{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:4IFGHYY2QKSRCSMXUO2LEHKSAB","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":"26c0db066b43d55f0d7f39fa5157ba326f40e4183790ee4321d4b78174eb9602","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-06-08T06:04:35Z","title_canon_sha256":"165193eacc57d3189c63c45c4a0f971188249eae355b9a02b02e2c4859c2e8b7"},"schema_version":"1.0","source":{"id":"1306.1886","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1306.1886","created_at":"2026-05-17T23:59:28Z"},{"alias_kind":"arxiv_version","alias_value":"1306.1886v3","created_at":"2026-05-17T23:59:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.1886","created_at":"2026-05-17T23:59:28Z"},{"alias_kind":"pith_short_12","alias_value":"4IFGHYY2QKSR","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_16","alias_value":"4IFGHYY2QKSRCSMX","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_8","alias_value":"4IFGHYY2","created_at":"2026-05-18T12:27:34Z"}],"graph_snapshots":[{"event_id":"sha256:036820292f0e5d9b46ada1d099440de04f781b069ffdbb16a522e2ca3be32acb","target":"graph","created_at":"2026-05-17T23:59:28Z","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":"Finite Element Exterior Calculus (FEEC) was developed by Arnold, Falk, Winther and others over the last decade to exploit the observation that mixed variational problems can be posed on a Hilbert complex, and Galerkin-type mixed methods can then be obtained by solving finite-dimensional subcomplex problems. Chen, Holst, and Xu (Math. Comp. 78 (2009) 35-53) established convergence and optimality of an adaptive mixed finite element method using Raviart-Thomas or Brezzi-Douglas-Marini elements for Poisson's equation on contractible domains in two dimensions, which can be viewed as a boundary prob","authors_text":"Adam Mihalik, Michael Holst, Ryan Szypowski, Yuwen Li","cross_cats":["math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-06-08T06:04:35Z","title":"Convergence and Optimality of Adaptive Methods for Poisson's Equation in the FEEC Framework"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.1886","kind":"arxiv","version":3},"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:dccbad1f3ebac643ff7196d308fdb9f1e7b105f1e3c81a427c70ac237431461a","target":"record","created_at":"2026-05-17T23:59:28Z","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":"26c0db066b43d55f0d7f39fa5157ba326f40e4183790ee4321d4b78174eb9602","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-06-08T06:04:35Z","title_canon_sha256":"165193eacc57d3189c63c45c4a0f971188249eae355b9a02b02e2c4859c2e8b7"},"schema_version":"1.0","source":{"id":"1306.1886","kind":"arxiv","version":3}},"canonical_sha256":"e20a63e31a82a5114997a3b4b21d52004b0bf3bb58ea31ce8b5d725b3cd315cd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e20a63e31a82a5114997a3b4b21d52004b0bf3bb58ea31ce8b5d725b3cd315cd","first_computed_at":"2026-05-17T23:59:28.044557Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:59:28.044557Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1RYod+KJO75DtWwuMZ03IevhMywWNYDQ5KsUOPudWoWbAHSCYR0PRe8J3N4oisAVhoNYYfj9/VAw8TxOhncBBQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:59:28.045214Z","signed_message":"canonical_sha256_bytes"},"source_id":"1306.1886","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dccbad1f3ebac643ff7196d308fdb9f1e7b105f1e3c81a427c70ac237431461a","sha256:036820292f0e5d9b46ada1d099440de04f781b069ffdbb16a522e2ca3be32acb"],"state_sha256":"2bbe74fde650368abd3852118aa47140c391371b40cc2533c1b906fe4762b0c6"}