{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:GRV4AZCVQ4AFVC2J6FYRB3SWHF","short_pith_number":"pith:GRV4AZCV","canonical_record":{"source":{"id":"1801.08703","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-01-26T08:08:33Z","cross_cats_sorted":[],"title_canon_sha256":"4189dc00f31fa74884c661cacec4dbee536389ea0106b7dd84237332a7c4dd59","abstract_canon_sha256":"70fe2149d3c975addd654d5246e89ecc912b0f5caa6ee8bd14d2101fded1962e"},"schema_version":"1.0"},"canonical_sha256":"346bc0645587005a8b49f17110ee563960183f9118c365b8b7a84c452347484c","source":{"kind":"arxiv","id":"1801.08703","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1801.08703","created_at":"2026-05-18T00:25:03Z"},{"alias_kind":"arxiv_version","alias_value":"1801.08703v1","created_at":"2026-05-18T00:25:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.08703","created_at":"2026-05-18T00:25:03Z"},{"alias_kind":"pith_short_12","alias_value":"GRV4AZCVQ4AF","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_16","alias_value":"GRV4AZCVQ4AFVC2J","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_8","alias_value":"GRV4AZCV","created_at":"2026-05-18T12:32:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:GRV4AZCVQ4AFVC2J6FYRB3SWHF","target":"record","payload":{"canonical_record":{"source":{"id":"1801.08703","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-01-26T08:08:33Z","cross_cats_sorted":[],"title_canon_sha256":"4189dc00f31fa74884c661cacec4dbee536389ea0106b7dd84237332a7c4dd59","abstract_canon_sha256":"70fe2149d3c975addd654d5246e89ecc912b0f5caa6ee8bd14d2101fded1962e"},"schema_version":"1.0"},"canonical_sha256":"346bc0645587005a8b49f17110ee563960183f9118c365b8b7a84c452347484c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:25:03.232768Z","signature_b64":"OUZBjm/M0SOhOLU8/1YG834nC9qp8xvRpVCA478WHJOi66Tjy0oZCDg2Z0I3QR7wa52TZavdn5+QBH4eRHP3DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"346bc0645587005a8b49f17110ee563960183f9118c365b8b7a84c452347484c","last_reissued_at":"2026-05-18T00:25:03.232232Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:25:03.232232Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1801.08703","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":"2026-05-18T00:25:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"U3cR8dkPQzT1CFiLaHXKlwKaEB0a9V/85Td3zHkNUD/AjdYC3Efaa/BiZcOI/9JNu7sZKYpAoKMCFUixwyV8AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T19:26:44.897560Z"},"content_sha256":"93b4d6072de053554b53b8a992d567d7de525c7334eb9695c744c583879a3c03","schema_version":"1.0","event_id":"sha256:93b4d6072de053554b53b8a992d567d7de525c7334eb9695c744c583879a3c03"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:GRV4AZCVQ4AFVC2J6FYRB3SWHF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Trapped modes and reflectionless modes as eigenfunctions of the same spectral problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Anne-Sophie Bonnet-Ben Dhia, Lucas Chesnel, Vincent Pagneux","submitted_at":"2018-01-26T08:08:33Z","abstract_excerpt":"We consider the reflection-transmission problem in a waveguide with obstacle. At certain frequencies, for some incident waves, intensity is perfectly transmitted and the reflected field decays exponentially at infinity. In this work, we show that such reflectionless modes can be characterized as eigenfunctions of an original non-selfadjoint spectral problem. In order to select ingoing waves on one side of the obstacle and outgoing waves on the other side, we use complex scalings (or Perfectly Matched Layers) with imaginary parts of different signs. We prove that the real eigenvalues of the obt"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.08703","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":"2026-05-18T00:25:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"53jIdgbCLLVXAxFqonUa425ozb1EGGG5HOmQ9mCJ2yYLs4qUtYTdQcQRwo6haOGl0pLSqCteyljjwtSpAHBvCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T19:26:44.897899Z"},"content_sha256":"5ddb87bbf18b0a20c9815773899d78ec97378ceafc9cc827bc58373dfe706c73","schema_version":"1.0","event_id":"sha256:5ddb87bbf18b0a20c9815773899d78ec97378ceafc9cc827bc58373dfe706c73"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GRV4AZCVQ4AFVC2J6FYRB3SWHF/bundle.json","state_url":"https://pith.science