{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:HYFBBXXHJDUINJAZFXO5XONBAI","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":"c22193e70b54c3a9c987ed3f447cb896db31acdbddeb84401ebf54bf942f327e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-06-24T08:35:38Z","title_canon_sha256":"61303dd64713c4b286cfdef9100e8bc28db004603d5c800ee36671d0a0a9d641"},"schema_version":"1.0","source":{"id":"1806.10191","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.10191","created_at":"2026-05-18T00:12:13Z"},{"alias_kind":"arxiv_version","alias_value":"1806.10191v1","created_at":"2026-05-18T00:12:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.10191","created_at":"2026-05-18T00:12:13Z"},{"alias_kind":"pith_short_12","alias_value":"HYFBBXXHJDUI","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_16","alias_value":"HYFBBXXHJDUINJAZ","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_8","alias_value":"HYFBBXXH","created_at":"2026-05-18T12:32:28Z"}],"graph_snapshots":[{"event_id":"sha256:bf1aac08f93177899f9617b2a133e565165142fdf769a9214645cf8976a4af29","target":"graph","created_at":"2026-05-18T00:12:13Z","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 this study we establish the existence and uniqueness of the solution of a coupled system of general elliptic equations with anisotropic diffusion , non-uniform advection and variably influencing reaction terms on Lipschitz continuous domain $\\Omega \\subset \\mathbb{R}^m $ (m$\\geq$1) with a Dirichlet boundary. Later we consider the finite element (FE) approximation of the coupled equations in a meshless framework based on weighted extended B-Spine functions (WEBS).The a priori error estimates corresponding to the finite element analysis are derived to establish the convergence of the correspo","authors_text":"Ayan Chakraborty, BV. Rathish Kumar","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-06-24T08:35:38Z","title":"Weighted Extended B-Spline Finite Element Analysis of a coupled system of general Elliptic equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.10191","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":"sha256:3d22bb619bbe4a6177baa5df04b33231c565a2497b09407b20d173f02c3cc2ee","target":"record","created_at":"2026-05-18T00:12:13Z","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":"c22193e70b54c3a9c987ed3f447cb896db31acdbddeb84401ebf54bf942f327e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-06-24T08:35:38Z","title_canon_sha256":"61303dd64713c4b286cfdef9100e8bc28db004603d5c800ee36671d0a0a9d641"},"schema_version":"1.0","source":{"id":"1806.10191","kind":"arxiv","version":1}},"canonical_sha256":"3e0a10dee748e886a4192ddddbb9a1023da81114d87deec90b4c55dd12613c6d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3e0a10dee748e886a4192ddddbb9a1023da81114d87deec90b4c55dd12613c6d","first_computed_at":"2026-05-18T00:12:13.214251Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:12:13.214251Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XPOeLa8xP0r67y5FPLiwqAFpgW5QgylCA3EPU4hPUIg/PH/4MDid1mPawWC7xcd2PfiQEMzoNehH4Ci72wz2DA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:12:13.214792Z","signed_message":"canonical_sha256_bytes"},"source_id":"1806.10191","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3d22bb619bbe4a6177baa5df04b33231c565a2497b09407b20d173f02c3cc2ee","sha256:bf1aac08f93177899f9617b2a133e565165142fdf769a9214645cf8976a4af29"],"state_sha256":"41fe67a69dc1a22f04da2c7b09a67d73347700851cdd4304038dc1d6624098ba"}