{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:T2ULSWV3ZSZCX3BXEXK7X3CMTE","short_pith_number":"pith:T2ULSWV3","canonical_record":{"source":{"id":"1704.01017","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-04-04T13:53:16Z","cross_cats_sorted":["math.NA"],"title_canon_sha256":"b145181243bdd1a580c5a9e7641fd5647200497f43fc3e89ab2dd7e5741ab949","abstract_canon_sha256":"378cbac4f2fa8136da540fb4752bf8289fd337651d4ef9e2a7a08687aded6388"},"schema_version":"1.0"},"canonical_sha256":"9ea8b95abbccb22bec3725d5fbec4c9920b16288ebbe036e5a518065a70e6272","source":{"kind":"arxiv","id":"1704.01017","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1704.01017","created_at":"2026-05-18T00:24:17Z"},{"alias_kind":"arxiv_version","alias_value":"1704.01017v1","created_at":"2026-05-18T00:24:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.01017","created_at":"2026-05-18T00:24:17Z"},{"alias_kind":"pith_short_12","alias_value":"T2ULSWV3ZSZC","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_16","alias_value":"T2ULSWV3ZSZCX3BX","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_8","alias_value":"T2ULSWV3","created_at":"2026-05-18T12:31:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:T2ULSWV3ZSZCX3BXEXK7X3CMTE","target":"record","payload":{"canonical_record":{"source":{"id":"1704.01017","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-04-04T13:53:16Z","cross_cats_sorted":["math.NA"],"title_canon_sha256":"b145181243bdd1a580c5a9e7641fd5647200497f43fc3e89ab2dd7e5741ab949","abstract_canon_sha256":"378cbac4f2fa8136da540fb4752bf8289fd337651d4ef9e2a7a08687aded6388"},"schema_version":"1.0"},"canonical_sha256":"9ea8b95abbccb22bec3725d5fbec4c9920b16288ebbe036e5a518065a70e6272","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:24:17.758396Z","signature_b64":"H8DMdl096XUhRL9Knzpsgv2NpfiuDEX4JgVNajdqNunQpzl+35UFeiOpdseHn3lKaPLwxo4VW0H3aHGhN0vEAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9ea8b95abbccb22bec3725d5fbec4c9920b16288ebbe036e5a518065a70e6272","last_reissued_at":"2026-05-18T00:24:17.757856Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:24:17.757856Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1704.01017","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:24:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"G+DSz084/rmEZFquNV3ZF1BSdvtvfS1zSVQHBe2WsmJeBvvMRe2H+6Mv8vOTS6FfAIc2DhLop084nQd9uzBaCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T22:31:09.392539Z"},"content_sha256":"b4187bdb074eb37d5e7d99c4903ae9866c79143f5b7723cedac5e8302831d5e6","schema_version":"1.0","event_id":"sha256:b4187bdb074eb37d5e7d99c4903ae9866c79143f5b7723cedac5e8302831d5e6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:T2ULSWV3ZSZCX3BXEXK7X3CMTE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Three-dimensional quasi-periodic shifted Green function throughout the spectrum--including Wood anomalies","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NA"],"primary_cat":"math.AP","authors_text":"Catalin Turc, Oscar P. Bruno, Stephanos Venakides, Stephen P. Shipman","submitted_at":"2017-04-04T13:53:16Z","abstract_excerpt":"This work presents an efficient method for evaluation of wave scattering by doubly periodic diffraction gratings at or near \"Wood anomaly frequencies\". At these frequencies, one or more grazing Rayleigh waves exist, and the lattice sum for the quasi-periodic Green function ceases to exist. We present a modification of this sum by adding two types of terms to it. The first type adds linear combinations of \"shifted\" Green functions, ensuring that the spatial singularities introduced by these terms are located below the grating and therefore outside of the physical domain. With suitable coefficie"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.01017","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:24:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"97K9ydly/2h5TRO6K2h4o4vLC7VHhulh2q8GLEZ0SNeBX5UTGqRMNtty0yEJ0+8QmWoKg4QYFakyV09kWZA8CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T22:31:09.393364Z"},"content_sha256":"67715a5c7991b5012e009a37a0640077f1088488650221d48bf716d57387ac13","schema_version":"1.0","event_id":"sha256:67715a5c7991b5012e009a37a0640077f1088488650221d48bf716d57387ac13"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/T2ULSWV3ZSZCX3BXEXK7X3CMTE/bundle.json","state_url":"https://pith.science/pith/T