{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2002:VZ4T7RL6F52TP7XO5CHOZXFZHM","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":"bcaec005e8111a4247f8ebbad5f107552486864a9d265319f05e243c5afbecf3","cross_cats_sorted":[],"license":"","primary_cat":"physics.class-ph","submitted_at":"2002-01-16T15:04:00Z","title_canon_sha256":"d0692980b674e4292c7b1cc8030237df1a79a0b4b1a6838d976c5228278cf3af"},"schema_version":"1.0","source":{"id":"physics/0201035","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"physics/0201035","created_at":"2026-05-18T04:40:46Z"},{"alias_kind":"arxiv_version","alias_value":"physics/0201035v1","created_at":"2026-05-18T04:40:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.physics/0201035","created_at":"2026-05-18T04:40:46Z"},{"alias_kind":"pith_short_12","alias_value":"VZ4T7RL6F52T","created_at":"2026-05-18T12:25:51Z"},{"alias_kind":"pith_short_16","alias_value":"VZ4T7RL6F52TP7XO","created_at":"2026-05-18T12:25:51Z"},{"alias_kind":"pith_short_8","alias_value":"VZ4T7RL6","created_at":"2026-05-18T12:25:51Z"}],"graph_snapshots":[{"event_id":"sha256:7850da83fa9bd63459ccaa56c5ab52857555f900c7336a3fde7496427be0353e","target":"graph","created_at":"2026-05-18T04:40:46Z","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":"Homogenization theory is used to calculate the macroscopic dielectric constant from the quantum microscopic dielectric function in a periodic medium. The method can be used to calculate any macroscopic constitutive relation, but it is illustrated here for the case of electrodynamics of matter. The so-called cell problem of homogenization theory is solved and an explicit expression is given for the macroscopic dielectric constant in a form akin to the Clausius-Mossotti or Lorentz-Lorenz relation. The validity of this expression is checked by showing that the macroscopic dielectric constant is c","authors_text":"Christian Brouder, Stephanie Rossano","cross_cats":[],"headline":"","license":"","primary_cat":"physics.class-ph","submitted_at":"2002-01-16T15:04:00Z","title":"Microscopic Calculation of the Constitutive Relations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"physics/0201035","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":"sha256:7a9a56e339a7c800d03e737159f271f090adaebf7de22769b37a64090ffdc328","target":"record","created_at":"2026-05-18T04:40:46Z","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":"bcaec005e8111a4247f8ebbad5f107552486864a9d265319f05e243c5afbecf3","cross_cats_sorted":[],"license":"","primary_cat":"physics.class-ph","submitted_at":"2002-01-16T15:04:00Z","title_canon_sha256":"d0692980b674e4292c7b1cc8030237df1a79a0b4b1a6838d976c5228278cf3af"},"schema_version":"1.0","source":{"id":"physics/0201035","kind":"arxiv","version":1}},"canonical_sha256":"ae793fc57e2f7537feeee88eecdcb93b13ad3aebb88f1b89a8433d70f6537f5b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ae793fc57e2f7537feeee88eecdcb93b13ad3aebb88f1b89a8433d70f6537f5b","first_computed_at":"2026-05-18T04:40:46.616898Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:40:46.616898Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"IC5A/BdjE0rKlp+bhOMtkyZHd2WFgu2qG1FvknrucWiB7YZGw/5hdMSlR14yUoeNBrMVrXvXQp2BRjsHhj4nBw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:40:46.617353Z","signed_message":"canonical_sha256_bytes"},"source_id":"physics/0201035","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7a9a56e339a7c800d03e737159f271f090adaebf7de22769b37a64090ffdc328","sha256:7850da83fa9bd63459ccaa56c5ab52857555f900c7336a3fde7496427be0353e"],"state_sha256":"3af381632c023ad32077389161333b360d81c4c7c1c1d75ec30797430aeba92c"}