{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:JJL6H6QOOHH5UIEVG2ID6BGBUA","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":"401ae2c620dc86d3c5f0816a7032a84dafa90f82b786409b3099730f02ba0dde","cross_cats_sorted":["math.OA"],"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.FA","submitted_at":"2010-04-01T12:40:50Z","title_canon_sha256":"742c22932b1be3dd5021bb69bf37fde9b44a5bd83885180c9a2e0b234e1b14c7"},"schema_version":"1.0","source":{"id":"1004.0121","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1004.0121","created_at":"2026-05-18T02:24:18Z"},{"alias_kind":"arxiv_version","alias_value":"1004.0121v2","created_at":"2026-05-18T02:24:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1004.0121","created_at":"2026-05-18T02:24:18Z"},{"alias_kind":"pith_short_12","alias_value":"JJL6H6QOOHH5","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_16","alias_value":"JJL6H6QOOHH5UIEV","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_8","alias_value":"JJL6H6QO","created_at":"2026-05-18T12:26:09Z"}],"graph_snapshots":[{"event_id":"sha256:9f0a08c34a12f83be2a0e8c32571b36876bde2ee2e03f98022d80a1a457afac5","target":"graph","created_at":"2026-05-18T02:24:18Z","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":"One of the major questions in the theory of Toeplitz operators on the Bergman space over the unit disk $\\mathbb D$ in the complex plane $\\mathbb C$ is a complete description of the commutant of a given Toeplitz operator, that is the set of all Toeplitz operators that commute with it. In \\cite{l}, the first author obtained a complete description of the commutant of Toeplitz operator $T$ with any quasihomogeneous symbol $\\phi(r)e^{ip\\theta}, p>0$ in case it has a Toeplitz p-th root $S$ with symbol $\\psi(r)e^{i\\theta}$, namely, commutant of $T$ is the closure of the linear space generated by powe","authors_text":"Issam Louhichi, N. V. Rao","cross_cats":["math.OA"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.FA","submitted_at":"2010-04-01T12:40:50Z","title":"Roots of Toeplitz Operators on the Bergman space"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1004.0121","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:dfb9aef43aa1f85527fb56048229f98b1301f7b74123d52d8ee19c60ebcaed48","target":"record","created_at":"2026-05-18T02:24:18Z","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":"401ae2c620dc86d3c5f0816a7032a84dafa90f82b786409b3099730f02ba0dde","cross_cats_sorted":["math.OA"],"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.FA","submitted_at":"2010-04-01T12:40:50Z","title_canon_sha256":"742c22932b1be3dd5021bb69bf37fde9b44a5bd83885180c9a2e0b234e1b14c7"},"schema_version":"1.0","source":{"id":"1004.0121","kind":"arxiv","version":2}},"canonical_sha256":"4a57e3fa0e71cfda209536903f04c1a02677561adf96c727e1a781c6b06dd5d4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4a57e3fa0e71cfda209536903f04c1a02677561adf96c727e1a781c6b06dd5d4","first_computed_at":"2026-05-18T02:24:18.257169Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:24:18.257169Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"q369prA9zL/gMkOMXRK+U8S7C4uHKoe7N5s8uSQWqvyQ0EHvXBKnAjPZ5JOY5eJ+biZ660UtjoLvc6pHQjZbDg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:24:18.257822Z","signed_message":"canonical_sha256_bytes"},"source_id":"1004.0121","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dfb9aef43aa1f85527fb56048229f98b1301f7b74123d52d8ee19c60ebcaed48","sha256:9f0a08c34a12f83be2a0e8c32571b36876bde2ee2e03f98022d80a1a457afac5"],"state_sha256":"636dc588202b5d38fbc7a2aafce0378efddbd7bef563573620648cd608e3bb92"}