{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:Q7GB74U4MQY67A7I2YSD5CUXYE","short_pith_number":"pith:Q7GB74U4","canonical_record":{"source":{"id":"1610.06961","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-10-21T21:43:32Z","cross_cats_sorted":[],"title_canon_sha256":"706711ef09ffc9e04154db519260f1ca4fb4e12d279a3570362d97dae6fbc264","abstract_canon_sha256":"6cc25596ec1442b63c1e0d60d0ebdbc4c047b00161f2b755bdb077c0bd2bf503"},"schema_version":"1.0"},"canonical_sha256":"87cc1ff29c6431ef83e8d6243e8a97c11fe934090fa81637ee47beae9c8796d6","source":{"kind":"arxiv","id":"1610.06961","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.06961","created_at":"2026-05-18T01:01:35Z"},{"alias_kind":"arxiv_version","alias_value":"1610.06961v1","created_at":"2026-05-18T01:01:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.06961","created_at":"2026-05-18T01:01:35Z"},{"alias_kind":"pith_short_12","alias_value":"Q7GB74U4MQY6","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_16","alias_value":"Q7GB74U4MQY67A7I","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_8","alias_value":"Q7GB74U4","created_at":"2026-05-18T12:30:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:Q7GB74U4MQY67A7I2YSD5CUXYE","target":"record","payload":{"canonical_record":{"source":{"id":"1610.06961","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-10-21T21:43:32Z","cross_cats_sorted":[],"title_canon_sha256":"706711ef09ffc9e04154db519260f1ca4fb4e12d279a3570362d97dae6fbc264","abstract_canon_sha256":"6cc25596ec1442b63c1e0d60d0ebdbc4c047b00161f2b755bdb077c0bd2bf503"},"schema_version":"1.0"},"canonical_sha256":"87cc1ff29c6431ef83e8d6243e8a97c11fe934090fa81637ee47beae9c8796d6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:01:35.525185Z","signature_b64":"ZbUYHrk5p69xIueiA463yQ0zWisnN0A9NKi4SeJ1fdKmTQL7rQZWgwwCNG4tSUVYvDu2D7m12sBJRESWvytIBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"87cc1ff29c6431ef83e8d6243e8a97c11fe934090fa81637ee47beae9c8796d6","last_reissued_at":"2026-05-18T01:01:35.524673Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:01:35.524673Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1610.06961","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":"2026-05-18T01:01:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4KL6cw67eoo9MNr4vPiTgNkWpm2qJqZdfEz452g6/3d/Yt9zREhCcovKdQNVX+epYW8nNMih3JsNYBysbTkECA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T22:18:32.479503Z"},"content_sha256":"9f63e9c1051fc53b19cbc7bd647c081b3b60848b79333706a318c88488cce2b6","schema_version":"1.0","event_id":"sha256:9f63e9c1051fc53b19cbc7bd647c081b3b60848b79333706a318c88488cce2b6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:Q7GB74U4MQY67A7I2YSD5CUXYE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Discreteness of interior transmission eigenvalues revisited","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Hoai-Minh Nguyen, Quoc Hung Nguyen","submitted_at":"2016-10-21T21:43:32Z","abstract_excerpt":"This paper is devoted to the discreteness of the transmission eigenvalue problems. It is known that this problem is not self-adjoint and a priori estimates are non-standard and do not hold in general. Two approaches are used. The first one is based on the multiplier technique and the second one is based on the Fourier analysis. The key point of the analysis is to establish the compactness and the uniqueness for Cauchy problems under various conditions. Using these approaches, we are able to rediscover quite a few known discreteness results in the literature and obtain various new results for w"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.06961","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":"2026-05-18T01:01:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZD/fIHYiQ26zgqHsLr3ADSCT75WALyygVkOIJHNYm1aw6WrytubkHeqHPADmBJHFm6CsprWPuUY1844sbbmHDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T22:18:32.479848Z"},"content_sha256":"6b9c46bb675df9cfc3fd7c87950a343088f75047ef3cb2319ad0b0faeeb44606","schema_version":"1.0","event_id":"sha256:6b9c46bb675df9cfc3fd7c87950a343088f75047ef3cb2319ad0b0faeeb44606"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Q7GB74U4MQY67A7I2YSD5CUXYE/bundle.json","state_url":"https://pith