2ULSWV3ZSZCX3BXEXK7X3CMTE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/T2ULSWV3ZSZCX3BXEXK7X3CMTE/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-10T22:31:09Z","links":{"resolver":"https://pith.science/pith/T2ULSWV3ZSZCX3BXEXK7X3CMTE","bundle":"https://pith.science/pith/T2ULSWV3ZSZCX3BXEXK7X3CMTE/bundle.json","state":"https://pith.science/pith/T2ULSWV3ZSZCX3BXEXK7X3CMTE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/T2ULSWV3ZSZCX3BXEXK7X3CMTE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:T2ULSWV3ZSZCX3BXEXK7X3CMTE","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":"378cbac4f2fa8136da540fb4752bf8289fd337651d4ef9e2a7a08687aded6388","cross_cats_sorted":["math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-04-04T13:53:16Z","title_canon_sha256":"b145181243bdd1a580c5a9e7641fd5647200497f43fc3e89ab2dd7e5741ab949"},"schema_version":"1.0","source":{"id":"1704.01017","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1704.01017","created_at":"2026-05-18T00:24:17Z"},{"alias_kind":"arxiv_version","alias_value":"1704.01017v1","created_at":"2026-05-18T00:24:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.01017","created_at":"2026-05-18T00:24:17Z"},{"alias_kind":"pith_short_12","alias_value":"T2ULSWV3ZSZC","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_16","alias_value":"T2ULSWV3ZSZCX3BX","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_8","alias_value":"T2ULSWV3","created_at":"2026-05-18T12:31:43Z"}],"graph_snapshots":[{"event_id":"sha256:67715a5c7991b5012e009a37a0640077f1088488650221d48bf716d57387ac13","target":"graph","created_at":"2026-05-18T00:24:17Z","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 work presents an efficient method for evaluation of wave scattering by doubly periodic diffraction gratings at or near \"Wood anomaly frequencies\". At these frequencies, one or more grazing Rayleigh waves exist, and the lattice sum for the quasi-periodic Green function ceases to exist. We present a modification of this sum by adding two types of terms to it. The first type adds linear combinations of \"shifted\" Green functions, ensuring that the spatial singularities introduced by these terms are located below the grating and therefore outside of the physical domain. With suitable coefficie","authors_text":"Catalin Turc, Oscar P. Bruno, Stephanos Venakides, Stephen P. Shipman","cross_cats":["math.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-04-04T13:53:16Z","title":"Three-dimensional quasi-periodic shifted Green function throughout the spectrum--including Wood anomalies"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.01017","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:b4187bdb074eb37d5e7d99c4903ae9866c79143f5b7723cedac5e8302831d5e6","target":"record","created_at":"2026-05-18T00:24:17Z","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":"378cbac4f2fa8136da540fb4752bf8289fd337651d4ef9e2a7a08687aded6388","cross_cats_sorted":["math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-04-04T13:53:16Z","title_canon_sha256":"b145181243bdd1a580c5a9e7641fd5647200497f43fc3e89ab2dd7e5741ab949"},"schema_version":"1.0","source":{"id":"1704.01017","kind":"arxiv","version":1}},"canonical_sha256":"9ea8b95abbccb22bec3725d5fbec4c9920b16288ebbe036e5a518065a70e6272","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9ea8b95abbccb22bec3725d5fbec4c9920b16288ebbe036e5a518065a70e6272","first_computed_at":"2026-05-18T00:24:17.757856Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:24:17.757856Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"H8DMdl096XUhRL9Knzpsgv2NpfiuDEX4JgVNajdqNunQpzl+35UFeiOpdseHn3lKaPLwxo4VW0H3aHGhN0vEAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:24:17.758396Z","signed_message":"canonical_sha256_bytes"},"source_id":"1704.01017","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b4187bdb074eb37d5e7d99c4903ae9866c79143f5b7723cedac5e8302831d5e6","sha256:67715a5c7991b5012e009a37a0640077f1088488650221d48bf716d57387ac13"],"state_sha256":"e620d0be83cd03d2f76b7254a48fc73dacf3135162bc8666646d73572fe362fd"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ne10sPU2b5P5SMvYzyAtfWLdCplSpgJht6sYks7giYldOPPm+sf5oPKfLvtSqvr0ahcLO8N1A/rL9Ta3tQ15DQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T22:31:09.397799Z","bundle_sha256":"a83cf07a2a3891d3db75220eb573feb73d790cc4b5ed81f61cd924f23f515606"}}