{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:G65PPKWICEADD3TKBM6DNBYMMI","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":"d7fcdca179fedbcab512ebbb79c114d71aba96417b6ca27ee25ce2e61b3a4f27","cross_cats_sorted":["cs.NA","physics.comp-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-09-02T10:31:49Z","title_canon_sha256":"0e8d5b6b16e9400efeec5a28cc35adab26e4be62a4af99270b541492a144ba34"},"schema_version":"1.0","source":{"id":"1609.01550","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.01550","created_at":"2026-06-04T18:09:59Z"},{"alias_kind":"arxiv_version","alias_value":"1609.01550v1","created_at":"2026-06-04T18:09:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.01550","created_at":"2026-06-04T18:09:59Z"},{"alias_kind":"pith_short_12","alias_value":"G65PPKWICEAD","created_at":"2026-06-04T18:09:59Z"},{"alias_kind":"pith_short_16","alias_value":"G65PPKWICEADD3TK","created_at":"2026-06-04T18:09:59Z"},{"alias_kind":"pith_short_8","alias_value":"G65PPKWI","created_at":"2026-06-04T18:09:59Z"}],"graph_snapshots":[{"event_id":"sha256:34d13378fd15d34eaa7a25911880275a891e6b00c582c4458775708c1307fcd6","target":"graph","created_at":"2026-06-04T18:09:59Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1609.01550/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, a new analytic method with a convergence-control parameter $c$ is first proposed. The parameter $c$ is used to adjust and control the convergence region and rate of the resulting series solution. It turns out that the convergence region and rate can be greatly enlarged by choosing a proper value of $c$. Furthermore, a numerical approach for finding the optimal value of the convergence-control parameter is given. At the same time, it is found that the traditional Adomian decomposition method is only a special case of the new method. The effectiveness and applicability of the new ","authors_text":"Songxin Liang, XiaoLong Zhang","cross_cats":["cs.NA","physics.comp-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-09-02T10:31:49Z","title":"A new analytic method with a convergence-control parameter for solving nonlinear problems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.01550","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:ce758c01f315d4241f2e171ca6a041f071b33084a900c62c8ec7aa7cc0c621f3","target":"record","created_at":"2026-06-04T18:09:59Z","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":"d7fcdca179fedbcab512ebbb79c114d71aba96417b6ca27ee25ce2e61b3a4f27","cross_cats_sorted":["cs.NA","physics.comp-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-09-02T10:31:49Z","title_canon_sha256":"0e8d5b6b16e9400efeec5a28cc35adab26e4be62a4af99270b541492a144ba34"},"schema_version":"1.0","source":{"id":"1609.01550","kind":"arxiv","version":1}},"canonical_sha256":"37baf7aac8110031ee6a0b3c36870c6204f352fc1e49e3c306dfd4f54b13c5e5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"37baf7aac8110031ee6a0b3c36870c6204f352fc1e49e3c306dfd4f54b13c5e5","first_computed_at":"2026-06-04T18:09:59.908131Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-04T18:09:59.908131Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ejMtfgGZT6aGMCDYx3U4U4lu58E1thSmuKwyYykslslfwu9Pgp0v256egqyhhX7BhxgpYxzxir5i14rYx/n9Dg==","signature_status":"signed_v1","signed_at":"2026-06-04T18:09:59.908656Z","signed_message":"canonical_sha256_bytes"},"source_id":"1609.01550","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ce758c01f315d4241f2e171ca6a041f071b33084a900c62c8ec7aa7cc0c621f3","sha256:34d13378fd15d34eaa7a25911880275a891e6b00c582c4458775708c1307fcd6"],"state_sha256":"ebaf1230a902cac065dd54ea16358037046d838c05c223ab5415aa2e09343211"}