{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:6R2DQFUI75SMDWG3ZB2NFWJUXI","short_pith_number":"pith:6R2DQFUI","canonical_record":{"source":{"id":"1001.5132","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2010-01-28T09:19:17Z","cross_cats_sorted":[],"title_canon_sha256":"2c8dc9169d34e82bfea00a2fae3e9128cabed7752582f2fb8b279388c88eac65","abstract_canon_sha256":"c9cd72bad9bcdb1f7bc74abfc92dd603e9188a92f07ed3749dc2b2c03c90cea1"},"schema_version":"1.0"},"canonical_sha256":"f474381688ff64c1d8dbc874d2d934ba041954da7db32a118ca38fdfc5f0604a","source":{"kind":"arxiv","id":"1001.5132","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"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:6R2DQFUI75SMDWG3ZB2NFWJUXI","target":"record","payload":{"canonical_record":{"source":{"id":"1001.5132","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2010-01-28T09:19:17Z","cross_cats_sorted":[],"title_canon_sha256":"2c8dc9169d34e82bfea00a2fae3e9128cabed7752582f2fb8b279388c88eac65","abstract_canon_sha256":"c9cd72bad9bcdb1f7bc74abfc92dd603e9188a92f07ed3749dc2b2c03c90cea1"},"schema_version":"1.0"},"canonical_sha256":"f474381688ff64c1d8dbc874d2d934ba041954da7db32a118ca38fdfc5f0604a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:38:33.277804Z","signature_b64":"HVrroBmvewDTb3lPDmDMJAHyamqgZtafz9ZHUkPZ21tLEuzqj/eoNwswm0o0pU3eAVj7IU3i+Ul99hU+L3HgBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f474381688ff64c1d8dbc874d2d934ba041954da7db32a118ca38fdfc5f0604a","last_reissued_at":"2026-05-18T03:38:33.277125Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:38:33.277125Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1001.5132","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:38:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZkhFQ6YHbEd8kMBHbabp0JYUzwRY9XjA31zrVlF+eKoqXhSEEWmD0EzQ5TFW8SLaXHgVtgS+EwgxGr71qHI9BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-05T06:56:40.701357Z"},"content_sha256":"ad97c5b728c18aad9a651bd22f79e18731138f86609a2d18e9d0c35a2f35fc61","schema_version":"1.0","event_id":"sha256:ad97c5b728c18aad9a651bd22f79e18731138f86609a2d18e9d0c35a2f35fc61"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:6R2DQFUI75SMDWG3ZB2NFWJUXI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Diophantine tori and nonselfadjoint inverse spectral problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SP","authors_text":"Michael A. Hall","submitted_at":"2010-01-28T09:19:17Z","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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1001.5132","kind":"arxiv","version":2},"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":"2026-05-18T03:38:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IQNJDtX+j5Zw08LxYtYYsmTcebNyKHLdLIL6aWzhklw7AtyMLogGeV6BgAStZ9742c/niRqU5mJB4EsWj1zHAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-05T06:56:40.701721Z"},"content_sha256":"74aaa348c7a3c52f2a937fccd424aff821c9cc500f246bf5ea449850d529dafe","schema_version":"1.0","event_id":"sha256:74aaa348c7a3c52f2a937fccd424aff821c9cc500f246bf5ea449850d529dafe"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6R2DQFUI75SMDWG3ZB2NFWJUXI/bundle.json","state_url":"https://pith.science/pith/6R2DQFUI75SMDWG3ZB2NFWJUXI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6R2DQFUI75SMDWG3ZB2NFWJUXI/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":"2026-07-05T06:56:40Z","links":{"resolver":"https://pith.science/pith/6R2DQFUI75SMDWG3ZB2NFWJUXI","bundle":"https://pith.science/pith/6R2DQFUI75SMDWG3ZB2NFWJUXI/bundle.json","state":"https://pith.science/pith/6R2DQFUI75SMDWG3ZB2NFWJUXI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6R2DQFUI75SMDWG3ZB2NFWJUXI/bundle.json"},"state":{"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"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Mnvg+eao4L7YKLMkhagDvKoHvZbBHjoGEZODKCceRmwyguZylvjMSewfntnsWabJBx9T5kwkUoeSSyUNwbDhAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-05T06:56:40.703752Z","bundle_sha256":"68d147c53a0605cb0799c86778345cc422b8d3b77162a9af3e3ed54bb7d9cf80"}}