{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:7UBQN3PCHB72WVBJSLAYRIJR3N","short_pith_number":"pith:7UBQN3PC","canonical_record":{"source":{"id":"1807.01159","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-06-30T16:58:13Z","cross_cats_sorted":[],"title_canon_sha256":"45f33a9b84995af7f339ab8289ccb635b36e91c86b2cb8a68b44a7dec533c1ce","abstract_canon_sha256":"9245309bb3c5f21064b1e5051162b45832bb9c26ad4ad186b3733f914e1d7ddc"},"schema_version":"1.0"},"canonical_sha256":"fd0306ede2387fab542992c188a131db55c352625a865d112aead3c4d2c2d606","source":{"kind":"arxiv","id":"1807.01159","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1807.01159","created_at":"2026-05-18T00:11:45Z"},{"alias_kind":"arxiv_version","alias_value":"1807.01159v1","created_at":"2026-05-18T00:11:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.01159","created_at":"2026-05-18T00:11:45Z"},{"alias_kind":"pith_short_12","alias_value":"7UBQN3PCHB72","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_16","alias_value":"7UBQN3PCHB72WVBJ","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_8","alias_value":"7UBQN3PC","created_at":"2026-05-18T12:32:11Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:7UBQN3PCHB72WVBJSLAYRIJR3N","target":"record","payload":{"canonical_record":{"source":{"id":"1807.01159","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-06-30T16:58:13Z","cross_cats_sorted":[],"title_canon_sha256":"45f33a9b84995af7f339ab8289ccb635b36e91c86b2cb8a68b44a7dec533c1ce","abstract_canon_sha256":"9245309bb3c5f21064b1e5051162b45832bb9c26ad4ad186b3733f914e1d7ddc"},"schema_version":"1.0"},"canonical_sha256":"fd0306ede2387fab542992c188a131db55c352625a865d112aead3c4d2c2d606","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:11:45.087066Z","signature_b64":"oClxrX5eByYSgeH4xvLIlg0nbBFTAA0sxOXK3f5PgC0j5lplE5D8YRBgVWVQvAynZvpONaCPj/dCJYEzYdviBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fd0306ede2387fab542992c188a131db55c352625a865d112aead3c4d2c2d606","last_reissued_at":"2026-05-18T00:11:45.086354Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:11:45.086354Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1807.01159","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:11:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1mFZWfykAXLHWV/JcdBqyAdYzoniZovKuO7tljHYUtuPFINCx0fNTaXSbemut+ii0fh19RO1h/HLNGpR2+0lDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T04:43:19.364450Z"},"content_sha256":"507e934dcbe2e8f487a812c092878e91006b8c8641c9b23eb176176f2406e4ba","schema_version":"1.0","event_id":"sha256:507e934dcbe2e8f487a812c092878e91006b8c8641c9b23eb176176f2406e4ba"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:7UBQN3PCHB72WVBJSLAYRIJR3N","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Non uniform weighted extended B-Spline finite element analysis of non linear elliptic partial differential equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Ayan Chakraborty, B.V.Rathish Kumar","submitted_at":"2018-06-30T16:58:13Z","abstract_excerpt":"We propose a non uniform web spline based finite element analysis for elliptic partial differential equation with the gradient type nonlinearity in their principal coefficients like p-laplacian equation and Quasi-Newtonian fluid flow equations. We discuss the well-posednes of the problems and also derive the apriori error estimates for the proposed finite element analysis and obtain convergence rate of $\\mathcal{O}(h^{\\alpha})$ for $\\alpha > 0$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.01159","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:11:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mtgMZpV6JepjnVwAoEID5gnvBGi9ALPx82AOHqbATXYc+gzXJI6uxdzjHkvefU0Z/jYhWScQMmLEBNsraeylDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T04:43:19.364796Z"},"content_sha256":"72e497a378aa4bb67943c2127798b6a62f1b5eb0ff60aa01da4f7eae09f46d08","schema_version":"1.0","event_id":"sha256:72e497a378aa4bb67943c2127798b6a62f1b5eb0ff60aa01da4f7eae09f46d08"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7UBQN3PCHB72WVBJSLAYRIJR3N/bundle.json","state_url":"https://pith.science/pith/7UBQN3PCHB72WVBJSLAYRIJR3N/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7UBQN3PCHB72WVBJSLAYRIJR3N/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-02T04:43:19Z","links":{"resolver":"https://pith.science/pith/7UBQN3PCHB72WVBJSLAYRIJR3N","bundle":"https://pith.science/pith/7UBQN3PCHB72WVBJSLAYRIJR3N/bundle.json","state":"https://pith.science/pith/7UBQN3PCHB72WVBJSLAYRIJR3N/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7UBQN3PCHB72WVBJSLAYRIJR3N/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:7UBQN3PCHB72WVBJSLAYRIJR3N","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":"9245309bb3c5f21064b1e5051162b45832bb9c26ad4ad186b3733f914e1d7ddc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-06-30T16:58:13Z","title_canon_sha256":"45f33a9b84995af7f339ab8289ccb635b36e91c86b2cb8a68b44a7dec533c1ce"},"schema_version":"1.0","source":{"id":"1807.01159","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1807.01159","created_at":"2026-05-18T00:11:45Z"},{"alias_kind":"arxiv_version","alias_value":"1807.01159v1","created_at":"2026-05-18T00:11:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.01159","created_at":"2026-05-18T00:11:45Z"},{"alias_kind":"pith_short_12","alias_value":"7UBQN3PCHB72","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_16","alias_value":"7UBQN3PCHB72WVBJ","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_8","alias_value":"7UBQN3PC","created_at":"2026-05-18T12:32:11Z"}],"graph_snapshots":[{"event_id":"sha256:72e497a378aa4bb67943c2127798b6a62f1b5eb0ff60aa01da4f7eae09f46d08","target":"graph","created_at":"2026-05-18T00:11:45Z","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":"We propose a non uniform web spline based finite element analysis for elliptic partial differential equation with the gradient type nonlinearity in their principal coefficients like p-laplacian equation and Quasi-Newtonian fluid flow equations. We discuss the well-posednes of the problems and also derive the apriori error estimates for the proposed finite element analysis and obtain convergence rate of $\\mathcal{O}(h^{\\alpha})$ for $\\alpha > 0$.","authors_text":"Ayan Chakraborty, B.V.Rathish Kumar","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-06-30T16:58:13Z","title":"Non uniform weighted extended B-Spline finite element analysis of non linear elliptic partial differential equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.01159","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":"sha256:507e934dcbe2e8f487a812c092878e91006b8c8641c9b23eb176176f2406e4ba","target":"record","created_at":"2026-05-18T00:11:45Z","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":"9245309bb3c5f21064b1e5051162b45832bb9c26ad4ad186b3733f914e1d7ddc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-06-30T16:58:13Z","title_canon_sha256":"45f33a9b84995af7f339ab8289ccb635b36e91c86b2cb8a68b44a7dec533c1ce"},"schema_version":"1.0","source":{"id":"1807.01159","kind":"arxiv","version":1}},"canonical_sha256":"fd0306ede2387fab542992c188a131db55c352625a865d112aead3c4d2c2d606","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fd0306ede2387fab542992c188a131db55c352625a865d112aead3c4d2c2d606","first_computed_at":"2026-05-18T00:11:45.086354Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:11:45.086354Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"oClxrX5eByYSgeH4xvLIlg0nbBFTAA0sxOXK3f5PgC0j5lplE5D8YRBgVWVQvAynZvpONaCPj/dCJYEzYdviBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:11:45.087066Z","signed_message":"canonical_sha256_bytes"},"source_id":"1807.01159","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:507e934dcbe2e8f487a812c092878e91006b8c8641c9b23eb176176f2406e4ba","sha256:72e497a378aa4bb67943c2127798b6a62f1b5eb0ff60aa01da4f7eae09f46d08"],"state_sha256":"cfc35a296585d4188952946decb20e09ce60bace795f4680bb93773f4a886bb0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NVhCq1v3s0Twz6hsFo0l2tNQgkHFvrSGoGtipz8XgEMxjWbvWC5YUp/WwkEa89CHSsiosgsMtlr3Hb0AwFw/Dw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T04:43:19.366726Z","bundle_sha256":"871a26c87bba14c1dcd96c52704b06f99e665207c6c6ff5c6c1c76ce55d291a9"}}