{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:5YZMGPB4M4R5BQVL6O5IOVRSAR","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":"d14f9b958c38a02921645e1753e72194aff858a627daacdc3234514619d04a4d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-03-05T02:20:05Z","title_canon_sha256":"53066bfb8dab91c7d44cd43573b2b7bf8662e90c50a2358473efce033a440f1f"},"schema_version":"1.0","source":{"id":"1203.0803","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1203.0803","created_at":"2026-05-18T03:38:14Z"},{"alias_kind":"arxiv_version","alias_value":"1203.0803v3","created_at":"2026-05-18T03:38:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.0803","created_at":"2026-05-18T03:38:14Z"},{"alias_kind":"pith_short_12","alias_value":"5YZMGPB4M4R5","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_16","alias_value":"5YZMGPB4M4R5BQVL","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_8","alias_value":"5YZMGPB4","created_at":"2026-05-18T12:26:56Z"}],"graph_snapshots":[{"event_id":"sha256:28c92c301c58ac78b3c6fa9361f763ce30b6ebacab6c799bb3294bc9c028062e","target":"graph","created_at":"2026-05-18T03:38:14Z","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) has been developed over the past decade as a framework for constructing and analyzing stable and accurate numerical methods for partial differential equations by employing differential complexes. The recent work of Arnold, Falk and Winther \\cite{ArFaWi2010} includes a well-developed theory of finite element methods for Hodge Laplace problems, including a priori error estimates. In this work we focus on developing a posteriori error estimates in which the computational error is bounded by some computable functional of the discrete solution and problem dat","authors_text":"Alan Demlow, Anil N. Hirani","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-03-05T02:20:05Z","title":"A posteriori error estimates for finite element exterior calculus: The de Rham complex"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.0803","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:a807ca5e314b67ebb4f0b84611405fdeca7f7ed50a45cdf0f3d807691cdb2dc5","target":"record","created_at":"2026-05-18T03:38:14Z","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":"d14f9b958c38a02921645e1753e72194aff858a627daacdc3234514619d04a4d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-03-05T02:20:05Z","title_canon_sha256":"53066bfb8dab91c7d44cd43573b2b7bf8662e90c50a2358473efce033a440f1f"},"schema_version":"1.0","source":{"id":"1203.0803","kind":"arxiv","version":3}},"canonical_sha256":"ee32c33c3c6723d0c2abf3ba875632044117cb8c543c85c8fe68be197573ed97","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ee32c33c3c6723d0c2abf3ba875632044117cb8c543c85c8fe68be197573ed97","first_computed_at":"2026-05-18T03:38:14.263822Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:38:14.263822Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"EvptSRUht7taBzl/ZCxE+jTlPWzCIVIGvdprS1Bxa5wifF+bXIhDBYJLyEW0PI2atZD78FXnzvUPMMez56w4DA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:38:14.264280Z","signed_message":"canonical_sha256_bytes"},"source_id":"1203.0803","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a807ca5e314b67ebb4f0b84611405fdeca7f7ed50a45cdf0f3d807691cdb2dc5","sha256:28c92c301c58ac78b3c6fa9361f763ce30b6ebacab6c799bb3294bc9c028062e"],"state_sha256":"18bc317f2265d5b150a62de2bb61f999a61fc6ca662ab4f18a3bb5eee8f94484"}