{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:MBAHHB3MSO266BW6IHKCS3KF2H","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":"92e8a831e77a8ab25d232b4312c03644b75bbc18b2933be2af5de50fda86fbd2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.mtrl-sci","submitted_at":"2014-12-10T22:33:26Z","title_canon_sha256":"f35c1fc125f1cfcccf1e13cd35774f8940b4b6dafe5a37dca587858caef16f80"},"schema_version":"1.0","source":{"id":"1412.4019","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.4019","created_at":"2026-05-18T02:31:28Z"},{"alias_kind":"arxiv_version","alias_value":"1412.4019v1","created_at":"2026-05-18T02:31:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.4019","created_at":"2026-05-18T02:31:28Z"},{"alias_kind":"pith_short_12","alias_value":"MBAHHB3MSO26","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_16","alias_value":"MBAHHB3MSO266BW6","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_8","alias_value":"MBAHHB3M","created_at":"2026-05-18T12:28:38Z"}],"graph_snapshots":[{"event_id":"sha256:5345be6e8817fc89d6c51d3ca0391be0726c3797eecb11365c905b692e77db76","target":"graph","created_at":"2026-05-18T02:31:28Z","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 refraction properties of phononic crystals are revealed by examining the anti-plane shear waves in doubly periodic elastic composites with unit cells containing rectangular and/or elliptical inclusions. The band-structure, group velocity, and energy-flux vector are calculated using a powerful variational method which accurately and efficiently yields all the field quantities over multiple frequency pass-bands. Equifrequency contours and energy-flux vectors are calculated as functions of the wave-vector. By superimposing the energy-flux vectors on equifrequency contours in the plane of the ","authors_text":"Sia Nemat-Nasser","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.mtrl-sci","submitted_at":"2014-12-10T22:33:26Z","title":"Refraction Characteristics of Phononic Crystals"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.4019","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:a2b44bf1727113a4a5c2efc4a06882830aabe6616697483c08c98353b7d745b1","target":"record","created_at":"2026-05-18T02:31:28Z","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":"92e8a831e77a8ab25d232b4312c03644b75bbc18b2933be2af5de50fda86fbd2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.mtrl-sci","submitted_at":"2014-12-10T22:33:26Z","title_canon_sha256":"f35c1fc125f1cfcccf1e13cd35774f8940b4b6dafe5a37dca587858caef16f80"},"schema_version":"1.0","source":{"id":"1412.4019","kind":"arxiv","version":1}},"canonical_sha256":"604073876c93b5ef06de41d4296d45d1d34509427383155831e325f96517c051","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"604073876c93b5ef06de41d4296d45d1d34509427383155831e325f96517c051","first_computed_at":"2026-05-18T02:31:28.090801Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:31:28.090801Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6drTpJGdPSTIZc/fIMBFQcIlCE3lkIEsssdQkOwoUU+tebojlGq1VDG+kCL+NFY5Xee8oQJ35b9OsEwXmQJXAg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:31:28.091274Z","signed_message":"canonical_sha256_bytes"},"source_id":"1412.4019","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a2b44bf1727113a4a5c2efc4a06882830aabe6616697483c08c98353b7d745b1","sha256:5345be6e8817fc89d6c51d3ca0391be0726c3797eecb11365c905b692e77db76"],"state_sha256":"fc827961581c0ae741570a6cb9ca15f617d3170a087fdb8b813d407acb23c1e4"}