{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2004:WKEYWZQGE5G5WLRKOWGB6BJS46","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":"674e0d08ab4e71dbafa78060acbebbf4fb9b1322907e9ba5a1374ccd2c5bbb10","cross_cats_sorted":["gr-qc","math.MP","math.SP"],"license":"","primary_cat":"math-ph","submitted_at":"2004-05-04T14:47:36Z","title_canon_sha256":"ee9589c749f24ee2f718341084deb9b57b888d3f163576d0d1b55b410c4d1c50"},"schema_version":"1.0","source":{"id":"math-ph/0405010","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math-ph/0405010","created_at":"2026-05-18T03:00:59Z"},{"alias_kind":"arxiv_version","alias_value":"math-ph/0405010v4","created_at":"2026-05-18T03:00:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math-ph/0405010","created_at":"2026-05-18T03:00:59Z"},{"alias_kind":"pith_short_12","alias_value":"WKEYWZQGE5G5","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_16","alias_value":"WKEYWZQGE5G5WLRK","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_8","alias_value":"WKEYWZQG","created_at":"2026-05-18T12:25:52Z"}],"graph_snapshots":[{"event_id":"sha256:ee3bdc7a90f5425beb0251a922def165a3ea66203e1b1faf4ed1980de3ef3a96","target":"graph","created_at":"2026-05-18T03:00:59Z","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 derive a spectral representation for the oblate spheroidal wave operator which is holomorphic in the aspherical parameter $\\Omega$ in a neighborhood of the real line. For real $\\Omega$, estimates are derived for all eigenvalue gaps uniformly in $\\Omega$.\n  The proof of the gap estimates is based on detailed estimates for complex solutions of the Riccati equation. The spectral representation for complex $\\Omega$ is derived using the theory of slightly non-selfadjoint perturbations.","authors_text":"Felix Finster, Harald Schmid","cross_cats":["gr-qc","math.MP","math.SP"],"headline":"","license":"","primary_cat":"math-ph","submitted_at":"2004-05-04T14:47:36Z","title":"Spectral Estimates and Non-Selfadjoint Perturbations of Spheroidal Wave Operators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/0405010","kind":"arxiv","version":4},"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:e9aff4ddcbd17a896592a19d221e9ed2308d8182174e1a03c516145ab1712318","target":"record","created_at":"2026-05-18T03:00:59Z","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":"674e0d08ab4e71dbafa78060acbebbf4fb9b1322907e9ba5a1374ccd2c5bbb10","cross_cats_sorted":["gr-qc","math.MP","math.SP"],"license":"","primary_cat":"math-ph","submitted_at":"2004-05-04T14:47:36Z","title_canon_sha256":"ee9589c749f24ee2f718341084deb9b57b888d3f163576d0d1b55b410c4d1c50"},"schema_version":"1.0","source":{"id":"math-ph/0405010","kind":"arxiv","version":4}},"canonical_sha256":"b2898b6606274ddb2e2a758c1f0532e7bf41145f755d68221ec6548f52029731","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b2898b6606274ddb2e2a758c1f0532e7bf41145f755d68221ec6548f52029731","first_computed_at":"2026-05-18T03:00:59.907960Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:00:59.907960Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OrINyXgZwklAiaSCzs8igKizhZGalCDkLgbfdXSEbJybtdEOKstSRIqjVTAiOP+5f6K4of6RrJoM4F/XY4swDg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:00:59.908846Z","signed_message":"canonical_sha256_bytes"},"source_id":"math-ph/0405010","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e9aff4ddcbd17a896592a19d221e9ed2308d8182174e1a03c516145ab1712318","sha256:ee3bdc7a90f5425beb0251a922def165a3ea66203e1b1faf4ed1980de3ef3a96"],"state_sha256":"1c6d5f39661de5e5ec72784cdf6ee00d301fad2c388a84e1adde5ea6c530b4b9"}