{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:AS5KTU7YTUOGHLXES4XYSOWGBN","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":"fb81a2c1dfc16f4ed41f3ea64afd1b6fdb5230d43890584c5a0c1362a6796d12","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-05-01T00:21:31Z","title_canon_sha256":"e5691342f3259a626698294ed9c02dd15a1bc8736ae72f6fde76721d0a054d77"},"schema_version":"1.0","source":{"id":"1805.00141","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.00141","created_at":"2026-05-18T00:08:20Z"},{"alias_kind":"arxiv_version","alias_value":"1805.00141v2","created_at":"2026-05-18T00:08:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.00141","created_at":"2026-05-18T00:08:20Z"},{"alias_kind":"pith_short_12","alias_value":"AS5KTU7YTUOG","created_at":"2026-05-18T12:32:13Z"},{"alias_kind":"pith_short_16","alias_value":"AS5KTU7YTUOGHLXE","created_at":"2026-05-18T12:32:13Z"},{"alias_kind":"pith_short_8","alias_value":"AS5KTU7Y","created_at":"2026-05-18T12:32:13Z"}],"graph_snapshots":[{"event_id":"sha256:830d2a2fba753fbb7aab55dd67ac9b7978ce131cf33155ba188544b644f50282","target":"graph","created_at":"2026-05-18T00:08:20Z","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":"On the unit ball B^n we consider the weighted Bergman spaces H_\\lambda and their Toeplitz operators with bounded symbols. It is known from our previous work that if a closed subgroup H of \\widetilde{\\SU(n,1)} has a multiplicity-free restriction for the holomorphic discrete series of $\\widetilde{\\SU(n,1)}$, then the family of Toeplitz operators with H-invariant symbols pairwise commute. In this work we consider the case of maximal abelian subgroups of \\widetilde{\\SU(n,1)} and provide a detailed proof of the pairwise commutativity of the corresponding Toeplitz operators. To achieve this we expli","authors_text":"G. Olafsson, M. Dawson, R. Quiroga-Barranco","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-05-01T00:21:31Z","title":"The Restriction Principle and Commuting Families of Toeplitz Operators on the Unit Ball"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.00141","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:cb124e9f10e46053b51d63676ad9da4f92c4e9fed6a5aa6fb3c4072e2f3c7f60","target":"record","created_at":"2026-05-18T00:08:20Z","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":"fb81a2c1dfc16f4ed41f3ea64afd1b6fdb5230d43890584c5a0c1362a6796d12","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-05-01T00:21:31Z","title_canon_sha256":"e5691342f3259a626698294ed9c02dd15a1bc8736ae72f6fde76721d0a054d77"},"schema_version":"1.0","source":{"id":"1805.00141","kind":"arxiv","version":2}},"canonical_sha256":"04baa9d3f89d1c63aee4972f893ac60b4e1a0e62afdcc7eb2ced7a0616d058bd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"04baa9d3f89d1c63aee4972f893ac60b4e1a0e62afdcc7eb2ced7a0616d058bd","first_computed_at":"2026-05-18T00:08:20.766255Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:08:20.766255Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6IOvoWwkKEIWUazP7ogImEKRTE9hKVYS9PdC5hNgF5YcuQMputv2pftQNs/4KX/igeo83J0LjFhSrz2iM9B8Ag==","signature_status":"signed_v1","signed_at":"2026-05-18T00:08:20.766754Z","signed_message":"canonical_sha256_bytes"},"source_id":"1805.00141","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cb124e9f10e46053b51d63676ad9da4f92c4e9fed6a5aa6fb3c4072e2f3c7f60","sha256:830d2a2fba753fbb7aab55dd67ac9b7978ce131cf33155ba188544b644f50282"],"state_sha256":"055f3f373ee06ec0e3955cb02c40e592e15154657af3286d1782b36edd7045ec"}