{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:2TPSGGNOV7VJLR4BYMLA54S2OB","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":"27149f54c4fb4ad751cebf2f23bf1481db5c8096b7c19b1eac34128e3e50ae35","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-03-07T15:14:59Z","title_canon_sha256":"d00724318bc3659760e6698494688345297a769b92a7d8a43f710ec7a35a0cb7"},"schema_version":"1.0","source":{"id":"1403.1775","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.1775","created_at":"2026-05-18T02:56:52Z"},{"alias_kind":"arxiv_version","alias_value":"1403.1775v1","created_at":"2026-05-18T02:56:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.1775","created_at":"2026-05-18T02:56:52Z"},{"alias_kind":"pith_short_12","alias_value":"2TPSGGNOV7VJ","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_16","alias_value":"2TPSGGNOV7VJLR4B","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_8","alias_value":"2TPSGGNO","created_at":"2026-05-18T12:28:11Z"}],"graph_snapshots":[{"event_id":"sha256:c5825b9f2243e91f52e7e824f32e73600ca60a1e206335289a81c8432726a76b","target":"graph","created_at":"2026-05-18T02:56:52Z","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"},"paper":{"abstract_excerpt":"In this paper we continue investigation of the interior problem of tomography that was started in \\cite{BKT2}. As is known, solving the interior problem {with prior data specified on a finite collection of intervals $I_i$} is equivalent to analytic continuation of a function from $I_i$ to an open set ${\\bf J}$. In the paper we prove that this analytic continuation can be obtained with the help of a simple explicit formula, which involves summation of a series. Our second result is that the operator of analytic continuation is not stable for any pair of Sobolev spaces regardless of how close th","authors_text":"Alexander Katsevich, Alexander Tovbis, Marco Bertola","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-03-07T15:14:59Z","title":"On Sobolev instability of the interior problem of tomography"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.1775","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":"sha256:62b6ae86b2af9b249d9462c9599b510ed2531a91671aabf8fa9b916952e48cde","target":"record","created_at":"2026-05-18T02:56:52Z","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":"27149f54c4fb4ad751cebf2f23bf1481db5c8096b7c19b1eac34128e3e50ae35","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-03-07T15:14:59Z","title_canon_sha256":"d00724318bc3659760e6698494688345297a769b92a7d8a43f710ec7a35a0cb7"},"schema_version":"1.0","source":{"id":"1403.1775","kind":"arxiv","version":1}},"canonical_sha256":"d4df2319aeafea95c781c3160ef25a7062b611f96bff7b3f010b8b66062b5c3e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d4df2319aeafea95c781c3160ef25a7062b611f96bff7b3f010b8b66062b5c3e","first_computed_at":"2026-05-18T02:56:52.575962Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:56:52.575962Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"uvf95x4w0R9QhfcPteS08K+FBTy9XppQDJfLUniXnS91euwWCtYi+6GrGXD06H1M+qZvH/6A3zu5d3jkrLOxDA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:56:52.576544Z","signed_message":"canonical_sha256_bytes"},"source_id":"1403.1775","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:62b6ae86b2af9b249d9462c9599b510ed2531a91671aabf8fa9b916952e48cde","sha256:c5825b9f2243e91f52e7e824f32e73600ca60a1e206335289a81c8432726a76b"],"state_sha256":"e515e4310f009abc030ae4230125105ad4eaf2ee95a1eb2b9190644d2e0a0ef7"}