{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:QQ3Y5OQAAAXXDSTPYWPWPQ6GRO","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":"b661c3ed0609b75189131fd23b1d14d8f88c83ca040c7ceb8863111ad193f132","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-06-23T22:21:47Z","title_canon_sha256":"25cbf8765574a8985ec3c39ecdeb0a38d9a6216ef1e19725d95af7eac18e1e54"},"schema_version":"1.0","source":{"id":"1306.5481","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1306.5481","created_at":"2026-05-18T01:49:08Z"},{"alias_kind":"arxiv_version","alias_value":"1306.5481v1","created_at":"2026-05-18T01:49:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.5481","created_at":"2026-05-18T01:49:08Z"},{"alias_kind":"pith_short_12","alias_value":"QQ3Y5OQAAAXX","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_16","alias_value":"QQ3Y5OQAAAXXDSTP","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_8","alias_value":"QQ3Y5OQA","created_at":"2026-05-18T12:27:57Z"}],"graph_snapshots":[{"event_id":"sha256:b0e9b5269b2057a24ffbb09654b785d3f083dc9f58b1a678a132a330172bef8f","target":"graph","created_at":"2026-05-18T01:49:08Z","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":"The spectrum of the interior transmission problem is related to the unique determination of the acoustic properties of a body in thermoacoustic imaging. Under a non-trapping hypothesis, we show that sparsity of the interior transmission spectrum implies a range separation condition for the thermoacoustic operator. In odd dimension greater than or equal to three, we prove that the transmission spectrum for a pair of radially symmetric non-trapping sound speeds is countable, and conclude that the ranges of the associated thermoacoustic maps have only trivial intersection.","authors_text":"David Finch, Kyle S. Hickmann","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-06-23T22:21:47Z","title":"Transmission eigenvalues and thermoacoustic tomography"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.5481","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:abc95f93be39c938ece87ab1fc359b97af2b754923c365a2662bcd5fb4dd6159","target":"record","created_at":"2026-05-18T01:49:08Z","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":"b661c3ed0609b75189131fd23b1d14d8f88c83ca040c7ceb8863111ad193f132","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-06-23T22:21:47Z","title_canon_sha256":"25cbf8765574a8985ec3c39ecdeb0a38d9a6216ef1e19725d95af7eac18e1e54"},"schema_version":"1.0","source":{"id":"1306.5481","kind":"arxiv","version":1}},"canonical_sha256":"84378eba00002f71ca6fc59f67c3c68bbad9f0af9829658297142ec119767c82","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"84378eba00002f71ca6fc59f67c3c68bbad9f0af9829658297142ec119767c82","first_computed_at":"2026-05-18T01:49:08.952590Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:49:08.952590Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2t7pjnn+aF4Ximqgm1/NmzPbtyebfyL4yMI6PzxPCyOGixTiC7znyifsOxsQJMbopWwuD3sXIcvApD0KmB6QCA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:49:08.953206Z","signed_message":"canonical_sha256_bytes"},"source_id":"1306.5481","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:abc95f93be39c938ece87ab1fc359b97af2b754923c365a2662bcd5fb4dd6159","sha256:b0e9b5269b2057a24ffbb09654b785d3f083dc9f58b1a678a132a330172bef8f"],"state_sha256":"7164a5761fe523fbea53c5b64cdd888d0161fac7696bc1700fe9a1dac9180337"}