{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:FJ4H4QMKFICMZNUQFGSBONBBSE","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":"cecc590be49d83d5be8210ea99da619a185b65dfac1b68849dfd04652944126f","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-07-17T02:40:11Z","title_canon_sha256":"62ed655bddaf123681932459864905b37c7fc4afee6d36d591303b3fc7436eca"},"schema_version":"1.0","source":{"id":"1907.07308","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1907.07308","created_at":"2026-05-17T23:40:22Z"},{"alias_kind":"arxiv_version","alias_value":"1907.07308v1","created_at":"2026-05-17T23:40:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.07308","created_at":"2026-05-17T23:40:22Z"},{"alias_kind":"pith_short_12","alias_value":"FJ4H4QMKFICM","created_at":"2026-05-18T12:33:15Z"},{"alias_kind":"pith_short_16","alias_value":"FJ4H4QMKFICMZNUQ","created_at":"2026-05-18T12:33:15Z"},{"alias_kind":"pith_short_8","alias_value":"FJ4H4QMK","created_at":"2026-05-18T12:33:15Z"}],"graph_snapshots":[{"event_id":"sha256:12a92439d3e95afeff01d71fb4bea99b330db4e84e79294f77a4ccc99339aaac","target":"graph","created_at":"2026-05-17T23:40:22Z","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":"Some corrections are made in our article, which was published in Appl. Anal. Optim. Vol. 3 (2019), No. 1, 103--127. These corrections are intended to transform the equation \\eqref{eq:1.1} \\begin{equation}\\label{eq:1.1} x(t) + \\int\\limits_a^t {K_1(t,s,x(s)) ds} + \\int\\limits_a^b {K_2(t,s,x(s)) ds} = g(t),\\;\\,a \\le t \\le b \\tag{1.1} \\end{equation} into a discretized form in a tighter and more accurate way without affecting the main results of the article.","authors_text":"Khuat Van Ninh, Ngo Thanh Binh","cross_cats":["cs.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-07-17T02:40:11Z","title":"Corrections on A numerical method for solving nonlinear Volterra--Fredholm integral equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.07308","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:ffc7c4423ae8e1faebee88a5188ec4d9171f885e1ff1535e6c4a0f2a2c5ec225","target":"record","created_at":"2026-05-17T23:40:22Z","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":"cecc590be49d83d5be8210ea99da619a185b65dfac1b68849dfd04652944126f","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-07-17T02:40:11Z","title_canon_sha256":"62ed655bddaf123681932459864905b37c7fc4afee6d36d591303b3fc7436eca"},"schema_version":"1.0","source":{"id":"1907.07308","kind":"arxiv","version":1}},"canonical_sha256":"2a787e418a2a04ccb69029a41734219102e89020527dd173c4b094415828e392","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2a787e418a2a04ccb69029a41734219102e89020527dd173c4b094415828e392","first_computed_at":"2026-05-17T23:40:22.745342Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:40:22.745342Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BWhPbynx4x0MzXQ6rdjP2+/S4B/3KQk2IqVgUYwr/oSojmXUz+t+WDp9Zey7RhCb+e5ML39gMg1iDLIXaKR4Aw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:40:22.746004Z","signed_message":"canonical_sha256_bytes"},"source_id":"1907.07308","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ffc7c4423ae8e1faebee88a5188ec4d9171f885e1ff1535e6c4a0f2a2c5ec225","sha256:12a92439d3e95afeff01d71fb4bea99b330db4e84e79294f77a4ccc99339aaac"],"state_sha256":"9a8e8fee0ca80aa1d472c76de30e142b43e031984e377fa2151150f543549410"}