{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:Z3W3FVEBPLXW7FU6F7EWDT7S72","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":"507ddc5f0274a1788418293b1ed0f20d9e4c77e9fa3ec0b09ed9cde16245ce04","cross_cats_sorted":["physics.chem-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.mtrl-sci","submitted_at":"2013-01-17T10:43:31Z","title_canon_sha256":"4491bf393d884694cbed42aacf2828f2c85560e86ad59a84eca4b842af6f789b"},"schema_version":"1.0","source":{"id":"1301.4040","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.4040","created_at":"2026-05-18T03:35:01Z"},{"alias_kind":"arxiv_version","alias_value":"1301.4040v1","created_at":"2026-05-18T03:35:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.4040","created_at":"2026-05-18T03:35:01Z"},{"alias_kind":"pith_short_12","alias_value":"Z3W3FVEBPLXW","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_16","alias_value":"Z3W3FVEBPLXW7FU6","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_8","alias_value":"Z3W3FVEB","created_at":"2026-05-18T12:28:09Z"}],"graph_snapshots":[{"event_id":"sha256:97ad3febea5c31f817b5690b33fa06d2576bc9b36341c59e7286771d4019baf7","target":"graph","created_at":"2026-05-18T03:35:01Z","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 discuss a $\\beta$-dependent family of electronic density scalings of the form $n_\\lambda(\\R)=\\lambda^{3\\beta+1}\\; n(\\lambda^\\beta \\R)$ in the context of density functional theory. In particular, we consider the following special cases: the Thomas-Fermi scaling ($\\beta=1/3$ and $\\lambda \\gg 1$), which is crucial for the semiclassical theory of neutral atoms; the uniform-electron-gas scaling ($\\beta=-1/3$ and $\\lambda\\gg 1$), that is important in the semiclassical theory of metallic clusters; the homogeneous density scaling ($\\beta=0$) which can be related to the self-interaction problem in d","authors_text":"Eduardo Fabiano, Lucian A. Constantin","cross_cats":["physics.chem-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.mtrl-sci","submitted_at":"2013-01-17T10:43:31Z","title":"Relevance of coordinate and particle-number scaling in density functional theory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.4040","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":"sha256:5fd37114368a5948704af6f542a06eb8ebf180dcd79f2dbb5af66e7421626e84","target":"record","created_at":"2026-05-18T03:35:01Z","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":"507ddc5f0274a1788418293b1ed0f20d9e4c77e9fa3ec0b09ed9cde16245ce04","cross_cats_sorted":["physics.chem-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.mtrl-sci","submitted_at":"2013-01-17T10:43:31Z","title_canon_sha256":"4491bf393d884694cbed42aacf2828f2c85560e86ad59a84eca4b842af6f789b"},"schema_version":"1.0","source":{"id":"1301.4040","kind":"arxiv","version":1}},"canonical_sha256":"ceedb2d4817aef6f969e2fc961cff2fe9794fa1553ddc94d891f67b279924a00","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ceedb2d4817aef6f969e2fc961cff2fe9794fa1553ddc94d891f67b279924a00","first_computed_at":"2026-05-18T03:35:01.517161Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:35:01.517161Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DgYTkKI5Bj5Ik5gDp46qc/5zmrnkYo6D0c1curxkVWz+e8aEWoRAuCsMmplV6HZoz/IoEk7I24mGeT3Wq2I+Cg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:35:01.517907Z","signed_message":"canonical_sha256_bytes"},"source_id":"1301.4040","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5fd37114368a5948704af6f542a06eb8ebf180dcd79f2dbb5af66e7421626e84","sha256:97ad3febea5c31f817b5690b33fa06d2576bc9b36341c59e7286771d4019baf7"],"state_sha256":"3ca9846b69d03018bd4cfac1603c521a7f2e702d118e449ea2dd354c5e83cd69"}