{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:F6EAWVEEUIGPKX73NZLQCDBOMP","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":"29837a9fef3dc03000cd93c7111d23b984f443b44a8a62f40e8b22ff585724a5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.mtrl-sci","submitted_at":"2010-06-14T09:38:43Z","title_canon_sha256":"5986ec841a9fc7f20b9077c1da8ad52192ce5cda5c0dd0a97bdc0bb1d8975ef0"},"schema_version":"1.0","source":{"id":"1006.2649","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1006.2649","created_at":"2026-05-18T02:06:53Z"},{"alias_kind":"arxiv_version","alias_value":"1006.2649v1","created_at":"2026-05-18T02:06:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1006.2649","created_at":"2026-05-18T02:06:53Z"},{"alias_kind":"pith_short_12","alias_value":"F6EAWVEEUIGP","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_16","alias_value":"F6EAWVEEUIGPKX73","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_8","alias_value":"F6EAWVEE","created_at":"2026-05-18T12:26:06Z"}],"graph_snapshots":[{"event_id":"sha256:34d4b7d53592dbb7501d0e594fea726cafdcdc355137116bb7e08288727e10ee","target":"graph","created_at":"2026-05-18T02:06:53Z","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 present in detail the formulation of the ab initio theory we have developed for the calculation of the macroscopic second-order susceptibility $\\chi^{(2)}$. We find a general expression for $\\chi^{(2)}$ valid for any fields, containing the ab initio relation between the \\textit{microscopic} and \\textit{macroscopic} formulation of the second-order responses. We consider the long wavelength limit and we develop our theory in the Time-Dependent Density-Functional Theory framework. This allows us to include straightforwardly many-body effects such as crystal local-field and excitonic effects. W","authors_text":"Eleonora Luppi, Hannes H\\\"ubener, Val\\'erie V\\'eniard","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.mtrl-sci","submitted_at":"2010-06-14T09:38:43Z","title":"Ab Initio Second-Order Nonlinear Optics in Solids: Second-Harmonic Generation Spectroscopy from Time-Dependent Density-Functional Theory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1006.2649","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:fc08f8828d3724249ad363b3b70cf46ccd82e19a17436f5a04ed8167eafc97b8","target":"record","created_at":"2026-05-18T02:06:53Z","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":"29837a9fef3dc03000cd93c7111d23b984f443b44a8a62f40e8b22ff585724a5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.mtrl-sci","submitted_at":"2010-06-14T09:38:43Z","title_canon_sha256":"5986ec841a9fc7f20b9077c1da8ad52192ce5cda5c0dd0a97bdc0bb1d8975ef0"},"schema_version":"1.0","source":{"id":"1006.2649","kind":"arxiv","version":1}},"canonical_sha256":"2f880b5484a20cf55ffb6e57010c2e63f083b495eab5944b53498eec9d9c4fe8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2f880b5484a20cf55ffb6e57010c2e63f083b495eab5944b53498eec9d9c4fe8","first_computed_at":"2026-05-18T02:06:53.926758Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:06:53.926758Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"i9Fxk7nreh0U5PUG7IVY1IP9acCB69nnnNNMaHSW/qz6A0+CbbFZjzdUzMbWJ+jvJ1OR7AfD8hZNdpK7zHcSAg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:06:53.927632Z","signed_message":"canonical_sha256_bytes"},"source_id":"1006.2649","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fc08f8828d3724249ad363b3b70cf46ccd82e19a17436f5a04ed8167eafc97b8","sha256:34d4b7d53592dbb7501d0e594fea726cafdcdc355137116bb7e08288727e10ee"],"state_sha256":"e70f42bd386d032c5974a2ec7e1743ff80e8c2fb347f3b16baffff888155a44c"}