{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:AWDTQTQ477R24GGXH5WZ5OZBHU","short_pith_number":"pith:AWDTQTQ4","canonical_record":{"source":{"id":"2406.14279","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2024-06-20T13:02:34Z","cross_cats_sorted":[],"title_canon_sha256":"d323e5dd7424f55f4155f55914466fcb62fd6b0b8e006c81e74504a9101cc9cc","abstract_canon_sha256":"f9a76524e7d39e551d47ad1bbbf317835d8da3053cf3786f1a480d258fab06c9"},"schema_version":"1.0"},"canonical_sha256":"0587384e1cffe3ae18d73f6d9ebb213d3a9b799466ef42ca72f607d5c22253a6","source":{"kind":"arxiv","id":"2406.14279","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2406.14279","created_at":"2026-07-05T08:34:41Z"},{"alias_kind":"arxiv_version","alias_value":"2406.14279v1","created_at":"2026-07-05T08:34:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2406.14279","created_at":"2026-07-05T08:34:41Z"},{"alias_kind":"pith_short_12","alias_value":"AWDTQTQ477R2","created_at":"2026-07-05T08:34:41Z"},{"alias_kind":"pith_short_16","alias_value":"AWDTQTQ477R24GGX","created_at":"2026-07-05T08:34:41Z"},{"alias_kind":"pith_short_8","alias_value":"AWDTQTQ4","created_at":"2026-07-05T08:34:41Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:AWDTQTQ477R24GGXH5WZ5OZBHU","target":"record","payload":{"canonical_record":{"source":{"id":"2406.14279","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2024-06-20T13:02:34Z","cross_cats_sorted":[],"title_canon_sha256":"d323e5dd7424f55f4155f55914466fcb62fd6b0b8e006c81e74504a9101cc9cc","abstract_canon_sha256":"f9a76524e7d39e551d47ad1bbbf317835d8da3053cf3786f1a480d258fab06c9"},"schema_version":"1.0"},"canonical_sha256":"0587384e1cffe3ae18d73f6d9ebb213d3a9b799466ef42ca72f607d5c22253a6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:34:41.352364Z","signature_b64":"Yg005g2558bE2kmE1qdGwF2vlZdhUm7DK3zjXC3tDCTgQelZ05f36jxUGWIEDCBZ8FOdBjLC64hy1LrVRbEUAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0587384e1cffe3ae18d73f6d9ebb213d3a9b799466ef42ca72f607d5c22253a6","last_reissued_at":"2026-07-05T08:34:41.351949Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:34:41.351949Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2406.14279","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":"2026-07-05T08:34:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9FJ8rXe3jOJNNLC0KyEKPgCSNtWf4dPutEWHSpubMcYZKrrCVrqWv70eaHHLfGNddgNhbfKH+vySh4rf4LwlAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T19:33:28.292397Z"},"content_sha256":"68390a00869a552f596fd52e73e1775daf37282d23633ae49da238526f17c8c1","schema_version":"1.0","event_id":"sha256:68390a00869a552f596fd52e73e1775daf37282d23633ae49da238526f17c8c1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:AWDTQTQ477R24GGXH5WZ5OZBHU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Uniqueness and modified Newton method for cracks from the far field patterns with a fixed incident direction","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jialei Li, XiaoDong Liu","submitted_at":"2024-06-20T13:02:34Z","abstract_excerpt":"We consider the inverse cracks scattering problems from the far field patterns with a fixed incident direction. We firstly show that the sound-soft cracks can be uniquely determined by the multi-frequency far field patterns with a fixed incident direction. The proof is based on a low frequency asymptotic analysis of the scattered field. One important feature of the uniqueness result is that the background can even be an unknown inhomogeneous medium. A modified Newton method is then proposed for the numerical reconstruction of the shapes and locations of the cracks. Compared to the classical Ne"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2406.14279","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2406.14279/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":"2026-07-05T08:34:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"piNktNtqG625RsTUXXmKCScg3BdDX7ToRhpMcibMrwWo/vPz3VSY63e8kv3NIPR34C6VuIw4MhQu5YXRK0HjDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T19:33:28.292920Z"},"content_sha256":"012f46932306d6ccaccd6ef89ed80bc2c956bc5522b2db260af54294c828e1dd","schema_version":"1.0","event_id":"sha256:012f46932306d6ccaccd6ef89ed80bc2c956bc5522b2db260af54294c828e1dd"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AWDTQTQ477R24GGXH5WZ5OZBHU/bundle.json","state_url":"https://pith.science/pith/AWDTQTQ477R24GGXH5WZ5OZBHU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AWDTQTQ477R24GGXH5WZ5OZBHU/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":"2026-08-12T19:33:28Z","links":{"resolver":"https://pith.science/pith/AWDTQTQ477R24GGXH5WZ5OZBHU","bundle":"https://pith.science/pith/AWDTQTQ477R24GGXH5WZ5OZBHU/bundle.json","state":"https://pith.science/pith/AWDTQTQ477R24GGXH5WZ5OZBHU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AWDTQTQ477R24GGXH5WZ5OZBHU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:AWDTQTQ477R24GGXH5WZ5OZBHU","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":"f9a76524e7d39e551d47ad1bbbf317835d8da3053cf3786f1a480d258fab06c9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2024-06-20T13:02:34Z","title_canon_sha256":"d323e5dd7424f55f4155f55914466fcb62fd6b0b8e006c81e74504a9101cc9cc"},"schema_version":"1.0","source":{"id":"2406.14279","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2406.14279","created_at":"2026-07-05T08:34:41Z"},{"alias_kind":"arxiv_version","alias_value":"2406.14279v1","created_at":"2026-07-05T08:34:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2406.14279","created_at":"2026-07-05T08:34:41Z"},{"alias_kind":"pith_short_12","alias_value":"AWDTQTQ477R2","created_at":"2026-07-05T08:34:41Z"},{"alias_kind":"pith_short_16","alias_value":"AWDTQTQ477R24GGX","created_at":"2026-07-05T08:34:41Z"},{"alias_kind":"pith_short_8","alias_value":"AWDTQTQ4","created_at":"2026-07-05T08:34:41Z"}],"graph_snapshots":[{"event_id":"sha256:012f46932306d6ccaccd6ef89ed80bc2c956bc5522b2db260af54294c828e1dd","target":"graph","created_at":"2026-07-05T08:34:41Z","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/2406.14279/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We consider the inverse cracks scattering problems from the far field patterns with a fixed incident direction. We firstly show that the sound-soft cracks can be uniquely determined by the multi-frequency far field patterns with a fixed incident direction. The proof is based on a low frequency asymptotic analysis of the scattered field. One important feature of the uniqueness result is that the background can even be an unknown inhomogeneous medium. A modified Newton method is then proposed for the numerical reconstruction of the shapes and locations of the cracks. Compared to the classical Ne","authors_text":"Jialei Li, XiaoDong Liu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2024-06-20T13:02:34Z","title":"Uniqueness and modified Newton method for cracks from the far field patterns with a fixed incident direction"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2406.14279","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":"sha256:68390a00869a552f596fd52e73e1775daf37282d23633ae49da238526f17c8c1","target":"record","created_at":"2026-07-05T08:34:41Z","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":"f9a76524e7d39e551d47ad1bbbf317835d8da3053cf3786f1a480d258fab06c9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2024-06-20T13:02:34Z","title_canon_sha256":"d323e5dd7424f55f4155f55914466fcb62fd6b0b8e006c81e74504a9101cc9cc"},"schema_version":"1.0","source":{"id":"2406.14279","kind":"arxiv","version":1}},"canonical_sha256":"0587384e1cffe3ae18d73f6d9ebb213d3a9b799466ef42ca72f607d5c22253a6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0587384e1cffe3ae18d73f6d9ebb213d3a9b799466ef42ca72f607d5c22253a6","first_computed_at":"2026-07-05T08:34:41.351949Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:34:41.351949Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Yg005g2558bE2kmE1qdGwF2vlZdhUm7DK3zjXC3tDCTgQelZ05f36jxUGWIEDCBZ8FOdBjLC64hy1LrVRbEUAg==","signature_status":"signed_v1","signed_at":"2026-07-05T08:34:41.352364Z","signed_message":"canonical_sha256_bytes"},"source_id":"2406.14279","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:68390a00869a552f596fd52e73e1775daf37282d23633ae49da238526f17c8c1","sha256:012f46932306d6ccaccd6ef89ed80bc2c956bc5522b2db260af54294c828e1dd"],"state_sha256":"d5a3831b79f2199822e768098ab1795ac03e803c339c66a20469e96f910917dc"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nYhCENCqc695/6N9gthx7ob7lVd2+BihMde4j3UeLsJiOyW+WXDpL9wJ+DSuupDUSOSvWYPGFKgGPnHfaXd9Cw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-12T19:33:28.297953Z","bundle_sha256":"cffd68f7bf21a5cea2ce7d19fc2dbdcbd4ac2394432816c1deb80cb09b7eddbd"}}