{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:IWCU3QPWH4SBATGA6TXZSO2W4V","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":"d9718c93bb4c7a24823f3790ccc2438634ca3111d953b5a6125705a73b6f1929","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2015-12-17T13:50:47Z","title_canon_sha256":"3b90e455e5611ab5790649f824453c6532b487f909f368dfcc23169c81f567ce"},"schema_version":"1.0","source":{"id":"1512.05580","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.05580","created_at":"2026-05-18T01:24:09Z"},{"alias_kind":"arxiv_version","alias_value":"1512.05580v1","created_at":"2026-05-18T01:24:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.05580","created_at":"2026-05-18T01:24:09Z"},{"alias_kind":"pith_short_12","alias_value":"IWCU3QPWH4SB","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_16","alias_value":"IWCU3QPWH4SBATGA","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_8","alias_value":"IWCU3QPW","created_at":"2026-05-18T12:29:27Z"}],"graph_snapshots":[{"event_id":"sha256:d16a9a047bf0d0f4ad33ddefbd058639b337a57a7793eef550b8b9b2577adc2d","target":"graph","created_at":"2026-05-18T01:24:09Z","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":"In this paper we extend Sylvester's approach via upper triangular compact operators to establish the discreteness of transmission eigenvalues for higher-order main terms and higher-order perturbations. The coefficients of the perturbations must be sufficiently smooth and the coefficients of the higher-order terms of the perturbation must vanish in a neighbourhood of the boundary of the underlying domain. The zeroeth order term must satisfy a suitable coercivity condition in a neighbourhood of the boundary.","authors_text":"Andoni Garc\\'ia, Esa V. Vesalainen, Miren Zubeldia","cross_cats":["math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2015-12-17T13:50:47Z","title":"Discreteness of Transmission Eigenvalues for Higher-Order Main Terms and Perturbations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.05580","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":"sha256:0e70979d5569e91328d24cfe0b7edb0e2019a9f6be400374f1a5c67c898e2ece","target":"record","created_at":"2026-05-18T01:24:09Z","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":"d9718c93bb4c7a24823f3790ccc2438634ca3111d953b5a6125705a73b6f1929","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2015-12-17T13:50:47Z","title_canon_sha256":"3b90e455e5611ab5790649f824453c6532b487f909f368dfcc23169c81f567ce"},"schema_version":"1.0","source":{"id":"1512.05580","kind":"arxiv","version":1}},"canonical_sha256":"45854dc1f63f24104cc0f4ef993b56e54ee1167d537fbdbade8adb8c037bea03","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"45854dc1f63f24104cc0f4ef993b56e54ee1167d537fbdbade8adb8c037bea03","first_computed_at":"2026-05-18T01:24:09.749631Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:24:09.749631Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bwiAU3zgL2jK3He/l2pieMGp/uj8vaWN6ceklXYr06a0dvfzOEp+UE6pquthxCZYvmvMSVLBDTUAh5JJo0q7AQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:24:09.750205Z","signed_message":"canonical_sha256_bytes"},"source_id":"1512.05580","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0e70979d5569e91328d24cfe0b7edb0e2019a9f6be400374f1a5c67c898e2ece","sha256:d16a9a047bf0d0f4ad33ddefbd058639b337a57a7793eef550b8b9b2577adc2d"],"state_sha256":"04a0bab5ff9f9af64f1a319363701cf19bd0683376a489624a8c878cf0589be7"}