{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:3VF4MLZZXJ6ZUWQA2YYXIYUEJR","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":"e69bf26d57883fcda7db00c97254148a57ccea2e8c4d74ccd0ff0a74e71ae3c0","cross_cats_sorted":["cs.NA"],"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.NA","submitted_at":"2025-08-04T05:36:33Z","title_canon_sha256":"18e0e953ac29cfd488b5d49fecf2eca70d3a3d573cd2afb9808852b10d166bd0"},"schema_version":"1.0","source":{"id":"2508.02077","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2508.02077","created_at":"2026-07-05T11:47:50Z"},{"alias_kind":"arxiv_version","alias_value":"2508.02077v1","created_at":"2026-07-05T11:47:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2508.02077","created_at":"2026-07-05T11:47:50Z"},{"alias_kind":"pith_short_12","alias_value":"3VF4MLZZXJ6Z","created_at":"2026-07-05T11:47:50Z"},{"alias_kind":"pith_short_16","alias_value":"3VF4MLZZXJ6ZUWQA","created_at":"2026-07-05T11:47:50Z"},{"alias_kind":"pith_short_8","alias_value":"3VF4MLZZ","created_at":"2026-07-05T11:47:50Z"}],"graph_snapshots":[{"event_id":"sha256:755960ce0102f6f19e675a7707b7f77e80f8e5b23d1c400f8858634a1124e72b","target":"graph","created_at":"2026-07-05T11:47:50Z","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/2508.02077/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we propose and analyze an adaptive Crouzeix-Raviart finite element method for computing the first Dirichlet eigenpair of the $p$-Laplacian problem. We prove that the sequence of error estimators produced by the adaptive algorithm has a vanishing limit and that, starting from a fine initial mesh, the relevant sequence of approximate eigenvalues converges to the first eigenvalue and the distance in a mesh-dependent broken norm between discrete eigenfunctions and the set composed of relevant continuous eigenfunctions also tends to zero. The analysis hinges on establishing a compact","authors_text":"Guanglian Li, Yifeng Xu, Yueqi Wang","cross_cats":["cs.NA"],"headline":"","license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.NA","submitted_at":"2025-08-04T05:36:33Z","title":"Adaptive Crouzeix-Raviart finite elements for the first eigenpair of $p$-Laplacian"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2508.02077","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":"sha256:7a3a380addafeb74bb54522b8958e1492c82bd60f5b9dd79d18aa1d59d329e8f","target":"record","created_at":"2026-07-05T11:47:50Z","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":"e69bf26d57883fcda7db00c97254148a57ccea2e8c4d74ccd0ff0a74e71ae3c0","cross_cats_sorted":["cs.NA"],"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.NA","submitted_at":"2025-08-04T05:36:33Z","title_canon_sha256":"18e0e953ac29cfd488b5d49fecf2eca70d3a3d573cd2afb9808852b10d166bd0"},"schema_version":"1.0","source":{"id":"2508.02077","kind":"arxiv","version":1}},"canonical_sha256":"dd4bc62f39ba7d9a5a00d6317462844c6c15dcea2de5bee93f791500cc7e93cf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dd4bc62f39ba7d9a5a00d6317462844c6c15dcea2de5bee93f791500cc7e93cf","first_computed_at":"2026-07-05T11:47:50.486970Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:47:50.486970Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"C5s7ZXYXHOa4BNE/A/Xp9oNaF4dgePIqNhWs5ZUF7VZ+Lg7Y3F2WNgtCsI/QQSD4j3ZYHKKuYZsMBFhDV6FJCA==","signature_status":"signed_v1","signed_at":"2026-07-05T11:47:50.487445Z","signed_message":"canonical_sha256_bytes"},"source_id":"2508.02077","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7a3a380addafeb74bb54522b8958e1492c82bd60f5b9dd79d18aa1d59d329e8f","sha256:755960ce0102f6f19e675a7707b7f77e80f8e5b23d1c400f8858634a1124e72b"],"state_sha256":"55ac0eea008e4c56e6b0a28ab98a3571d147a336685c97109b431dfd1114cc11"}