{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:MISDSHOBRREHEEZR42STD5FOYZ","short_pith_number":"pith:MISDSHOB","canonical_record":{"source":{"id":"2606.07786","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2026-06-05T18:58:15Z","cross_cats_sorted":[],"title_canon_sha256":"819031fc85e254aa9b6bd6fdb24a8c805ed6f53d839ad6d75d5b93e4b0414662","abstract_canon_sha256":"bf063d6f4d1d31e26ef77b9762ce8fedd8a19a89d86e2815ef5fa5f55368a824"},"schema_version":"1.0"},"canonical_sha256":"6224391dc18c48721331e6a531f4aec641b2b26033257944a21c0531d75c2340","source":{"kind":"arxiv","id":"2606.07786","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.07786","created_at":"2026-06-09T01:04:52Z"},{"alias_kind":"arxiv_version","alias_value":"2606.07786v1","created_at":"2026-06-09T01:04:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.07786","created_at":"2026-06-09T01:04:52Z"},{"alias_kind":"pith_short_12","alias_value":"MISDSHOBRREH","created_at":"2026-06-09T01:04:52Z"},{"alias_kind":"pith_short_16","alias_value":"MISDSHOBRREHEEZR","created_at":"2026-06-09T01:04:52Z"},{"alias_kind":"pith_short_8","alias_value":"MISDSHOB","created_at":"2026-06-09T01:04:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:MISDSHOBRREHEEZR42STD5FOYZ","target":"record","payload":{"canonical_record":{"source":{"id":"2606.07786","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2026-06-05T18:58:15Z","cross_cats_sorted":[],"title_canon_sha256":"819031fc85e254aa9b6bd6fdb24a8c805ed6f53d839ad6d75d5b93e4b0414662","abstract_canon_sha256":"bf063d6f4d1d31e26ef77b9762ce8fedd8a19a89d86e2815ef5fa5f55368a824"},"schema_version":"1.0"},"canonical_sha256":"6224391dc18c48721331e6a531f4aec641b2b26033257944a21c0531d75c2340","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-09T01:04:52.185221Z","signature_b64":"mvhXWm4OXigLuFq/xVC12CrpSQNrAXjfGy5xJCG2lquGmHV8Qf3+U0yjMX3O662D5RnRkkTXOy0TyY4mmAg8BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6224391dc18c48721331e6a531f4aec641b2b26033257944a21c0531d75c2340","last_reissued_at":"2026-06-09T01:04:52.184825Z","signature_status":"signed_v1","first_computed_at":"2026-06-09T01:04:52.184825Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2606.07786","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":"2026-06-09T01:04:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bhgFCnrxmqxIeUAmoLAFi1PmS1A8Ts2VvU/izpph/eyuVcHDy6uKbAkDEVkAz1UpyQ1/ktocDAwgybXz5FLQAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T23:49:23.879609Z"},"content_sha256":"e3ee01c5f800018fb05d78a7710867818aeaebd7d8c65f269ae09a6b4c8d1cd1","schema_version":"1.0","event_id":"sha256:e3ee01c5f800018fb05d78a7710867818aeaebd7d8c65f269ae09a6b4c8d1cd1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:MISDSHOBRREHEEZR42STD5FOYZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Spectral structures of elastic-electromagnetic transmission eigenvalue problems","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Hongyu Liu, Huaian Diao, Xinyu Ding, Yueran Geng","submitted_at":"2026-06-05T18:58:15Z","abstract_excerpt":"The time-harmonic elastic-electromagnetic interior transmission eigenvalue problem (EEITEP) arises when an elastic body becomes invisible to an incident electromagnetic wave. This spectral problem is typically non-elliptic and non-self-adjoint, making its analysis delicate. In this paper, we study the discreteness of transmission eigenvalues and the boundary localization of the associated eigenfunctions. For a general bounded Lipschitz domain, we prove that the set of positive transmission eigenvalues, if non-empty, is discrete with $\\infty$ as its only possible accumulation point. For a radia"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.07786","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/2606.07786/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":"2026-06-09T01:04:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TlC0nvw6na7DAOzNlR0GI5qqVsuE0gt5LZZ/xCSNYPGFUQxBAcDAXbxgjAD6zi2dcth6Qr4qqgM3k4i21QM/Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T23:49:23.880338Z"},"content_sha256":"63f6f1f3686679b800d005e21b1b19ab9702d7c364aa654158730b6abd6d7d3e","schema_version":"1.0","event_id":"sha256:63f6f1f3686679b800d005e21b1b19ab9702d7c364aa654158730b6abd6d7d3e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MISDSHOBRREHEEZR42STD5FOYZ/bundle.json","state_url":"https://pith.science/pith/MISDSHOBRREHEEZR42STD5FOYZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MISDSHOBRREHEEZR42STD5FOYZ/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":"2026-06-11T23:49:23Z","links":{"resolver":"https://pith.science/pith/MISDSHOBRREHEEZR42STD5FOYZ","bundle":"https://pith.science/pith/MISDSHOBRREHEEZR42STD5FOYZ/bundle.json","state":"https://pith.science/pith/MISDSHOBRREHEEZR42STD5FOYZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MISDSHOBRREHEEZR42STD5FOYZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:MISDSHOBRREHEEZR42STD5FOYZ","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":"bf063d6f4d1d31e26ef77b9762ce8fedd8a19a89d86e2815ef5fa5f55368a824","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2026-06-05T18:58:15Z","title_canon_sha256":"819031fc85e254aa9b6bd6fdb24a8c805ed6f53d839ad6d75d5b93e4b0414662"},"schema_version":"1.0","source":{"id":"2606.07786","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.07786","created_at":"2026-06-09T01:04:52Z"},{"alias_kind":"arxiv_version","alias_value":"2606.07786v1","created_at":"2026-06-09T01:04:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.07786","created_at":"2026-06-09T01:04:52Z"},{"alias_kind":"pith_short_12","alias_value":"MISDSHOBRREH","created_at":"2026-06-09T01:04:52Z"},{"alias_kind":"pith_short_16","alias_value":"MISDSHOBRREHEEZR","created_at":"2026-06-09T01:04:52Z"},{"alias_kind":"pith_short_8","alias_value":"MISDSHOB","created_at":"2026-06-09T01:04:52Z"}],"graph_snapshots":[{"event_id":"sha256:63f6f1f3686679b800d005e21b1b19ab9702d7c364aa654158730b6abd6d7d3e","target":"graph","created_at":"2026-06-09T01:04:52Z","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/2606.07786/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The time-harmonic elastic-electromagnetic interior transmission eigenvalue problem (EEITEP) arises when an elastic body becomes invisible to an incident electromagnetic wave. This spectral problem is typically non-elliptic and non-self-adjoint, making its analysis delicate. In this paper, we study the discreteness of transmission eigenvalues and the boundary localization of the associated eigenfunctions. For a general bounded Lipschitz domain, we prove that the set of positive transmission eigenvalues, if non-empty, is discrete with $\\infty$ as its only possible accumulation point. For a radia","authors_text":"Hongyu Liu, Huaian Diao, Xinyu Ding, Yueran Geng","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2026-06-05T18:58:15Z","title":"Spectral structures of elastic-electromagnetic transmission eigenvalue problems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.07786","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:e3ee01c5f800018fb05d78a7710867818aeaebd7d8c65f269ae09a6b4c8d1cd1","target":"record","created_at":"2026-06-09T01:04:52Z","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":"bf063d6f4d1d31e26ef77b9762ce8fedd8a19a89d86e2815ef5fa5f55368a824","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2026-06-05T18:58:15Z","title_canon_sha256":"819031fc85e254aa9b6bd6fdb24a8c805ed6f53d839ad6d75d5b93e4b0414662"},"schema_version":"1.0","source":{"id":"2606.07786","kind":"arxiv","version":1}},"canonical_sha256":"6224391dc18c48721331e6a531f4aec641b2b26033257944a21c0531d75c2340","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6224391dc18c48721331e6a531f4aec641b2b26033257944a21c0531d75c2340","first_computed_at":"2026-06-09T01:04:52.184825Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-09T01:04:52.184825Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mvhXWm4OXigLuFq/xVC12CrpSQNrAXjfGy5xJCG2lquGmHV8Qf3+U0yjMX3O662D5RnRkkTXOy0TyY4mmAg8BA==","signature_status":"signed_v1","signed_at":"2026-06-09T01:04:52.185221Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.07786","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e3ee01c5f800018fb05d78a7710867818aeaebd7d8c65f269ae09a6b4c8d1cd1","sha256:63f6f1f3686679b800d005e21b1b19ab9702d7c364aa654158730b6abd6d7d3e"],"state_sha256":"c77430ee9f78727cb77400d76378461a2f328362edfb57b94b785054001fe932"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VVrZmW0v/sU59ipxtmmC/prVfC6oQAbbd4SdbZY6VMQ1AUr51bbhsKksvRI06axSoClUppBRNZzGb9cysPL1DQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T23:49:23.884492Z","bundle_sha256":"faaecd17f5a34e5db8c570f6b87a0ec002794446256d8096bb9ed18b0bd19cbd"}}