{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:4UZFLAC77DYIMEEVEWEFWD3QNZ","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":"7b68264dcee4fd1f90becbd011e6df94ac6a28c3ffae0503f32e5130e4351a31","cross_cats_sorted":["math.CV","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-12-25T10:14:38Z","title_canon_sha256":"4e60df57ff0252173fdd220e248dc66d6b66358fe59c81943ebda80788a5f8f3"},"schema_version":"1.0","source":{"id":"1212.6014","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.6014","created_at":"2026-05-18T01:16:35Z"},{"alias_kind":"arxiv_version","alias_value":"1212.6014v1","created_at":"2026-05-18T01:16:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.6014","created_at":"2026-05-18T01:16:35Z"},{"alias_kind":"pith_short_12","alias_value":"4UZFLAC77DYI","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_16","alias_value":"4UZFLAC77DYIMEEV","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_8","alias_value":"4UZFLAC7","created_at":"2026-05-18T12:26:53Z"}],"graph_snapshots":[{"event_id":"sha256:795714e5f3fbd73d5b2166a1907452c5f798b094ec24f5201e4c53d2c29fc52f","target":"graph","created_at":"2026-05-18T01:16:35Z","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":"We survey recent results concerning the hereditary completeness of some special systems of functions and the spectral synthesis problem for a related class of linear operators. We present a solution of the spectral synthesis problem for systems of exponentials in $L^2(-\\pi, \\pi)$. Analogous results are obtained for the systems of reproducing kernels in the de Branges spaces of entire functions. We also apply these results (via a functional model) to the spectral theory of rank one perturbations of compact self-adjoint operators.","authors_text":"Alexander Borichev, Anton Baranov, Dmitry Yakubovich, Yurii Belov","cross_cats":["math.CV","math.SP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-12-25T10:14:38Z","title":"Recent developments in spectral synthesis for exponential systems and for non-self-adjoint operators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.6014","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:f2d917d13519fdc37f3e5b51b3d1864595c91f1656114e01f10d1a10a09955a6","target":"record","created_at":"2026-05-18T01:16:35Z","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":"7b68264dcee4fd1f90becbd011e6df94ac6a28c3ffae0503f32e5130e4351a31","cross_cats_sorted":["math.CV","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-12-25T10:14:38Z","title_canon_sha256":"4e60df57ff0252173fdd220e248dc66d6b66358fe59c81943ebda80788a5f8f3"},"schema_version":"1.0","source":{"id":"1212.6014","kind":"arxiv","version":1}},"canonical_sha256":"e53255805ff8f086109525885b0f706e5fd2b4759598b19f832f86401d93cc44","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e53255805ff8f086109525885b0f706e5fd2b4759598b19f832f86401d93cc44","first_computed_at":"2026-05-18T01:16:35.297350Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:16:35.297350Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MK50ekDU7GzZtcGdN/3Enjpv6fWye+Qj6qcZ7OsyaNMeEsxroiDfhQ64GxSNNa5gkbq5ka9w7b/69vZq2VurAw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:16:35.297987Z","signed_message":"canonical_sha256_bytes"},"source_id":"1212.6014","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f2d917d13519fdc37f3e5b51b3d1864595c91f1656114e01f10d1a10a09955a6","sha256:795714e5f3fbd73d5b2166a1907452c5f798b094ec24f5201e4c53d2c29fc52f"],"state_sha256":"10557708c3c28f1cdd6f383fd5b57e36d4f903bc99cbfdaac93277b3ce9b3781"}