{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2002:ALS4UDSDNPMPWZNZ6BY64N4E2O","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":"e118c7a0dc30990b1675ea2512537156d367bf0cc2a8da879c9c6e3cc8d91754","cross_cats_sorted":[],"license":"","primary_cat":"physics.comp-ph","submitted_at":"2002-09-10T15:22:25Z","title_canon_sha256":"dfc2b4a674caf071caef6ecfd059d8eb4f1c7ee6ecd25823328301843fe7e899"},"schema_version":"1.0","source":{"id":"physics/0209040","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"physics/0209040","created_at":"2026-07-04T14:43:48Z"},{"alias_kind":"arxiv_version","alias_value":"physics/0209040v2","created_at":"2026-07-04T14:43:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.physics/0209040","created_at":"2026-07-04T14:43:48Z"},{"alias_kind":"pith_short_12","alias_value":"ALS4UDSDNPMP","created_at":"2026-07-04T14:43:48Z"},{"alias_kind":"pith_short_16","alias_value":"ALS4UDSDNPMPWZNZ","created_at":"2026-07-04T14:43:48Z"},{"alias_kind":"pith_short_8","alias_value":"ALS4UDSD","created_at":"2026-07-04T14:43:48Z"}],"graph_snapshots":[{"event_id":"sha256:6956192dccc2dee2f7521975807879ef2545019e424066dd58e13fba245e28ea","target":"graph","created_at":"2026-07-04T14:43:48Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/physics/0209040/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"It is shown how various ideas that are well established for the solution of Poisson's equation using plane wave and multigrid methods can be combined with wavelet concepts. The combination of wavelet concepts and multigrid techniques turns out to be particularly fruitful. We propose a modified multigrid V cycle scheme that is not only much simpler, but also more efficient than the standard V cycle. Whereas in the traditional V cycle the residue is passed to the coarser grid levels, this new scheme does not require the calculation of a residue. Instead it works with copies of the charge density","authors_text":"S. Goedecker","cross_cats":[],"headline":"","license":"","primary_cat":"physics.comp-ph","submitted_at":"2002-09-10T15:22:25Z","title":"Combining multigrid and wavelet ideas to construct more efficient multiscale algorithms for the solution of Poisson's equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"physics/0209040","kind":"arxiv","version":2},"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:f579b9c6cdfd7b242dbe8b64fdaaacb17b2b819df3464aa9a37ed7890a196207","target":"record","created_at":"2026-07-04T14:43:48Z","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":"e118c7a0dc30990b1675ea2512537156d367bf0cc2a8da879c9c6e3cc8d91754","cross_cats_sorted":[],"license":"","primary_cat":"physics.comp-ph","submitted_at":"2002-09-10T15:22:25Z","title_canon_sha256":"dfc2b4a674caf071caef6ecfd059d8eb4f1c7ee6ecd25823328301843fe7e899"},"schema_version":"1.0","source":{"id":"physics/0209040","kind":"arxiv","version":2}},"canonical_sha256":"02e5ca0e436bd8fb65b9f071ee3784d398bc29b7fbfbca91563a6fca1252f5cd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"02e5ca0e436bd8fb65b9f071ee3784d398bc29b7fbfbca91563a6fca1252f5cd","first_computed_at":"2026-07-04T14:43:48.601204Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T14:43:48.601204Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8fSXjjmEQDrMioAvIWlmWGWSk7QzousiulD0tKtXVGoqNN8etjOR9XYD5D8n9OjCUCO9ILMAA6CaEVizes7OBw==","signature_status":"signed_v1","signed_at":"2026-07-04T14:43:48.601604Z","signed_message":"canonical_sha256_bytes"},"source_id":"physics/0209040","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f579b9c6cdfd7b242dbe8b64fdaaacb17b2b819df3464aa9a37ed7890a196207","sha256:6956192dccc2dee2f7521975807879ef2545019e424066dd58e13fba245e28ea"],"state_sha256":"28900cde96e47511d2e67b068a0d01b293202ff59c045752d33818ec8c07ce0a"}