{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:GI26T6OMAXX3M6Z32ZHZNKKEA5","short_pith_number":"pith:GI26T6OM","canonical_record":{"source":{"id":"1002.4640","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2010-02-24T21:27:43Z","cross_cats_sorted":["math.OA"],"title_canon_sha256":"c2d13155ef051c2e81a77290b19228b5e381ae1056f4cb036ce6a9752e4bab1b","abstract_canon_sha256":"fbd2b13fcd7bb15f6a6393f4f43dd015b8bc152b93e2502d97d7b232919e0cc6"},"schema_version":"1.0"},"canonical_sha256":"3235e9f9cc05efb67b3bd64f96a944075c1492df0dd536be0f3861e6c8349447","source":{"kind":"arxiv","id":"1002.4640","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1002.4640","created_at":"2026-05-18T03:08:27Z"},{"alias_kind":"arxiv_version","alias_value":"1002.4640v2","created_at":"2026-05-18T03:08:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1002.4640","created_at":"2026-05-18T03:08:27Z"},{"alias_kind":"pith_short_12","alias_value":"GI26T6OMAXX3","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_16","alias_value":"GI26T6OMAXX3M6Z3","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_8","alias_value":"GI26T6OM","created_at":"2026-05-18T12:26:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:GI26T6OMAXX3M6Z32ZHZNKKEA5","target":"record","payload":{"canonical_record":{"source":{"id":"1002.4640","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2010-02-24T21:27:43Z","cross_cats_sorted":["math.OA"],"title_canon_sha256":"c2d13155ef051c2e81a77290b19228b5e381ae1056f4cb036ce6a9752e4bab1b","abstract_canon_sha256":"fbd2b13fcd7bb15f6a6393f4f43dd015b8bc152b93e2502d97d7b232919e0cc6"},"schema_version":"1.0"},"canonical_sha256":"3235e9f9cc05efb67b3bd64f96a944075c1492df0dd536be0f3861e6c8349447","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:08:27.546654Z","signature_b64":"5socsf0N6ddheboLUrjs18dghQXS0nYjl1PWEclQy4zzl/P48sXpib0esQMfKPE27o0/a0vrnSvBnBeT6JxoDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3235e9f9cc05efb67b3bd64f96a944075c1492df0dd536be0f3861e6c8349447","last_reissued_at":"2026-05-18T03:08:27.545819Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:08:27.545819Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1002.4640","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":"2026-05-18T03:08:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"il2Ln+Lme6Ch+9fYRtzgvh9hS8xnxphwhfPWrejcPt6XK64JRZZOky2XqrkIqHLNf5JmJcSXkMLCmOLBpuYjBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T21:55:35.952615Z"},"content_sha256":"060be07e62454e67c1a7a0920eddf791d66e9702b1ee51af948e8a9792664703","schema_version":"1.0","event_id":"sha256:060be07e62454e67c1a7a0920eddf791d66e9702b1ee51af948e8a9792664703"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:GI26T6OMAXX3M6Z32ZHZNKKEA5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Essential Spectra of Quasi-parabolic Composition Operators on Hardy Spaces of Analytic Functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OA"],"primary_cat":"math.FA","authors_text":"Ugur Gul","submitted_at":"2010-02-24T21:27:43Z","abstract_excerpt":"In this work we study the essential spectra of composition operators on Hardy spaces of analytic functions which might be termed as \"quasi-parabolic\". This is the class of composition operators on H^{2} with symbols whose conjugate with the Cayley transform on the upper half-plane are of the form \\phi(z) = z+\\psi(z) where \\psi\\in H^{2}(\\mathbb{H}) and \\Im(\\psi(z)) >\\delta > 0. We especially examine the case where \\psi is discontinuous at infinity. A new method is devised to show that this type of composition operators fall in a C*-algebra of Toeplitz operators and Fourier multipliers. This met"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1002.4640","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":"2026-05-18T03:08:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"n6J3qfBG+BX5y/mAk6I0+5ctOnJUta8zs//YR0Zj1oMEl1rb48q58dCN7Ab1UxMRvoC8T2w5yw1R82KP2d1YBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T21:55:35.952958Z"},"content_sha256":"8a19c88810643212f8ab12432167781642caf11c6be680cdefd68d22685d89bb","schema_version":"1.0","event_id":"sha256:8a19c88810643212f8ab12432167781642caf11c6be680cdefd68d22685d89bb"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GI26T6OMAXX3M6Z32ZHZNKKEA5/bundle.json","state_url":"https://pith.science/pith/GI26T