{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:YS47VG242XNEOL5W6IQDAJS2KD","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":"df423677ea455304410e17e94aa25afe92beed4a7cacc0431436836e5b633be4","cross_cats_sorted":["cond-mat.mtrl-sci"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.class-ph","submitted_at":"2009-08-06T18:06:13Z","title_canon_sha256":"a100cf875a4e3ce37430e657bb619a395104e67216ad926cfeb584cfd24f14aa"},"schema_version":"1.0","source":{"id":"0908.0922","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0908.0922","created_at":"2026-05-18T03:31:42Z"},{"alias_kind":"arxiv_version","alias_value":"0908.0922v1","created_at":"2026-05-18T03:31:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0908.0922","created_at":"2026-05-18T03:31:42Z"},{"alias_kind":"pith_short_12","alias_value":"YS47VG242XNE","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_16","alias_value":"YS47VG242XNEOL5W","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_8","alias_value":"YS47VG24","created_at":"2026-05-18T12:26:02Z"}],"graph_snapshots":[{"event_id":"sha256:3c84e19436c84e434973e14255bb549d903cf063ee17a922aace7ab0a3ad3a2a","target":"graph","created_at":"2026-05-18T03:31:42Z","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 electromagnetic wave propagation in an anisotropic dielectric media with two generic matrices $\\epsilon^{ij}$ and $\\mu^{ij}$ of permittivity and permeability is studied. These matrices are not required to be symmetric, positive definite, and even invertible. In the framework of a metric-free electrodynamics approach, compact tensorial dispersion relation is derived. The resulted formula are useful for a theoretical study of electromagnetic wave propagation in a classical media and in a modern type of media with a generic linear constitutive relation including metamaterials.","authors_text":"Yakov Itin","cross_cats":["cond-mat.mtrl-sci"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.class-ph","submitted_at":"2009-08-06T18:06:13Z","title":"Dispersion relation for anisotropic media"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0908.0922","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":"sha256:06bada09bd879afb1bec98cc8714503735eaa3af75bf9f1c484de51d1914499f","target":"record","created_at":"2026-05-18T03:31:42Z","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":"df423677ea455304410e17e94aa25afe92beed4a7cacc0431436836e5b633be4","cross_cats_sorted":["cond-mat.mtrl-sci"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.class-ph","submitted_at":"2009-08-06T18:06:13Z","title_canon_sha256":"a100cf875a4e3ce37430e657bb619a395104e67216ad926cfeb584cfd24f14aa"},"schema_version":"1.0","source":{"id":"0908.0922","kind":"arxiv","version":1}},"canonical_sha256":"c4b9fa9b5cd5da472fb6f22030265a50fb9e77705e375b6ec1c2e94e43cd6ae6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c4b9fa9b5cd5da472fb6f22030265a50fb9e77705e375b6ec1c2e94e43cd6ae6","first_computed_at":"2026-05-18T03:31:42.012266Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:31:42.012266Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DqPGKDW3bmbpJhfdQBkqhZwkb3+Nmtx9Aa6iEHgeU9TttxfSeBpvQKJsYCwvubgmZfR+cGMytuYgAtyzMOs8CA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:31:42.012777Z","signed_message":"canonical_sha256_bytes"},"source_id":"0908.0922","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:06bada09bd879afb1bec98cc8714503735eaa3af75bf9f1c484de51d1914499f","sha256:3c84e19436c84e434973e14255bb549d903cf063ee17a922aace7ab0a3ad3a2a"],"state_sha256":"a4ba954abee22b48dadb2d9947d96a6ccb38db7a009b5a06e20f553f31136052"}