{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:QBRICDPETYMQARRCBYHQA33OW5","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":"5653e0e649b2ec49d87f433ccea03f20ce64ebed545df3c426e067fdd1ec51c7","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2026-07-30T14:04:03Z","title_canon_sha256":"b20aca3cdb09cf70a2de707dfc408fa71c8a6b4efbcd02a2908379a14845b9d9"},"schema_version":"1.0","source":{"id":"2607.28235","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.28235","created_at":"2026-07-31T01:36:53Z"},{"alias_kind":"arxiv_version","alias_value":"2607.28235v1","created_at":"2026-07-31T01:36:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.28235","created_at":"2026-07-31T01:36:53Z"},{"alias_kind":"pith_short_12","alias_value":"QBRICDPETYMQ","created_at":"2026-07-31T01:36:53Z"},{"alias_kind":"pith_short_16","alias_value":"QBRICDPETYMQARRC","created_at":"2026-07-31T01:36:53Z"},{"alias_kind":"pith_short_8","alias_value":"QBRICDPE","created_at":"2026-07-31T01:36:53Z"}],"graph_snapshots":[{"event_id":"sha256:47302defc5b836c8e9e1aaa5b46b8080aa480ae51c73d6bbd1d62c809b5220db","target":"graph","created_at":"2026-07-31T01:36:53Z","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/2607.28235/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Algebraic multigrid (AMG) methods are robust and efficient black-box preconditioners for linear systems arising from low-order discretizations of elliptic partial differential equations, but their performance often deteriorates for high-order methods. We introduce an algebraic-geometric multilevel preconditioner for continuous lagrangian finite element discretizations. The method automatically constructs prolongation operators and a Galerkin hierarchy using only the coordinates of finite element support points, without requiring a prescribed mesh hierarchy or domain decomposition. The support-","authors_text":"Davide Polverino, Luca Heltai, Marco Feder","cross_cats":["cs.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2026-07-30T14:04:03Z","title":"R3MG-C: a high-order algebraic-geometric multilevel preconditioner for continuous finite element discretizations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.28235","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:a657011a577f43d0bc916c822bb96c00e66fdf98decebe58c2949f3d4aa01cee","target":"record","created_at":"2026-07-31T01:36:53Z","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":"5653e0e649b2ec49d87f433ccea03f20ce64ebed545df3c426e067fdd1ec51c7","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2026-07-30T14:04:03Z","title_canon_sha256":"b20aca3cdb09cf70a2de707dfc408fa71c8a6b4efbcd02a2908379a14845b9d9"},"schema_version":"1.0","source":{"id":"2607.28235","kind":"arxiv","version":1}},"canonical_sha256":"8062810de49e190046220e0f006f6eb76308c5337865caf4a63448c1bbaaabdf","receipt":{"builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8062810de49e190046220e0f006f6eb76308c5337865caf4a63448c1bbaaabdf","first_computed_at":"2026-07-31T01:36:53.133820Z","kind":"pith_receipt","last_reissued_at":"2026-07-31T01:36:53.133820Z","receipt_version":"0.3","signature_status":"unsigned_v0"},"source_id":"2607.28235","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a657011a577f43d0bc916c822bb96c00e66fdf98decebe58c2949f3d4aa01cee","sha256:47302defc5b836c8e9e1aaa5b46b8080aa480ae51c73d6bbd1d62c809b5220db"],"state_sha256":"c1f6b404f89881167a9442d07498bcf3e1fa2649932c7d3e0f42ec4d2c1e1f80"}