{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:Z52F4O6ATORHLGMLXM2B3MGP66","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":"0c7eaa98021739bebe42fd99bc9402961112388e4e8bd774f3e2a9e987aa7d2c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2026-06-24T14:26:48Z","title_canon_sha256":"9a1d41d805cb71905c3f51375b0766ad72075f105c023d52c09f49e05869e559"},"schema_version":"1.0","source":{"id":"2606.25885","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.25885","created_at":"2026-06-25T01:18:42Z"},{"alias_kind":"arxiv_version","alias_value":"2606.25885v1","created_at":"2026-06-25T01:18:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.25885","created_at":"2026-06-25T01:18:42Z"},{"alias_kind":"pith_short_12","alias_value":"Z52F4O6ATORH","created_at":"2026-06-25T01:18:42Z"},{"alias_kind":"pith_short_16","alias_value":"Z52F4O6ATORHLGML","created_at":"2026-06-25T01:18:42Z"},{"alias_kind":"pith_short_8","alias_value":"Z52F4O6A","created_at":"2026-06-25T01:18:42Z"}],"graph_snapshots":[{"event_id":"sha256:5dd71c61925a6a0c4072f57cd6a323f27c373a81ba74c647c37484c60b2e10a5","target":"graph","created_at":"2026-06-25T01:18:42Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2606.25885/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Recently, a generalization of the Ces\\`aro operator to several variables was introduced as a tuple acting on the Drury-Arveson space \\cite{P}. We determine the norm of these Ces\\`aro-type operators and utilize it along with this Ces\\`aro tuple definition to generalize the classical Rhaly operator and recover some basic facts about this operator when applied to the generalization.","authors_text":"Michael R. Pilla","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2026-06-24T14:26:48Z","title":"Rhaly-Type Operators in Several Complex Variables"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.25885","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":"sha256:012b5e7b87296cb2266f55842f39dd8f832428d3e86ff38e930e670df273d6c8","target":"record","created_at":"2026-06-25T01:18:42Z","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":"0c7eaa98021739bebe42fd99bc9402961112388e4e8bd774f3e2a9e987aa7d2c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2026-06-24T14:26:48Z","title_canon_sha256":"9a1d41d805cb71905c3f51375b0766ad72075f105c023d52c09f49e05869e559"},"schema_version":"1.0","source":{"id":"2606.25885","kind":"arxiv","version":1}},"canonical_sha256":"cf745e3bc09ba275998bbb341db0cff7ae4fe4ed889be067fbae2c955203c5c8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cf745e3bc09ba275998bbb341db0cff7ae4fe4ed889be067fbae2c955203c5c8","first_computed_at":"2026-06-25T01:18:42.253198Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-25T01:18:42.253198Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"R9HiWeJyaEKyJGrqDaGmMmS5G0z/eXIoOM2WxovJLjva+PL/B1nBaK2zsG5W0CEhV1EOuvcpGRTAS2iJdAIHDw==","signature_status":"signed_v1","signed_at":"2026-06-25T01:18:42.253553Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.25885","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:012b5e7b87296cb2266f55842f39dd8f832428d3e86ff38e930e670df273d6c8","sha256:5dd71c61925a6a0c4072f57cd6a323f27c373a81ba74c647c37484c60b2e10a5"],"state_sha256":"d040dbd69a431021bf6715d750fa8e14f0fea99f75c67211fa5267e186b6b5fc"}