{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2006:AYRWQE5PQKWUZJZ26KVST3P7EY","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":"3bfc4569fd9ebd7cd17dcac1883a8283494df17b92bc3ffb4020949330383caf","cross_cats_sorted":[],"license":"","primary_cat":"cond-mat.mtrl-sci","submitted_at":"2006-12-16T18:08:41Z","title_canon_sha256":"807b5532b64a234985498e0a3ab05fd1d5ce8d9e47786abc474381a5e0e99bd3"},"schema_version":"1.0","source":{"id":"cond-mat/0612430","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"cond-mat/0612430","created_at":"2026-05-18T01:39:38Z"},{"alias_kind":"arxiv_version","alias_value":"cond-mat/0612430v1","created_at":"2026-05-18T01:39:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.cond-mat/0612430","created_at":"2026-05-18T01:39:38Z"},{"alias_kind":"pith_short_12","alias_value":"AYRWQE5PQKWU","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"AYRWQE5PQKWUZJZ2","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"AYRWQE5P","created_at":"2026-05-18T12:25:53Z"}],"graph_snapshots":[{"event_id":"sha256:57b14abe9c62577b1be62f1d68aa467b01c806ddaae34df303e70944c01799ab","target":"graph","created_at":"2026-05-18T01:39:38Z","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":"We construct a Laplacian-level meta-generalized gradient approximation (meta-GGA) for the non-interacting (Kohn-Sham orbital) positive kinetic energy density $\\tau$ of an electronic ground state of density $n$. This meta-GGA is designed to recover the fourth-order gradient expansion $\\tau^{GE4}$ in the appropiate slowly-varying limit and the von Weizs\\\"{a}cker expression $\\tau^{W}=|\\nabla n|^2/(8n)$ in the rapidly-varying limit. It is constrained to satisfy the rigorous lower bound $\\tau^{W}(\\mathbf{r})\\leq\\tau(\\mathbf{r})$. Our meta-GGA is typically a strong improvement over the gradient expa","authors_text":"John P. Perdew, Lucian A. Constantin","cross_cats":[],"headline":"","license":"","primary_cat":"cond-mat.mtrl-sci","submitted_at":"2006-12-16T18:08:41Z","title":"Laplacian-level density functionals for the kinetic energy density and exchange-correlation energy"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cond-mat/0612430","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":"sha256:8110b5c84d2c5eb8be5a70d759c7548199a1743c2c9690c86713e8d7f927243a","target":"record","created_at":"2026-05-18T01:39:38Z","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":"3bfc4569fd9ebd7cd17dcac1883a8283494df17b92bc3ffb4020949330383caf","cross_cats_sorted":[],"license":"","primary_cat":"cond-mat.mtrl-sci","submitted_at":"2006-12-16T18:08:41Z","title_canon_sha256":"807b5532b64a234985498e0a3ab05fd1d5ce8d9e47786abc474381a5e0e99bd3"},"schema_version":"1.0","source":{"id":"cond-mat/0612430","kind":"arxiv","version":1}},"canonical_sha256":"06236813af82ad4ca73af2ab29edff26147a5f99c6dc89688c45737f2b343fce","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"06236813af82ad4ca73af2ab29edff26147a5f99c6dc89688c45737f2b343fce","first_computed_at":"2026-05-18T01:39:38.706114Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:39:38.706114Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0qm/4s9kqHcVJdAVtOskwYkrE/cIW6hVLuzvxHAT1+YHJ7xulpKr0uxLSsXpnERxFGTEMLsDV5/eKNeQC1+FDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:39:38.706852Z","signed_message":"canonical_sha256_bytes"},"source_id":"cond-mat/0612430","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8110b5c84d2c5eb8be5a70d759c7548199a1743c2c9690c86713e8d7f927243a","sha256:57b14abe9c62577b1be62f1d68aa467b01c806ddaae34df303e70944c01799ab"],"state_sha256":"a702783619239b8fc5456c2e18e8540c56d594876db4f07e25174115bc38a0ff"}