{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:TQ3BVBYWZGCG5URQPUC4MV7ASE","short_pith_number":"pith:TQ3BVBYW","canonical_record":{"source":{"id":"1105.4801","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-05-24T15:25:43Z","cross_cats_sorted":["math.SP"],"title_canon_sha256":"03623db6b4abfb2432ae501c8ab47cbc36f75ef02c750189a50f56cf515414d3","abstract_canon_sha256":"30293d6394554f5647c8ea56c963a8556f999720ddee0fcb62af6e62336e76bd"},"schema_version":"1.0"},"canonical_sha256":"9c361a8716c9846ed2307d05c657e09134d835eab03da2fe878af69fd6c09361","source":{"kind":"arxiv","id":"1105.4801","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1105.4801","created_at":"2026-05-18T04:21:21Z"},{"alias_kind":"arxiv_version","alias_value":"1105.4801v1","created_at":"2026-05-18T04:21:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.4801","created_at":"2026-05-18T04:21:21Z"},{"alias_kind":"pith_short_12","alias_value":"TQ3BVBYWZGCG","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_16","alias_value":"TQ3BVBYWZGCG5URQ","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_8","alias_value":"TQ3BVBYW","created_at":"2026-05-18T12:26:42Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:TQ3BVBYWZGCG5URQPUC4MV7ASE","target":"record","payload":{"canonical_record":{"source":{"id":"1105.4801","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-05-24T15:25:43Z","cross_cats_sorted":["math.SP"],"title_canon_sha256":"03623db6b4abfb2432ae501c8ab47cbc36f75ef02c750189a50f56cf515414d3","abstract_canon_sha256":"30293d6394554f5647c8ea56c963a8556f999720ddee0fcb62af6e62336e76bd"},"schema_version":"1.0"},"canonical_sha256":"9c361a8716c9846ed2307d05c657e09134d835eab03da2fe878af69fd6c09361","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:21:21.783138Z","signature_b64":"ly19lDZM2s2KmDTbSGuI/y91L+KXQiodphzZDcEaJml9Nz72/lNyp1L3hsjpjo+Ccz8+8BSgSlb4jdLCwH9eDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9c361a8716c9846ed2307d05c657e09134d835eab03da2fe878af69fd6c09361","last_reissued_at":"2026-05-18T04:21:21.782614Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:21:21.782614Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1105.4801","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:21:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xtIJYd3g4rI/LMPJIL6RKLf7JNu6VsxArlxVboD7ziWv0vWK5ioq8XmpzgOCfqMCTGjgLUS6uKeyBXzWieBYAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T08:46:59.220720Z"},"content_sha256":"98ab9791db6b743e5226b1c758d96a1a72fb0c24daea262be4314d9744fa2e53","schema_version":"1.0","event_id":"sha256:98ab9791db6b743e5226b1c758d96a1a72fb0c24daea262be4314d9744fa2e53"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:TQ3BVBYWZGCG5URQPUC4MV7ASE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Eigenvalues and subelliptic estimates for non-selfadjoint semiclassical operators with double characteristics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.SP"],"primary_cat":"math.AP","authors_text":"Karel Pravda-Starov, Michael Hitrik","submitted_at":"2011-05-24T15:25:43Z","abstract_excerpt":"For a class of non-selfadjoint $h$--pseudodifferential operators with double characteristics, we give a precise description of the spectrum and establish accurate semiclassical resolvent estimates in a neighborhood of the origin. Specifically, assuming that the quadratic approximations of the principal symbol of the operator along the double characteristics enjoy a partial ellipticity property along a suitable subspace of the phase space, namely their singular space, we give a precise description of the spectrum of the operator in an ${\\cal O}(h)$--neighborhood of the origin. Moreover, when al"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.4801","kind":"arxiv","version":1},"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":"2026-05-18T04:21:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0WE3sL7t+UWxGtf+VQTEX+hvxp8L4a5mny0C1PEp+8CbroOw6BGm5CW3OsYd933RRtJjE1tGWB03NYsUDP7yBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T08:46:59.221399Z"},"content_sha256":"ed59efaeb04c2f0aa89e5069e5e7922d25e8a80c51fd4525e094b700f2ee00ec","schema_version":"1.0","event_id":"sha256:ed59efaeb04c2f0aa89e5069e5e7922d25e8a80c51fd4525e094b700f2ee00ec"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TQ3BVBYWZGCG5URQPUC4MV7ASE/bundle.json","state_url":"https://pith.science