{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:SLNKSDK2EMBPXJN23RKXYPBME4","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":"23681642537c44eb38c00828e9f20794de3c9bfb6cc521148fd360e05b1118c3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.flu-dyn","submitted_at":"2014-09-28T11:11:20Z","title_canon_sha256":"1ed4a821bea188d91c917d100b2bb9fb5bbf2a1845e2f300845a555ee59b26fb"},"schema_version":"1.0","source":{"id":"1409.7892","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.7892","created_at":"2026-05-18T02:41:40Z"},{"alias_kind":"arxiv_version","alias_value":"1409.7892v1","created_at":"2026-05-18T02:41:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.7892","created_at":"2026-05-18T02:41:40Z"},{"alias_kind":"pith_short_12","alias_value":"SLNKSDK2EMBP","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_16","alias_value":"SLNKSDK2EMBPXJN2","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_8","alias_value":"SLNKSDK2","created_at":"2026-05-18T12:28:49Z"}],"graph_snapshots":[{"event_id":"sha256:2c4b020c00907a4f9a901cbb124ce6406c5fb59527a042628bfc9d369eac72a8","target":"graph","created_at":"2026-05-18T02:41:40Z","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":"A very simple and accurate numerical method which is applicable to systems of differentio-integral equations with quite general boundary conditions has been devised. Although the basic idea of this method stems from the Keller Box method, it solves the problem of systems of differential equations involving integral operators not previously considered by the Keller Box method. Two main preparatory stages are required: (i) a merging procedure for differential equations and conditions without integral operators and; (ii) a reduction procedure for differential equations and conditions with integra","authors_text":"Graham Wilks, Jian-Jun Shu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.flu-dyn","submitted_at":"2014-09-28T11:11:20Z","title":"An accurate numerical method for systems of differentio-integral equations associated with multiphase flow"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.7892","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:c3192c0c51ad6d38eeb94b67d821a1fa2559e1cdc31f27f00dca7e13fb2b582c","target":"record","created_at":"2026-05-18T02:41:40Z","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":"23681642537c44eb38c00828e9f20794de3c9bfb6cc521148fd360e05b1118c3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.flu-dyn","submitted_at":"2014-09-28T11:11:20Z","title_canon_sha256":"1ed4a821bea188d91c917d100b2bb9fb5bbf2a1845e2f300845a555ee59b26fb"},"schema_version":"1.0","source":{"id":"1409.7892","kind":"arxiv","version":1}},"canonical_sha256":"92daa90d5a2302fba5badc557c3c2c27100687f13b2492140eef0386ba8d0495","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"92daa90d5a2302fba5badc557c3c2c27100687f13b2492140eef0386ba8d0495","first_computed_at":"2026-05-18T02:41:40.277592Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:41:40.277592Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"471V0YWurjB6gjxhGCBkbAXLsoAjlOc9opH22JIdVi34LyMTW+Asbb5xdjqnoRvu7IkKgZyY9IYyIPYdpyUYDg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:41:40.278135Z","signed_message":"canonical_sha256_bytes"},"source_id":"1409.7892","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c3192c0c51ad6d38eeb94b67d821a1fa2559e1cdc31f27f00dca7e13fb2b582c","sha256:2c4b020c00907a4f9a901cbb124ce6406c5fb59527a042628bfc9d369eac72a8"],"state_sha256":"d2dc7eae4010a43ac8c79f4d6b878bede6dc94e5a110cdd2d04ff660e66ab980"}