{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:N4Z5HRXATFGE5S67RO6GQRCZZH","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":"3e5d257ee3af712c9bcdf9b284d89cf88858fc0b29724f0bb720a18fd48a002a","cross_cats_sorted":["gr-qc"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.comp-ph","submitted_at":"2011-04-18T08:20:08Z","title_canon_sha256":"d8d14ecf72e0fb28c7e53de7d4aaa527bf7b911f70c272bb2f5ad59696c30291"},"schema_version":"1.0","source":{"id":"1104.3408","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1104.3408","created_at":"2026-05-18T02:02:23Z"},{"alias_kind":"arxiv_version","alias_value":"1104.3408v1","created_at":"2026-05-18T02:02:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1104.3408","created_at":"2026-05-18T02:02:23Z"},{"alias_kind":"pith_short_12","alias_value":"N4Z5HRXATFGE","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_16","alias_value":"N4Z5HRXATFGE5S67","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_8","alias_value":"N4Z5HRXA","created_at":"2026-05-18T12:26:37Z"}],"graph_snapshots":[{"event_id":"sha256:d087b567d06e0c31f1bcc1a6bb6d5862e9c4776abeabca4e75d466b6badd2060","target":"graph","created_at":"2026-05-18T02:02:23Z","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 construct a pseudospectral method for the solution of time-dependent, non-linear partial differential equations on a three-dimensional spherical shell. The problem we address is the treatment of tensor fields on the sphere. As a test case we consider the evolution of a single black hole in numerical general relativity. A natural strategy would be the expansion in tensor spherical harmonics in spherical coordinates. Instead, we consider the simpler and potentially more efficient possibility of a double Fourier expansion on the sphere for tensors in Cartesian coordinates. As usual for the dou","authors_text":"Bernd Bruegmann","cross_cats":["gr-qc"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.comp-ph","submitted_at":"2011-04-18T08:20:08Z","title":"A pseudospectral matrix method for time-dependent tensor fields on a spherical shell"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.3408","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":"sha256:457e467e94fe146bb11f1f2c7e9f715498c6af22613fa23651e6ebd86adac665","target":"record","created_at":"2026-05-18T02:02:23Z","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":"3e5d257ee3af712c9bcdf9b284d89cf88858fc0b29724f0bb720a18fd48a002a","cross_cats_sorted":["gr-qc"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.comp-ph","submitted_at":"2011-04-18T08:20:08Z","title_canon_sha256":"d8d14ecf72e0fb28c7e53de7d4aaa527bf7b911f70c272bb2f5ad59696c30291"},"schema_version":"1.0","source":{"id":"1104.3408","kind":"arxiv","version":1}},"canonical_sha256":"6f33d3c6e0994c4ecbdf8bbc684459c9c8134269be2f23310bfff5704084371c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6f33d3c6e0994c4ecbdf8bbc684459c9c8134269be2f23310bfff5704084371c","first_computed_at":"2026-05-18T02:02:23.814013Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:02:23.814013Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Sdhn+GgP+kEWg9yZWkHyJwhkEVJ1g7zbyIv9Dz/7gW7OAYmEbLXUpVc8yJz7Pd/dcncp1YXN5q5dxXeDNrqPCg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:02:23.814707Z","signed_message":"canonical_sha256_bytes"},"source_id":"1104.3408","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:457e467e94fe146bb11f1f2c7e9f715498c6af22613fa23651e6ebd86adac665","sha256:d087b567d06e0c31f1bcc1a6bb6d5862e9c4776abeabca4e75d466b6badd2060"],"state_sha256":"df21fc8b91cb4c5d6e430b73acb109e060fd6584dd3a14f8ec585d724670d3c3"}