{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:6UMV4KSNSUJSVEWBR3B4MTRZX4","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":"894d75ec40b5cb74ba3fb6d7947b6063b25ad9851acebab2f88ac017b34fbf67","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.optics","submitted_at":"2013-07-05T08:24:38Z","title_canon_sha256":"e72a0efac460f0b1e04af53492d011cddd1b41cf5115128432545918e384da1e"},"schema_version":"1.0","source":{"id":"1307.1544","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.1544","created_at":"2026-05-18T03:19:12Z"},{"alias_kind":"arxiv_version","alias_value":"1307.1544v1","created_at":"2026-05-18T03:19:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.1544","created_at":"2026-05-18T03:19:12Z"},{"alias_kind":"pith_short_12","alias_value":"6UMV4KSNSUJS","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_16","alias_value":"6UMV4KSNSUJSVEWB","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_8","alias_value":"6UMV4KSN","created_at":"2026-05-18T12:27:36Z"}],"graph_snapshots":[{"event_id":"sha256:e3dc54320a615ccca694a5ca68e43db1d2bb4dd1251e09f4b33f485e114f76c3","target":"graph","created_at":"2026-05-18T03:19:12Z","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":"This paper considers the refraction and diffraction of waves in three-dimensional crystals formed by anisotropically scattering centers. The partial wave expansion method is used to consider the effect of multiple rescattering of waves by centers composing a crystal. The expression for the refractive index of a crystal is derived. It is shown that instead of the diagonal elements of the scattering matrix $\\mathbf{T}$, appearing in the expression for the refractive index of a chaotic medium, the derived expression includes the diagonal elements of the reaction matrix $\\mathbf{K}$. This fact is ","authors_text":"E.A. Gurnevich, V.G. Baryshevsky","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.optics","submitted_at":"2013-07-05T08:24:38Z","title":"Multiple Scattering of Waves in 3D Crystals (Natural or Photonic) Formed by Anisotropically Scattering Centers"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.1544","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":"sha256:9df74295a15887df2651097c139a260c3a9203aeaa2b8b795eeeb29cb6490b3d","target":"record","created_at":"2026-05-18T03:19:12Z","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":"894d75ec40b5cb74ba3fb6d7947b6063b25ad9851acebab2f88ac017b34fbf67","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.optics","submitted_at":"2013-07-05T08:24:38Z","title_canon_sha256":"e72a0efac460f0b1e04af53492d011cddd1b41cf5115128432545918e384da1e"},"schema_version":"1.0","source":{"id":"1307.1544","kind":"arxiv","version":1}},"canonical_sha256":"f5195e2a4d95132a92c18ec3c64e39bf13d8ab0712f4b9bbe954dfcec1476baf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f5195e2a4d95132a92c18ec3c64e39bf13d8ab0712f4b9bbe954dfcec1476baf","first_computed_at":"2026-05-18T03:19:12.598795Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:19:12.598795Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"m8aXEAeIrrqFZl/1QTrfsRh5SHFyKU98EWDm5JhGgl9qZvESdX/1KutPOTtmbVbq+Su3zRqAEmcxM4MGWhv2DA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:19:12.599177Z","signed_message":"canonical_sha256_bytes"},"source_id":"1307.1544","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9df74295a15887df2651097c139a260c3a9203aeaa2b8b795eeeb29cb6490b3d","sha256:e3dc54320a615ccca694a5ca68e43db1d2bb4dd1251e09f4b33f485e114f76c3"],"state_sha256":"07121182d2abbdd614ade0db978b37edd7eda7e466f6acc787ac80f5b8d17d45"}