{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:MJANE67VWLO2E3DDDPMNTKD6XI","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":"d4b8b5bbf35455ac63df72d91e159b4bee1fd36c6a03c192095879889b793b03","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.mtrl-sci","submitted_at":"2015-02-23T22:30:38Z","title_canon_sha256":"895aef8eb9e5143ed54993e9414dadf852987266cda3b07c7888d57e366cdc65"},"schema_version":"1.0","source":{"id":"1502.06646","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1502.06646","created_at":"2026-05-18T01:35:11Z"},{"alias_kind":"arxiv_version","alias_value":"1502.06646v5","created_at":"2026-05-18T01:35:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.06646","created_at":"2026-05-18T01:35:11Z"},{"alias_kind":"pith_short_12","alias_value":"MJANE67VWLO2","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_16","alias_value":"MJANE67VWLO2E3DD","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_8","alias_value":"MJANE67V","created_at":"2026-05-18T12:29:32Z"}],"graph_snapshots":[{"event_id":"sha256:bdffa095cbdfe1bf0a7c6246232e35ca23b6fba4f08e067fda1de9e4c4a6407e","target":"graph","created_at":"2026-05-18T01:35:11Z","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":"The Quasi-harmonic (QH) approximation uses harmonic vibrational frequencies omega(H,Q,V), computed at volumes V near the volume where the Born-Oppenheimer (BO) energy is minimum. When this is used in the harmonic free energy, QH approximation gives a good zeroth order theory of thermal expansion, and first order theory of bulk modulus. Here, n-th order means smaller than the leading term by n powers of epsilon, where epsilon is the ratio hbar omega(Q)/E(el) or kT/E(el), and E(el) is an electronic energy scale, typically 2 to 10 eV. Experiment often shows evidence for next order corrections. Wh","authors_text":"Philip B. Allen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.mtrl-sci","submitted_at":"2015-02-23T22:30:38Z","title":"Anharmonic Phonon Quasiparticle Theory of Zero-point and Thermal Shifts in Insulators: Heat Capacity, Bulk Modulus, and Thermal Expansion"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.06646","kind":"arxiv","version":5},"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:ea2dcb8d7ce2c1d59fa5f9ec614330f0e220c2efd90ea00d4d1bc3716bbc5119","target":"record","created_at":"2026-05-18T01:35:11Z","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":"d4b8b5bbf35455ac63df72d91e159b4bee1fd36c6a03c192095879889b793b03","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.mtrl-sci","submitted_at":"2015-02-23T22:30:38Z","title_canon_sha256":"895aef8eb9e5143ed54993e9414dadf852987266cda3b07c7888d57e366cdc65"},"schema_version":"1.0","source":{"id":"1502.06646","kind":"arxiv","version":5}},"canonical_sha256":"6240d27bf5b2dda26c631bd8d9a87eba0973040444bf3c6d2b1773fa61f94aca","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6240d27bf5b2dda26c631bd8d9a87eba0973040444bf3c6d2b1773fa61f94aca","first_computed_at":"2026-05-18T01:35:11.137208Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:35:11.137208Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"q47VXSkrlL4sC8PEFVh27viYMX27AbnUDFqx+9BuqXFh8DrlQq6hKR/HT+F3lxP8fcurbEQLwqzQsajgEnLDBw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:35:11.138619Z","signed_message":"canonical_sha256_bytes"},"source_id":"1502.06646","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ea2dcb8d7ce2c1d59fa5f9ec614330f0e220c2efd90ea00d4d1bc3716bbc5119","sha256:bdffa095cbdfe1bf0a7c6246232e35ca23b6fba4f08e067fda1de9e4c4a6407e"],"state_sha256":"bf140922d2ec8b5536169d3f89ed777e946d90a4333106fe0715f4be75a0392c"}