6OMAXX3M6Z32ZHZNKKEA5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GI26T6OMAXX3M6Z32ZHZNKKEA5/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":"2026-06-26T21:55:35Z","links":{"resolver":"https://pith.science/pith/GI26T6OMAXX3M6Z32ZHZNKKEA5","bundle":"https://pith.science/pith/GI26T6OMAXX3M6Z32ZHZNKKEA5/bundle.json","state":"https://pith.science/pith/GI26T6OMAXX3M6Z32ZHZNKKEA5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GI26T6OMAXX3M6Z32ZHZNKKEA5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:GI26T6OMAXX3M6Z32ZHZNKKEA5","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":"fbd2b13fcd7bb15f6a6393f4f43dd015b8bc152b93e2502d97d7b232919e0cc6","cross_cats_sorted":["math.OA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2010-02-24T21:27:43Z","title_canon_sha256":"c2d13155ef051c2e81a77290b19228b5e381ae1056f4cb036ce6a9752e4bab1b"},"schema_version":"1.0","source":{"id":"1002.4640","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1002.4640","created_at":"2026-05-18T03:08:27Z"},{"alias_kind":"arxiv_version","alias_value":"1002.4640v2","created_at":"2026-05-18T03:08:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1002.4640","created_at":"2026-05-18T03:08:27Z"},{"alias_kind":"pith_short_12","alias_value":"GI26T6OMAXX3","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_16","alias_value":"GI26T6OMAXX3M6Z3","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_8","alias_value":"GI26T6OM","created_at":"2026-05-18T12:26:07Z"}],"graph_snapshots":[{"event_id":"sha256:8a19c88810643212f8ab12432167781642caf11c6be680cdefd68d22685d89bb","target":"graph","created_at":"2026-05-18T03:08:27Z","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":"In this work we study the essential spectra of composition operators on Hardy spaces of analytic functions which might be termed as \"quasi-parabolic\". This is the class of composition operators on H^{2} with symbols whose conjugate with the Cayley transform on the upper half-plane are of the form \\phi(z) = z+\\psi(z) where \\psi\\in H^{2}(\\mathbb{H}) and \\Im(\\psi(z)) >\\delta > 0. We especially examine the case where \\psi is discontinuous at infinity. A new method is devised to show that this type of composition operators fall in a C*-algebra of Toeplitz operators and Fourier multipliers. This met","authors_text":"Ugur Gul","cross_cats":["math.OA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2010-02-24T21:27:43Z","title":"Essential Spectra of Quasi-parabolic Composition Operators on Hardy Spaces of Analytic Functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1002.4640","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":"sha256:060be07e62454e67c1a7a0920eddf791d66e9702b1ee51af948e8a9792664703","target":"record","created_at":"2026-05-18T03:08:27Z","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":"fbd2b13fcd7bb15f6a6393f4f43dd015b8bc152b93e2502d97d7b232919e0cc6","cross_cats_sorted":["math.OA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2010-02-24T21:27:43Z","title_canon_sha256":"c2d13155ef051c2e81a77290b19228b5e381ae1056f4cb036ce6a9752e4bab1b"},"schema_version":"1.0","source":{"id":"1002.4640","kind":"arxiv","version":2}},"canonical_sha256":"3235e9f9cc05efb67b3bd64f96a944075c1492df0dd536be0f3861e6c8349447","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3235e9f9cc05efb67b3bd64f96a944075c1492df0dd536be0f3861e6c8349447","first_computed_at":"2026-05-18T03:08:27.545819Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:08:27.545819Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5socsf0N6ddheboLUrjs18dghQXS0nYjl1PWEclQy4zzl/P48sXpib0esQMfKPE27o0/a0vrnSvBnBeT6JxoDg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:08:27.546654Z","signed_message":"canonical_sha256_bytes"},"source_id":"1002.4640","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:060be07e62454e67c1a7a0920eddf791d66e9702b1ee51af948e8a9792664703","sha256:8a19c88810643212f8ab12432167781642caf11c6be680cdefd68d22685d89bb"],"state_sha256":"581c7ff041fffc84eea9d76b4c15b20328de57b848ddc9e87b4201da41e5c443"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"33jSVDjvMdob6V790F+1ZH4doq/CTSl6DFuVcPYQBwBp0d540kAhnQtpsEr3jKKGWaPRBwlg05yrq8gPnpzYAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T21:55:35.955122Z","bundle_sha256":"310fb9af774153a954d11ae4dec041d35166a9113c168114932365eca95e3c94"}}