{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:DIIXFJYNLMULJ6ZELU4DOOJFRJ","short_pith_number":"pith:DIIXFJYN","canonical_record":{"source":{"id":"1908.04764","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-08-05T14:26:12Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"59e3441ecb228ed9e6c3a8eb6d6b6f14576b9acca1da0dd475cd5369be0ead7d","abstract_canon_sha256":"97a2f61f7f510503114cabe2b5d7310459d70a4817ab40537c70660d0f49c272"},"schema_version":"1.0"},"canonical_sha256":"1a1172a70d5b28b4fb245d383739258a68aac1117d90ae02e36f30b3dd5a26a0","source":{"kind":"arxiv","id":"1908.04764","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.04764","created_at":"2026-07-05T02:14:40Z"},{"alias_kind":"arxiv_version","alias_value":"1908.04764v2","created_at":"2026-07-05T02:14:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.04764","created_at":"2026-07-05T02:14:40Z"},{"alias_kind":"pith_short_12","alias_value":"DIIXFJYNLMUL","created_at":"2026-07-05T02:14:40Z"},{"alias_kind":"pith_short_16","alias_value":"DIIXFJYNLMULJ6ZE","created_at":"2026-07-05T02:14:40Z"},{"alias_kind":"pith_short_8","alias_value":"DIIXFJYN","created_at":"2026-07-05T02:14:40Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:DIIXFJYNLMULJ6ZELU4DOOJFRJ","target":"record","payload":{"canonical_record":{"source":{"id":"1908.04764","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-08-05T14:26:12Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"59e3441ecb228ed9e6c3a8eb6d6b6f14576b9acca1da0dd475cd5369be0ead7d","abstract_canon_sha256":"97a2f61f7f510503114cabe2b5d7310459d70a4817ab40537c70660d0f49c272"},"schema_version":"1.0"},"canonical_sha256":"1a1172a70d5b28b4fb245d383739258a68aac1117d90ae02e36f30b3dd5a26a0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T02:14:40.258178Z","signature_b64":"p3K3z2gW9vQJBy74+WJcZTV3BYymc/rSMHpQUaAOJvggQcr19s//oczUixSZvRf3wJpn05gE2bhvzOIKoDFjBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1a1172a70d5b28b4fb245d383739258a68aac1117d90ae02e36f30b3dd5a26a0","last_reissued_at":"2026-07-05T02:14:40.257651Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T02:14:40.257651Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1908.04764","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T02:14:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YDjN96sqJ414Yur2iAYPFaUq2nbTfYcUjJyLTspuzTH3TdG3NiaXNd+arEL+Hc4Q83q4B9BvTlhYkQY8jzOrBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T14:22:28.112779Z"},"content_sha256":"51f3116c3114de4ff974c341e1bbc2d15594e4a8c9867f659828959b0d71cac0","schema_version":"1.0","event_id":"sha256:51f3116c3114de4ff974c341e1bbc2d15594e4a8c9867f659828959b0d71cac0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:DIIXFJYNLMULJ6ZELU4DOOJFRJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Sommerfeld--type integrals for discrete diffraction problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"A. I. Korolkov, A. V. Shanin","submitted_at":"2019-08-05T14:26:12Z","abstract_excerpt":"Three problems for a discrete analogue of the Helmholtz equation are studied analytically using the plane wave decomposition and the Sommerfeld integral approach. They are: 1) the problem with a point source on an entire plane; 2) the problem of diffraction by a Dirichlet half-line; 3) the problem of diffraction by a Dirichlet right angle. It is shown that total field can be represented as an integral of an algebraic function over a contour drawn on some manifold. The latter is a torus. As the result, the explicit solutions are obtained in terms of recursive relations (for the Green's function"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.04764","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1908.04764/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T02:14:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"L88U1U+6E0GJNWCcRn5X9UFsFcGBo0XLC9qlBO1rImoIzgultWALqWKS+7pEOcV80CzJ/nyTZiVZ0Ey/GsBQDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T14:22:28.113667Z"},"content_sha256":"e151a039c9c7d817863602e871c3257a49dc82abab1691d82c8fecbcb7083a1a","schema_version":"1.0","event_id":"sha256:e151a039c9c7d817863602e871c3257a49dc82abab1691d82c8fecbcb7083a1a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DIIXFJYNLMULJ6ZELU4DOOJFRJ/bundle.json","state_url":"https://pith.science/pith/DIIXFJYNLMULJ6ZELU4DOOJFRJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DIIXFJYNLMULJ6ZELU4DOOJFRJ/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":"2026-08-16T14:22:28Z","links":{"resolver":"https://pith.science/pith/DIIXFJYNLMULJ6ZELU4DOOJFRJ","bundle":"https://pith.science/pith/DIIXFJYNLMULJ6ZELU4DOOJFRJ/bundle.json","state":"https://pith.science/pith/DIIXFJYNLMULJ6ZELU4DOOJFRJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DIIXFJYNLMULJ6ZELU4DOOJFRJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:DIIXFJYNLMULJ6ZELU4DOOJFRJ","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":"97a2f61f7f510503114cabe2b5d7310459d70a4817ab40537c70660d0f49c272","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-08-05T14:26:12Z","title_canon_sha256":"59e3441ecb228ed9e6c3a8eb6d6b6f14576b9acca1da0dd475cd5369be0ead7d"},"schema_version":"1.0","source":{"id":"1908.04764","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.04764","created_at":"2026-07-05T02:14:40Z"},{"alias_kind":"arxiv_version","alias_value":"1908.04764v2","created_at":"2026-07-05T02:14:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.04764","created_at":"2026-07-05T02:14:40Z"},{"alias_kind":"pith_short_12","alias_value":"DIIXFJYNLMUL","created_at":"2026-07-05T02:14:40Z"},{"alias_kind":"pith_short_16","alias_value":"DIIXFJYNLMULJ6ZE","created_at":"2026-07-05T02:14:40Z"},{"alias_kind":"pith_short_8","alias_value":"DIIXFJYN","created_at":"2026-07-05T02:14:40Z"}],"graph_snapshots":[{"event_id":"sha256:e151a039c9c7d817863602e871c3257a49dc82abab1691d82c8fecbcb7083a1a","target":"graph","created_at":"2026-07-05T02:14:40Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1908.04764/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Three problems for a discrete analogue of the Helmholtz equation are studied analytically using the plane wave decomposition and the Sommerfeld integral approach. They are: 1) the problem with a point source on an entire plane; 2) the problem of diffraction by a Dirichlet half-line; 3) the problem of diffraction by a Dirichlet right angle. It is shown that total field can be represented as an integral of an algebraic function over a contour drawn on some manifold. The latter is a torus. As the result, the explicit solutions are obtained in terms of recursive relations (for the Green's function","authors_text":"A. I. Korolkov, A. V. Shanin","cross_cats":["cs.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-08-05T14:26:12Z","title":"Sommerfeld--type integrals for discrete diffraction problems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.04764","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":"sha256:51f3116c3114de4ff974c341e1bbc2d15594e4a8c9867f659828959b0d71cac0","target":"record","created_at":"2026-07-05T02:14:40Z","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":"97a2f61f7f510503114cabe2b5d7310459d70a4817ab40537c70660d0f49c272","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-08-05T14:26:12Z","title_canon_sha256":"59e3441ecb228ed9e6c3a8eb6d6b6f14576b9acca1da0dd475cd5369be0ead7d"},"schema_version":"1.0","source":{"id":"1908.04764","kind":"arxiv","version":2}},"canonical_sha256":"1a1172a70d5b28b4fb245d383739258a68aac1117d90ae02e36f30b3dd5a26a0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1a1172a70d5b28b4fb245d383739258a68aac1117d90ae02e36f30b3dd5a26a0","first_computed_at":"2026-07-05T02:14:40.257651Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:14:40.257651Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"p3K3z2gW9vQJBy74+WJcZTV3BYymc/rSMHpQUaAOJvggQcr19s//oczUixSZvRf3wJpn05gE2bhvzOIKoDFjBQ==","signature_status":"signed_v1","signed_at":"2026-07-05T02:14:40.258178Z","signed_message":"canonical_sha256_bytes"},"source_id":"1908.04764","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:51f3116c3114de4ff974c341e1bbc2d15594e4a8c9867f659828959b0d71cac0","sha256:e151a039c9c7d817863602e871c3257a49dc82abab1691d82c8fecbcb7083a1a"],"state_sha256":"f6bfcb4e07ee82576cfe6665f2bbf614eb9491fc8a8f336e3c95cbeada718ecd"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GqmaWhdkB6VxOsiqn2nTxr6frIbzrYCFJf/qrbhBiPhZSKk4XoMVt+ijcbJvUCEgObBi9TlgyJSuGuPIk0hGDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-16T14:22:28.119097Z","bundle_sha256":"29383fd659922218b892a098ecfa57569b904d0e3573ab58adea9afe6ed918ab"}}