.science/pith/Q7GB74U4MQY67A7I2YSD5CUXYE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Q7GB74U4MQY67A7I2YSD5CUXYE/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":"2026-06-20T22:18:32Z","links":{"resolver":"https://pith.science/pith/Q7GB74U4MQY67A7I2YSD5CUXYE","bundle":"https://pith.science/pith/Q7GB74U4MQY67A7I2YSD5CUXYE/bundle.json","state":"https://pith.science/pith/Q7GB74U4MQY67A7I2YSD5CUXYE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Q7GB74U4MQY67A7I2YSD5CUXYE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:Q7GB74U4MQY67A7I2YSD5CUXYE","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":"6cc25596ec1442b63c1e0d60d0ebdbc4c047b00161f2b755bdb077c0bd2bf503","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-10-21T21:43:32Z","title_canon_sha256":"706711ef09ffc9e04154db519260f1ca4fb4e12d279a3570362d97dae6fbc264"},"schema_version":"1.0","source":{"id":"1610.06961","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.06961","created_at":"2026-05-18T01:01:35Z"},{"alias_kind":"arxiv_version","alias_value":"1610.06961v1","created_at":"2026-05-18T01:01:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.06961","created_at":"2026-05-18T01:01:35Z"},{"alias_kind":"pith_short_12","alias_value":"Q7GB74U4MQY6","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_16","alias_value":"Q7GB74U4MQY67A7I","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_8","alias_value":"Q7GB74U4","created_at":"2026-05-18T12:30:39Z"}],"graph_snapshots":[{"event_id":"sha256:6b9c46bb675df9cfc3fd7c87950a343088f75047ef3cb2319ad0b0faeeb44606","target":"graph","created_at":"2026-05-18T01:01:35Z","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 devoted to the discreteness of the transmission eigenvalue problems. It is known that this problem is not self-adjoint and a priori estimates are non-standard and do not hold in general. Two approaches are used. The first one is based on the multiplier technique and the second one is based on the Fourier analysis. The key point of the analysis is to establish the compactness and the uniqueness for Cauchy problems under various conditions. Using these approaches, we are able to rediscover quite a few known discreteness results in the literature and obtain various new results for w","authors_text":"Hoai-Minh Nguyen, Quoc Hung Nguyen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-10-21T21:43:32Z","title":"Discreteness of interior transmission eigenvalues revisited"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.06961","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":"sha256:9f63e9c1051fc53b19cbc7bd647c081b3b60848b79333706a318c88488cce2b6","target":"record","created_at":"2026-05-18T01:01:35Z","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":"6cc25596ec1442b63c1e0d60d0ebdbc4c047b00161f2b755bdb077c0bd2bf503","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-10-21T21:43:32Z","title_canon_sha256":"706711ef09ffc9e04154db519260f1ca4fb4e12d279a3570362d97dae6fbc264"},"schema_version":"1.0","source":{"id":"1610.06961","kind":"arxiv","version":1}},"canonical_sha256":"87cc1ff29c6431ef83e8d6243e8a97c11fe934090fa81637ee47beae9c8796d6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"87cc1ff29c6431ef83e8d6243e8a97c11fe934090fa81637ee47beae9c8796d6","first_computed_at":"2026-05-18T01:01:35.524673Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:01:35.524673Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZbUYHrk5p69xIueiA463yQ0zWisnN0A9NKi4SeJ1fdKmTQL7rQZWgwwCNG4tSUVYvDu2D7m12sBJRESWvytIBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:01:35.525185Z","signed_message":"canonical_sha256_bytes"},"source_id":"1610.06961","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9f63e9c1051fc53b19cbc7bd647c081b3b60848b79333706a318c88488cce2b6","sha256:6b9c46bb675df9cfc3fd7c87950a343088f75047ef3cb2319ad0b0faeeb44606"],"state_sha256":"a54d6a690ddf3ce7a08e6c1a42e9ae9e698a1e4a0399ae1f7ffa5b204ed6b235"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OL0B4o1ZzM3LiF94SJQL+mRtkpJ17FWlWOZTz7l2GLLB0/hOaw6NhXJqDuzRqi7viIm2UiwdJXwOdJWaiVA0AQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T22:18:32.481735Z","bundle_sha256":"2015562cf7b95f5c9478b8ce6ab5c93342020296cadb7e1d316c26fce5b3de82"}}