{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:CYUNI5PLZT7ASKA2J6TIHRNGAE","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":"7b77fa76929d794f529fb0767c822f6e1bf8e639533236c953a14a37906066cc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2026-06-26T16:05:38Z","title_canon_sha256":"771772a5fe6b876686a9ce1a23b353b4498d7394aa30121f6c01adeb87051970"},"schema_version":"1.0","source":{"id":"2606.28214","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.28214","created_at":"2026-06-29T01:15:09Z"},{"alias_kind":"arxiv_version","alias_value":"2606.28214v1","created_at":"2026-06-29T01:15:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.28214","created_at":"2026-06-29T01:15:09Z"},{"alias_kind":"pith_short_12","alias_value":"CYUNI5PLZT7A","created_at":"2026-06-29T01:15:09Z"},{"alias_kind":"pith_short_16","alias_value":"CYUNI5PLZT7ASKA2","created_at":"2026-06-29T01:15:09Z"},{"alias_kind":"pith_short_8","alias_value":"CYUNI5PL","created_at":"2026-06-29T01:15:09Z"}],"graph_snapshots":[{"event_id":"sha256:220149af829a77bf4d2f4091d424a3b30857fdaafe9cf19344eaf4ed02949ce6","target":"graph","created_at":"2026-06-29T01:15:09Z","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/2606.28214/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let $(T_1,\\ldots,T_d)$ be a commuting $d$-tuple of Ritt$_E$ operators on some UMD Banach space $X$. We show that $(T_1,\\ldots,T_d)$ admits a bounded $H^\\infty$-functional calculus if and only if $T_k$ is an $R$-Ritt$_E$ operator for every $k=1,\\ldots,d$, and the $d$-tuple $(T_1,\\ldots,T_d)$ admits an isometric dilation $(U_1,\\ldots,U_d)$ on some UMD Banach space $Y$ such that $(U_1,\\ldots,U_d)$ is polynomially bounded. In the case where $X$ further possesses property $(\\alpha)$, we establish other characterizations of the $H^\\infty$-functional calculus property for $(T_1,\\ldots,T_d)$ in terms ","authors_text":"Christian Le Merdy, M. N. Reshmi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2026-06-26T16:05:38Z","title":"Connecting $H^\\infty$-functional calculus and isometric dilations for commuting families of Ritt$_E$ operators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.28214","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":"sha256:449f243f05d71b1d3abd25e4e4b4e0a61679d4170d19aa05c0864fbb652c2cd3","target":"record","created_at":"2026-06-29T01:15:09Z","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":"7b77fa76929d794f529fb0767c822f6e1bf8e639533236c953a14a37906066cc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2026-06-26T16:05:38Z","title_canon_sha256":"771772a5fe6b876686a9ce1a23b353b4498d7394aa30121f6c01adeb87051970"},"schema_version":"1.0","source":{"id":"2606.28214","kind":"arxiv","version":1}},"canonical_sha256":"1628d475ebccfe09281a4fa683c5a6010433a90033eb082fd263cd2abd220828","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1628d475ebccfe09281a4fa683c5a6010433a90033eb082fd263cd2abd220828","first_computed_at":"2026-06-29T01:15:09.495848Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-29T01:15:09.495848Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+sDk4a8//B1yeE6rExU9morzUcUTCkalxTG3HZlDZdjOUbfKiY3EP9IiE71CG+85c3+nLctjG5BQLq7WA527BA==","signature_status":"signed_v1","signed_at":"2026-06-29T01:15:09.496265Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.28214","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:449f243f05d71b1d3abd25e4e4b4e0a61679d4170d19aa05c0864fbb652c2cd3","sha256:220149af829a77bf4d2f4091d424a3b30857fdaafe9cf19344eaf4ed02949ce6"],"state_sha256":"87c473b681906661e0ad2c1a9a7f2a704ac71e54bccdbbd99a829417e67faf3f"}