/pith/TQ3BVBYWZGCG5URQPUC4MV7ASE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TQ3BVBYWZGCG5URQPUC4MV7ASE/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":"2026-05-30T08:46:59Z","links":{"resolver":"https://pith.science/pith/TQ3BVBYWZGCG5URQPUC4MV7ASE","bundle":"https://pith.science/pith/TQ3BVBYWZGCG5URQPUC4MV7ASE/bundle.json","state":"https://pith.science/pith/TQ3BVBYWZGCG5URQPUC4MV7ASE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TQ3BVBYWZGCG5URQPUC4MV7ASE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:TQ3BVBYWZGCG5URQPUC4MV7ASE","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":"30293d6394554f5647c8ea56c963a8556f999720ddee0fcb62af6e62336e76bd","cross_cats_sorted":["math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-05-24T15:25:43Z","title_canon_sha256":"03623db6b4abfb2432ae501c8ab47cbc36f75ef02c750189a50f56cf515414d3"},"schema_version":"1.0","source":{"id":"1105.4801","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1105.4801","created_at":"2026-05-18T04:21:21Z"},{"alias_kind":"arxiv_version","alias_value":"1105.4801v1","created_at":"2026-05-18T04:21:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.4801","created_at":"2026-05-18T04:21:21Z"},{"alias_kind":"pith_short_12","alias_value":"TQ3BVBYWZGCG","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_16","alias_value":"TQ3BVBYWZGCG5URQ","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_8","alias_value":"TQ3BVBYW","created_at":"2026-05-18T12:26:42Z"}],"graph_snapshots":[{"event_id":"sha256:ed59efaeb04c2f0aa89e5069e5e7922d25e8a80c51fd4525e094b700f2ee00ec","target":"graph","created_at":"2026-05-18T04:21:21Z","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":"For a class of non-selfadjoint $h$--pseudodifferential operators with double characteristics, we give a precise description of the spectrum and establish accurate semiclassical resolvent estimates in a neighborhood of the origin. Specifically, assuming that the quadratic approximations of the principal symbol of the operator along the double characteristics enjoy a partial ellipticity property along a suitable subspace of the phase space, namely their singular space, we give a precise description of the spectrum of the operator in an ${\\cal O}(h)$--neighborhood of the origin. Moreover, when al","authors_text":"Karel Pravda-Starov, Michael Hitrik","cross_cats":["math.SP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-05-24T15:25:43Z","title":"Eigenvalues and subelliptic estimates for non-selfadjoint semiclassical operators with double characteristics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.4801","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":"sha256:98ab9791db6b743e5226b1c758d96a1a72fb0c24daea262be4314d9744fa2e53","target":"record","created_at":"2026-05-18T04:21:21Z","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":"30293d6394554f5647c8ea56c963a8556f999720ddee0fcb62af6e62336e76bd","cross_cats_sorted":["math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-05-24T15:25:43Z","title_canon_sha256":"03623db6b4abfb2432ae501c8ab47cbc36f75ef02c750189a50f56cf515414d3"},"schema_version":"1.0","source":{"id":"1105.4801","kind":"arxiv","version":1}},"canonical_sha256":"9c361a8716c9846ed2307d05c657e09134d835eab03da2fe878af69fd6c09361","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9c361a8716c9846ed2307d05c657e09134d835eab03da2fe878af69fd6c09361","first_computed_at":"2026-05-18T04:21:21.782614Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:21:21.782614Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ly19lDZM2s2KmDTbSGuI/y91L+KXQiodphzZDcEaJml9Nz72/lNyp1L3hsjpjo+Ccz8+8BSgSlb4jdLCwH9eDA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:21:21.783138Z","signed_message":"canonical_sha256_bytes"},"source_id":"1105.4801","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:98ab9791db6b743e5226b1c758d96a1a72fb0c24daea262be4314d9744fa2e53","sha256:ed59efaeb04c2f0aa89e5069e5e7922d25e8a80c51fd4525e094b700f2ee00ec"],"state_sha256":"01024f7717659c1670d4d5da9d0dcdfa95000743b20c422dfc8e676186ea7a68"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oUQCX6RwZdJklwDgJhXMb+F05YwQFnkbRfTMtIGC1rvuBS8t9NIVLN0Xm8p+OhpNL1ikmlbxy7U9pCCjuXRjCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T08:46:59.224797Z","bundle_sha256":"bd2e46e66c1ee4231b0aaab8672770d47b2c605414cd599e6c44635629dd4f2d"}}