{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:3CSB2C7Z2S42ZTZVMBMZ5L724Y","short_pith_number":"pith:3CSB2C7Z","canonical_record":{"source":{"id":"1302.0161","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-02-01T12:28:57Z","cross_cats_sorted":["math.NA"],"title_canon_sha256":"66509a7e8a5ace06f1322c59f1e5aaae1c4b700ff6e6b9358da85886afb6256c","abstract_canon_sha256":"35f5a9c08af96992fc69ed48f5a7750f26cc5f412e52528c84c409af276ca596"},"schema_version":"1.0"},"canonical_sha256":"d8a41d0bf9d4b9accf3560599eaffae61213dc18f6b619cee16b6becbc4dcb52","source":{"kind":"arxiv","id":"1302.0161","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.0161","created_at":"2026-05-18T03:34:47Z"},{"alias_kind":"arxiv_version","alias_value":"1302.0161v1","created_at":"2026-05-18T03:34:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.0161","created_at":"2026-05-18T03:34:47Z"},{"alias_kind":"pith_short_12","alias_value":"3CSB2C7Z2S42","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_16","alias_value":"3CSB2C7Z2S42ZTZV","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_8","alias_value":"3CSB2C7Z","created_at":"2026-05-18T12:27:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:3CSB2C7Z2S42ZTZVMBMZ5L724Y","target":"record","payload":{"canonical_record":{"source":{"id":"1302.0161","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-02-01T12:28:57Z","cross_cats_sorted":["math.NA"],"title_canon_sha256":"66509a7e8a5ace06f1322c59f1e5aaae1c4b700ff6e6b9358da85886afb6256c","abstract_canon_sha256":"35f5a9c08af96992fc69ed48f5a7750f26cc5f412e52528c84c409af276ca596"},"schema_version":"1.0"},"canonical_sha256":"d8a41d0bf9d4b9accf3560599eaffae61213dc18f6b619cee16b6becbc4dcb52","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:34:47.187927Z","signature_b64":"flLI5lBJdUZRFLj3e4WSgIaxUDmCZjDvYm1y2XzjF17aqh8lsIZBy55BdS/EPzAf6YiUZvSMDhSyFQbOiGjUAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d8a41d0bf9d4b9accf3560599eaffae61213dc18f6b619cee16b6becbc4dcb52","last_reissued_at":"2026-05-18T03:34:47.187106Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:34:47.187106Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1302.0161","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":"2026-05-18T03:34:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LNN8e8dxFtsjyN6FiXAaHr4pCSL+ISUiNNcje81LRVkVz9Y2/ASh/P2m+l9dowjuxZG7DlDtGBFkeCcpBm/GBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T19:55:12.624279Z"},"content_sha256":"50a3e2197fac87b6f803fc8f293044dfd0477ed8219f261ce12081f2ea9d1adc","schema_version":"1.0","event_id":"sha256:50a3e2197fac87b6f803fc8f293044dfd0477ed8219f261ce12081f2ea9d1adc"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:3CSB2C7Z2S42ZTZVMBMZ5L724Y","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A novel integral equation for scattering by locally rough surfaces and application to the inverse problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NA"],"primary_cat":"math.AP","authors_text":"Bo Zhang, Haiwen Zhang","submitted_at":"2013-02-01T12:28:57Z","abstract_excerpt":"This paper is concerned with the direct and inverse acoustic or electromagnetic scattering problems by a locally perturbed, perfectly reflecting, infinite plane (which is called a locally rough surface in this paper). We propose a novel integral equation formulation for the direct scattering problem which is defined on a bounded curve (consisting of a bounded part of the infinite plane containing the local perturbation and the lower part of a circle) with two corners. This novel integral equation can be solved efficiently by using the Nystrom method with a graded mesh introduced previously by "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.0161","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":"2026-05-18T03:34:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iErefRwHV3UNeZHGH6oYKKt2Q87VNIUqBSm6ejcPi5G/KleRzhKiYMyuPHPT8w/6g6mStzv9wNNxfmE/9LP5AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T19:55:12.624970Z"},"content_sha256":"b06fd72c0b40cf9fe6801b3b2271d3a59f9e27246a0b38de3fa675c5b4fd372f","schema_version":"1.0","event_id":"sha256:b06fd72c0b40cf9fe6801b3b2271d3a59f9e27246a0b38de3fa675c5b4fd372f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3CSB2C7Z2S42ZTZVMBMZ5L724Y/bundle.json","state_url":"https://pith.science