{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:6R2DQFUI75SMDWG3ZB2NFWJUXI","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":"c9cd72bad9bcdb1f7bc74abfc92dd603e9188a92f07ed3749dc2b2c03c90cea1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2010-01-28T09:19:17Z","title_canon_sha256":"2c8dc9169d34e82bfea00a2fae3e9128cabed7752582f2fb8b279388c88eac65"},"schema_version":"1.0","source":{"id":"1001.5132","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1001.5132","created_at":"2026-05-18T03:38:33Z"},{"alias_kind":"arxiv_version","alias_value":"1001.5132v2","created_at":"2026-05-18T03:38:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1001.5132","created_at":"2026-05-18T03:38:33Z"},{"alias_kind":"pith_short_12","alias_value":"6R2DQFUI75SM","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_16","alias_value":"6R2DQFUI75SMDWG3","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_8","alias_value":"6R2DQFUI","created_at":"2026-05-18T12:26:04Z"}],"graph_snapshots":[{"event_id":"sha256:74aaa348c7a3c52f2a937fccd424aff821c9cc500f246bf5ea449850d529dafe","target":"graph","created_at":"2026-05-18T03:38:33Z","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 study a semiclassical inverse spectral problem based on a spectral asymptotics result of arXiv:math/0502032, which applies to small non-selfadjoint perturbations of selfadjoint $h$-pseudodifferential operators in dimension 2. The eigenvalues in a suitable complex window have an expansion in terms of a quantum Birkhoff normal form for the operator near several Lagrangian tori which are invariant under the classical dynamics and satisfy a Diophantine condition. In this work we prove that the normal form near a single Diophantine torus is uniquely determined by the associated eigenvalues. We a","authors_text":"Michael A. Hall","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2010-01-28T09:19:17Z","title":"Diophantine tori and nonselfadjoint inverse spectral problems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1001.5132","kind":"arxiv","version":2},"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:ad97c5b728c18aad9a651bd22f79e18731138f86609a2d18e9d0c35a2f35fc61","target":"record","created_at":"2026-05-18T03:38:33Z","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":"c9cd72bad9bcdb1f7bc74abfc92dd603e9188a92f07ed3749dc2b2c03c90cea1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2010-01-28T09:19:17Z","title_canon_sha256":"2c8dc9169d34e82bfea00a2fae3e9128cabed7752582f2fb8b279388c88eac65"},"schema_version":"1.0","source":{"id":"1001.5132","kind":"arxiv","version":2}},"canonical_sha256":"f474381688ff64c1d8dbc874d2d934ba041954da7db32a118ca38fdfc5f0604a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f474381688ff64c1d8dbc874d2d934ba041954da7db32a118ca38fdfc5f0604a","first_computed_at":"2026-05-18T03:38:33.277125Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:38:33.277125Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HVrroBmvewDTb3lPDmDMJAHyamqgZtafz9ZHUkPZ21tLEuzqj/eoNwswm0o0pU3eAVj7IU3i+Ul99hU+L3HgBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:38:33.277804Z","signed_message":"canonical_sha256_bytes"},"source_id":"1001.5132","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ad97c5b728c18aad9a651bd22f79e18731138f86609a2d18e9d0c35a2f35fc61","sha256:74aaa348c7a3c52f2a937fccd424aff821c9cc500f246bf5ea449850d529dafe"],"state_sha256":"47fce2cd8544dac22d5a13c65993b0924d15199b19de45f371bbedabe10915a7"}