{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:FCORO4JSC5O6Y37EQIQ55NFAPX","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":"8651065c5285dcc54d8dd00e5f9edd838baf3901e41e6f8e4731ff207ae7d5d2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-06-16T08:13:43Z","title_canon_sha256":"017dde192f71d9939b222f4bbb671c09b45033b5c8ba1fe99ee8509d60935d67"},"schema_version":"1.0","source":{"id":"1606.05085","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.05085","created_at":"2026-05-18T01:12:22Z"},{"alias_kind":"arxiv_version","alias_value":"1606.05085v1","created_at":"2026-05-18T01:12:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.05085","created_at":"2026-05-18T01:12:22Z"},{"alias_kind":"pith_short_12","alias_value":"FCORO4JSC5O6","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_16","alias_value":"FCORO4JSC5O6Y37E","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_8","alias_value":"FCORO4JS","created_at":"2026-05-18T12:30:15Z"}],"graph_snapshots":[{"event_id":"sha256:f13c64e2cd21e77905dab16443e8af118bbe65f3d1fa5845de180e1c65ef427e","target":"graph","created_at":"2026-05-18T01:12:22Z","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":"We derive a priori error estimates for the standard Galerkin and streamline diffusion finite element methods for the Fermi pencil-beam equation obtained from a fully three dimensional Fokker-Planck equation in space ${\\mathbf x}=(x,y,z)$ and velocity $\\tilde {\\mathbf v}=(\\mu, \\eta, \\xi)$ variables. The Fokker-Planck term appears as a Laplace-Beltrami operator in the unit sphere. The diffusion term in the Fermi equation is obtained as a projection of the FP operator onto the tangent plane to the unit sphere at the pole $(1,0,0)$ and in the direction of $ {\\mathbf v}_0=(1,\\eta, \\xi)$. Hence the ","authors_text":"C. Standar, L. Beilina, M. Asadzadeh, M. Naseer","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-06-16T08:13:43Z","title":"A priori error estimates and computational studies for a Fermi pencil-beam equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.05085","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":"sha256:6b139d8546f04121fa9505558d3597f64d1428629c0d82caeeb78a8727581c3f","target":"record","created_at":"2026-05-18T01:12:22Z","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":"8651065c5285dcc54d8dd00e5f9edd838baf3901e41e6f8e4731ff207ae7d5d2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-06-16T08:13:43Z","title_canon_sha256":"017dde192f71d9939b222f4bbb671c09b45033b5c8ba1fe99ee8509d60935d67"},"schema_version":"1.0","source":{"id":"1606.05085","kind":"arxiv","version":1}},"canonical_sha256":"289d177132175dec6fe48221deb4a07deae0aa7837b2c8544568e80a9070b55a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"289d177132175dec6fe48221deb4a07deae0aa7837b2c8544568e80a9070b55a","first_computed_at":"2026-05-18T01:12:22.060204Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:12:22.060204Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cBwKiy6QR01yxGrWfeu9F2c+keXSI9vmP8LKwm01h/ig9391rouYbRkEFaM9QDTR9uk3tt7U5C/JOAXOqSK6Bw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:12:22.060530Z","signed_message":"canonical_sha256_bytes"},"source_id":"1606.05085","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6b139d8546f04121fa9505558d3597f64d1428629c0d82caeeb78a8727581c3f","sha256:f13c64e2cd21e77905dab16443e8af118bbe65f3d1fa5845de180e1c65ef427e"],"state_sha256":"60d1d410b4ec330aeefc26738175c53d92a0106e9aef449cb27115fa34ac404c"}