/pith/3CSB2C7Z2S42ZTZVMBMZ5L724Y/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3CSB2C7Z2S42ZTZVMBMZ5L724Y/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":"2026-06-06T19:55:12Z","links":{"resolver":"https://pith.science/pith/3CSB2C7Z2S42ZTZVMBMZ5L724Y","bundle":"https://pith.science/pith/3CSB2C7Z2S42ZTZVMBMZ5L724Y/bundle.json","state":"https://pith.science/pith/3CSB2C7Z2S42ZTZVMBMZ5L724Y/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3CSB2C7Z2S42ZTZVMBMZ5L724Y/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:3CSB2C7Z2S42ZTZVMBMZ5L724Y","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":"35f5a9c08af96992fc69ed48f5a7750f26cc5f412e52528c84c409af276ca596","cross_cats_sorted":["math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-02-01T12:28:57Z","title_canon_sha256":"66509a7e8a5ace06f1322c59f1e5aaae1c4b700ff6e6b9358da85886afb6256c"},"schema_version":"1.0","source":{"id":"1302.0161","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.0161","created_at":"2026-05-18T03:34:47Z"},{"alias_kind":"arxiv_version","alias_value":"1302.0161v1","created_at":"2026-05-18T03:34:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.0161","created_at":"2026-05-18T03:34:47Z"},{"alias_kind":"pith_short_12","alias_value":"3CSB2C7Z2S42","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_16","alias_value":"3CSB2C7Z2S42ZTZV","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_8","alias_value":"3CSB2C7Z","created_at":"2026-05-18T12:27:32Z"}],"graph_snapshots":[{"event_id":"sha256:b06fd72c0b40cf9fe6801b3b2271d3a59f9e27246a0b38de3fa675c5b4fd372f","target":"graph","created_at":"2026-05-18T03:34:47Z","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 is concerned with the direct and inverse acoustic or electromagnetic scattering problems by a locally perturbed, perfectly reflecting, infinite plane (which is called a locally rough surface in this paper). We propose a novel integral equation formulation for the direct scattering problem which is defined on a bounded curve (consisting of a bounded part of the infinite plane containing the local perturbation and the lower part of a circle) with two corners. This novel integral equation can be solved efficiently by using the Nystrom method with a graded mesh introduced previously by ","authors_text":"Bo Zhang, Haiwen Zhang","cross_cats":["math.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-02-01T12:28:57Z","title":"A novel integral equation for scattering by locally rough surfaces and application to the inverse problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.0161","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":"sha256:50a3e2197fac87b6f803fc8f293044dfd0477ed8219f261ce12081f2ea9d1adc","target":"record","created_at":"2026-05-18T03:34:47Z","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":"35f5a9c08af96992fc69ed48f5a7750f26cc5f412e52528c84c409af276ca596","cross_cats_sorted":["math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-02-01T12:28:57Z","title_canon_sha256":"66509a7e8a5ace06f1322c59f1e5aaae1c4b700ff6e6b9358da85886afb6256c"},"schema_version":"1.0","source":{"id":"1302.0161","kind":"arxiv","version":1}},"canonical_sha256":"d8a41d0bf9d4b9accf3560599eaffae61213dc18f6b619cee16b6becbc4dcb52","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d8a41d0bf9d4b9accf3560599eaffae61213dc18f6b619cee16b6becbc4dcb52","first_computed_at":"2026-05-18T03:34:47.187106Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:34:47.187106Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"flLI5lBJdUZRFLj3e4WSgIaxUDmCZjDvYm1y2XzjF17aqh8lsIZBy55BdS/EPzAf6YiUZvSMDhSyFQbOiGjUAw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:34:47.187927Z","signed_message":"canonical_sha256_bytes"},"source_id":"1302.0161","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:50a3e2197fac87b6f803fc8f293044dfd0477ed8219f261ce12081f2ea9d1adc","sha256:b06fd72c0b40cf9fe6801b3b2271d3a59f9e27246a0b38de3fa675c5b4fd372f"],"state_sha256":"81d6c53fa14f4bfa5d3401b511b4f5db5e449b759a51a2f095b7d65a78f3ca9c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oPvArixBO9IUSspQX9YwTmkIZYumbZujiE4gPk91nmaP/Y4ndLshoBh46Rgt/OKracUfUs0noBKpAYmMomFvBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T19:55:12.628381Z","bundle_sha256":"71e3e41598b6c932b05091f8592310f16ef4b594b557fead17a6507381882dc6"}}