/pith/GRV4AZCVQ4AFVC2J6FYRB3SWHF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GRV4AZCVQ4AFVC2J6FYRB3SWHF/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":"2026-06-02T19:26:44Z","links":{"resolver":"https://pith.science/pith/GRV4AZCVQ4AFVC2J6FYRB3SWHF","bundle":"https://pith.science/pith/GRV4AZCVQ4AFVC2J6FYRB3SWHF/bundle.json","state":"https://pith.science/pith/GRV4AZCVQ4AFVC2J6FYRB3SWHF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GRV4AZCVQ4AFVC2J6FYRB3SWHF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:GRV4AZCVQ4AFVC2J6FYRB3SWHF","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":"70fe2149d3c975addd654d5246e89ecc912b0f5caa6ee8bd14d2101fded1962e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-01-26T08:08:33Z","title_canon_sha256":"4189dc00f31fa74884c661cacec4dbee536389ea0106b7dd84237332a7c4dd59"},"schema_version":"1.0","source":{"id":"1801.08703","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1801.08703","created_at":"2026-05-18T00:25:03Z"},{"alias_kind":"arxiv_version","alias_value":"1801.08703v1","created_at":"2026-05-18T00:25:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.08703","created_at":"2026-05-18T00:25:03Z"},{"alias_kind":"pith_short_12","alias_value":"GRV4AZCVQ4AF","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_16","alias_value":"GRV4AZCVQ4AFVC2J","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_8","alias_value":"GRV4AZCV","created_at":"2026-05-18T12:32:25Z"}],"graph_snapshots":[{"event_id":"sha256:5ddb87bbf18b0a20c9815773899d78ec97378ceafc9cc827bc58373dfe706c73","target":"graph","created_at":"2026-05-18T00:25:03Z","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 consider the reflection-transmission problem in a waveguide with obstacle. At certain frequencies, for some incident waves, intensity is perfectly transmitted and the reflected field decays exponentially at infinity. In this work, we show that such reflectionless modes can be characterized as eigenfunctions of an original non-selfadjoint spectral problem. In order to select ingoing waves on one side of the obstacle and outgoing waves on the other side, we use complex scalings (or Perfectly Matched Layers) with imaginary parts of different signs. We prove that the real eigenvalues of the obt","authors_text":"Anne-Sophie Bonnet-Ben Dhia, Lucas Chesnel, Vincent Pagneux","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-01-26T08:08:33Z","title":"Trapped modes and reflectionless modes as eigenfunctions of the same spectral problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.08703","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":"sha256:93b4d6072de053554b53b8a992d567d7de525c7334eb9695c744c583879a3c03","target":"record","created_at":"2026-05-18T00:25:03Z","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":"70fe2149d3c975addd654d5246e89ecc912b0f5caa6ee8bd14d2101fded1962e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-01-26T08:08:33Z","title_canon_sha256":"4189dc00f31fa74884c661cacec4dbee536389ea0106b7dd84237332a7c4dd59"},"schema_version":"1.0","source":{"id":"1801.08703","kind":"arxiv","version":1}},"canonical_sha256":"346bc0645587005a8b49f17110ee563960183f9118c365b8b7a84c452347484c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"346bc0645587005a8b49f17110ee563960183f9118c365b8b7a84c452347484c","first_computed_at":"2026-05-18T00:25:03.232232Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:25:03.232232Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OUZBjm/M0SOhOLU8/1YG834nC9qp8xvRpVCA478WHJOi66Tjy0oZCDg2Z0I3QR7wa52TZavdn5+QBH4eRHP3DQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:25:03.232768Z","signed_message":"canonical_sha256_bytes"},"source_id":"1801.08703","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:93b4d6072de053554b53b8a992d567d7de525c7334eb9695c744c583879a3c03","sha256:5ddb87bbf18b0a20c9815773899d78ec97378ceafc9cc827bc58373dfe706c73"],"state_sha256":"aaa8ea0927dea36fed08d6897386409d75fc55c96bcd75f8e86ce74d30f6b74c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jr08t6YpbiR+0KhHbFPCnSr63oew8iEerUTslBhG2Kr1pSJ19P2Vdl/zR6o0QYqJyWeRodCh9ZWEZacBJnM4BQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T19:26:44.899686Z","bundle_sha256":"ab72edd637accca56f417a19ef5b406f1da85c84cd53cc7ad3beaf18cb128ada"}}