{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:QYZ2VV36TZBFZFSQ7M2UINM3SD","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":"927eb232928d81b82dab20c2d96cf92f3e3f1b13cbbe290ecfeb96ba29dab3ac","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-09-02T13:15:54Z","title_canon_sha256":"d886e9d45c9ccfe233b14462c52a5e4fd6a1b0f2cfc621a0ac9c310f49fbcb29"},"schema_version":"1.0","source":{"id":"1509.00683","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.00683","created_at":"2026-05-18T00:53:12Z"},{"alias_kind":"arxiv_version","alias_value":"1509.00683v2","created_at":"2026-05-18T00:53:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.00683","created_at":"2026-05-18T00:53:12Z"},{"alias_kind":"pith_short_12","alias_value":"QYZ2VV36TZBF","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_16","alias_value":"QYZ2VV36TZBFZFSQ","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_8","alias_value":"QYZ2VV36","created_at":"2026-05-18T12:29:39Z"}],"graph_snapshots":[{"event_id":"sha256:9153b06f93fd56f8248f8575d41768827cd7c31ac6a1039136a7000f1efccfed","target":"graph","created_at":"2026-05-18T00:53:12Z","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":"We analyze the propagation of waves in unbounded photonic crystals, the waves are described by a Helmholtz equation with $x$-dependent coefficients. The scattering problem must be completed with a radiation condition at infinity, which was not available for $x$-dependent coefficients. We develop an outgoing wave condition with the help of a Bloch wave expansion. Our radiation condition admits a (weak) uniqueness result, formulated in terms of the Bloch measure of solutions. We use the new radiation condition to analyze the transmission problem where, at fixed frequency, a wave hits the interfa","authors_text":"Agnes Lamacz, Ben Schweizer","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-09-02T13:15:54Z","title":"Outgoing wave conditions in photonic crystals and transmission properties at interfaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.00683","kind":"arxiv","version":2},"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":"sha256:83adba96422bd19194ff6d7ebc24de1c807e378736491c761c729dd22ec968bc","target":"record","created_at":"2026-05-18T00:53:12Z","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":"927eb232928d81b82dab20c2d96cf92f3e3f1b13cbbe290ecfeb96ba29dab3ac","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-09-02T13:15:54Z","title_canon_sha256":"d886e9d45c9ccfe233b14462c52a5e4fd6a1b0f2cfc621a0ac9c310f49fbcb29"},"schema_version":"1.0","source":{"id":"1509.00683","kind":"arxiv","version":2}},"canonical_sha256":"8633aad77e9e425c9650fb3544359b90e1b4194e5ef6ffcdf509cb99457393b8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8633aad77e9e425c9650fb3544359b90e1b4194e5ef6ffcdf509cb99457393b8","first_computed_at":"2026-05-18T00:53:12.563958Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:53:12.563958Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QI8bnOkpaUWexCm25qxwc8ZhQjaexUIaGELnOV3ifLidktD/xrzHN714dj7vaJ33DnmP5INlaQXtGYA1+T3wDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:53:12.564489Z","signed_message":"canonical_sha256_bytes"},"source_id":"1509.00683","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:83adba96422bd19194ff6d7ebc24de1c807e378736491c761c729dd22ec968bc","sha256:9153b06f93fd56f8248f8575d41768827cd7c31ac6a1039136a7000f1efccfed"],"state_sha256":"a1eaa70e3b4e2fceaf3abcb01a6c86003d77f9658548806ae904ec41f54aa6b3"}