01:05:04Z","title":"An improved convergence theorem for the Newton method under relaxed continuity assumptions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.03543","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:a2085796b169dac0ab195391300eee079559e394e38c3abe5bd48310704e0891","target":"record","created_at":"2026-05-18T02:24:58Z","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":"b0e01492ad7013b00715b3ce7bd7fce0b594e5f68227fd1caafbb1ec39acdd18","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-03-12T01:05:04Z","title_canon_sha256":"715d78db32973fc94415bac4cf8c19112202f58c2f4fc29f173d4f66bf8fc2a7"},"schema_version":"1.0","source":{"id":"1503.03543","kind":"arxiv","version":1}},"canonical_sha256":"38ce2288df478f671b89fc7475a23a3a58aa5d1905f605c58c196579c65bae5c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"38ce2288df478f671b89fc7475a23a3a58aa5d1905f605c58c196579c65bae5c","first_computed_at":"2026-05-18T02:24:58.266680Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:24:58.266680Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"llADdjoXa2I7Y/Vd95KNYP5226Pzujqi7NFWa3tHx94hQppHareTWJCT5fG/eGFGpvJIIPTjvaXvK9kGl+hkCA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:24:58.267394Z","signed_message":"canonical_sha256_bytes"},"source_id":"1503.03543","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a2085796b169dac0ab195391300eee079559e394e38c3abe5bd48310704e0891","sha256:1a117c3ef2fc264b0b85d11fba231e63a5bcffebaa3785d5e612544f1c4fc7ec"],"state_sha256":"81c992bb93f47c86f31dd36f79749c28dda6d39a59a70d1adc9375a102627d35"}