{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:KFYAWAM5GPHP2LLJXLPLLI2ZS2","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":"5cafeba853af6826206816701bd1d5f8f78e4ead50cb11573a90fe30689ebcd8","cross_cats_sorted":["cs.NA"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2021-04-28T21:30:03Z","title_canon_sha256":"09f9b69a2a5d4c9318f29c7480f06e78a71fdf8cca76322d3360c2a8a5990397"},"schema_version":"1.0","source":{"id":"2105.01739","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2105.01739","created_at":"2026-07-05T02:37:47Z"},{"alias_kind":"arxiv_version","alias_value":"2105.01739v1","created_at":"2026-07-05T02:37:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2105.01739","created_at":"2026-07-05T02:37:47Z"},{"alias_kind":"pith_short_12","alias_value":"KFYAWAM5GPHP","created_at":"2026-07-05T02:37:47Z"},{"alias_kind":"pith_short_16","alias_value":"KFYAWAM5GPHP2LLJ","created_at":"2026-07-05T02:37:47Z"},{"alias_kind":"pith_short_8","alias_value":"KFYAWAM5","created_at":"2026-07-05T02:37:47Z"}],"graph_snapshots":[{"event_id":"sha256:1e1749db26b388ab5bffef36cc04652d88a204e0ec900262378e220f8b7173b4","target":"graph","created_at":"2026-07-05T02:37:47Z","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/2105.01739/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The multigrid algorithm is an efficient numerical method for solving a variety of elliptic partial differential equations (PDEs). The method damps errors at progressively finer grid scales, resulting in faster convergence compared to standard iterative methods such as Gauss-Seidel. The prolongation, or coarse-to-fine interpolation operator within the multigrid algorithm lends itself to a data-driven treatment with ML super resolution, commonly used to increase the resolution of images. We (i) propose the novel integration of a super resolution generative adversarial network (GAN) model with th","authors_text":"Francisco Holguin, Gavin Portwood, GS Sidharth","cross_cats":["cs.NA"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2021-04-28T21:30:03Z","title":"Multigrid Solver With Super-Resolved Interpolation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2105.01739","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":"sha256:052adf7c2d793647c489a482cc6eaa14faa1c89b9acb5a6a51e46fcf855d7ddd","target":"record","created_at":"2026-07-05T02:37:47Z","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":"5cafeba853af6826206816701bd1d5f8f78e4ead50cb11573a90fe30689ebcd8","cross_cats_sorted":["cs.NA"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2021-04-28T21:30:03Z","title_canon_sha256":"09f9b69a2a5d4c9318f29c7480f06e78a71fdf8cca76322d3360c2a8a5990397"},"schema_version":"1.0","source":{"id":"2105.01739","kind":"arxiv","version":1}},"canonical_sha256":"51700b019d33cefd2d69badeb5a35996bbbb5aa2de01df5aa29458ae2b87ef52","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"51700b019d33cefd2d69badeb5a35996bbbb5aa2de01df5aa29458ae2b87ef52","first_computed_at":"2026-07-05T02:37:47.639897Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:37:47.639897Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"iPbcih2RGxyY2E4xbHRi+9ZPHXJxNtTMAlelagTS0n09Dcd6BKX8F+RuvomvpNjg03zv12YKa0u4gOl8pEDvDg==","signature_status":"signed_v1","signed_at":"2026-07-05T02:37:47.640376Z","signed_message":"canonical_sha256_bytes"},"source_id":"2105.01739","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:052adf7c2d793647c489a482cc6eaa14faa1c89b9acb5a6a51e46fcf855d7ddd","sha256:1e1749db26b388ab5bffef36cc04652d88a204e0ec900262378e220f8b7173b4"],"state_sha256":"ed1f2548079837447fb86bfd9e63a85db1f37a11d5c925c38f1f2e7b501ca730"}