{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:CAIXIAZEJDG3GOCBHGZE2CFWKZ","short_pith_number":"pith:CAIXIAZE","canonical_record":{"source":{"id":"1701.06623","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-01-23T20:38:11Z","cross_cats_sorted":[],"title_canon_sha256":"ca2402afa4272b24fb5f34e42be6e5b891db0f66f65f99aa115223bff8a6dc61","abstract_canon_sha256":"c46ae06b8dec1b6e1490fd8b58e1365ec06c6fcc5d38dcd0e57ea37f84473637"},"schema_version":"1.0"},"canonical_sha256":"101174032448cdb3384139b24d08b6565746b46a35aa8171684220d21c95fa9a","source":{"kind":"arxiv","id":"1701.06623","version":5},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.06623","created_at":"2026-05-17T23:52:08Z"},{"alias_kind":"arxiv_version","alias_value":"1701.06623v5","created_at":"2026-05-17T23:52:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.06623","created_at":"2026-05-17T23:52:08Z"},{"alias_kind":"pith_short_12","alias_value":"CAIXIAZEJDG3","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_16","alias_value":"CAIXIAZEJDG3GOCB","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_8","alias_value":"CAIXIAZE","created_at":"2026-05-18T12:31:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:CAIXIAZEJDG3GOCBHGZE2CFWKZ","target":"record","payload":{"canonical_record":{"source":{"id":"1701.06623","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-01-23T20:38:11Z","cross_cats_sorted":[],"title_canon_sha256":"ca2402afa4272b24fb5f34e42be6e5b891db0f66f65f99aa115223bff8a6dc61","abstract_canon_sha256":"c46ae06b8dec1b6e1490fd8b58e1365ec06c6fcc5d38dcd0e57ea37f84473637"},"schema_version":"1.0"},"canonical_sha256":"101174032448cdb3384139b24d08b6565746b46a35aa8171684220d21c95fa9a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:52:08.609524Z","signature_b64":"CGFDVSAU52fCH0p4SzApm5rsqVaCZL4xAwRfNFgj7Udm270mgU9PsImgKio/7YIALH7fjNBVq+gnW6y6UI6FCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"101174032448cdb3384139b24d08b6565746b46a35aa8171684220d21c95fa9a","last_reissued_at":"2026-05-17T23:52:08.609063Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:52:08.609063Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1701.06623","source_version":5,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:52:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"q1zshUDfrTQmirulkzVYkrOjKH3zqulrfn+LhYpMKfWzttA8TtBo/yyE6yKFUuwvVmt9yk60YcL0TmLLaDtTAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T09:22:36.538708Z"},"content_sha256":"44942c511c8aab3c24e2aafb40194ea92e6accc0debe98999969fbfadf7d8d8a","schema_version":"1.0","event_id":"sha256:44942c511c8aab3c24e2aafb40194ea92e6accc0debe98999969fbfadf7d8d8a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:CAIXIAZEJDG3GOCBHGZE2CFWKZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"$H^\\infty$-calculus for semigroup generators on BMO","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Brian Simanek, Tao Mei, Tim Ferguson","submitted_at":"2017-01-23T20:38:11Z","abstract_excerpt":"We prove that the negative infinitesimal generator $L$ of a semigroup of positive contractions on $L^\\infty$ has a bounded $H^\\infty(S_\\eta^0)$-calculus on the associated Poisson semigroup-BMO space for any angle $\\eta>\\pi/2$, provided the semigroup satisfies Bakry-Emry's $\\Gamma_2 $ criterion. Our arguments only rely on the properties of the underlying semigroup and works well in the noncommutative setting. A key ingredient of our argument is a quasi monotone property for the subordinated semigroup $T_{t,\\alpha}=e^{-tL^\\alpha},0<\\alpha<1$, that is proved in the first half of the article."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.06623","kind":"arxiv","version":5},"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":"2026-05-17T23:52:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"B+XIV3Cls5KOUfDGV5Q6XY6gX8qetLzdxbtisrv+yphW46MpKQr3jEgelIDmOEX+oi8FntJ4r/+8Ea/LB0kMDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T09:22:36.539231Z"},"content_sha256":"acc31b376bc8bb4189a727a38a66b6ac4a33f42def0e28f50a49db1c6d63c876","schema_version":"1.0","event_id":"sha256:acc31b376bc8bb4189a727a38a66b6ac4a33f42def0e28f50a49db1c6d63c876"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CAIXIAZEJDG3GOCBHGZE2CFWKZ/bundle.json","state_url":"https://pith.science/pith/CAIXIAZEJDG3GOCBHGZE2CFWKZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CAIXIAZEJDG3GOCBHGZE2CFWKZ/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":"2026-05-25T09:22:36Z","links":{"resolver":"https://pith.science/pith/CAIXIAZEJDG3GOCBHGZE2CFWKZ","bundle":"https://pith.science/pith/CAIXIAZEJDG3GOCBHGZE2CFWKZ/bundle.json","state":"https://pith.science/pith/CAIXIAZEJDG3GOCBHGZE2CFWKZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CAIXIAZEJDG3GOCBHGZE2CFWKZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:CAIXIAZEJDG3GOCBHGZE2CFWKZ","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":"c46ae06b8dec1b6e1490fd8b58e1365ec06c6fcc5d38dcd0e57ea37f84473637","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-01-23T20:38:11Z","title_canon_sha256":"ca2402afa4272b24fb5f34e42be6e5b891db0f66f65f99aa115223bff8a6dc61"},"schema_version":"1.0","source":{"id":"1701.06623","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.06623","created_at":"2026-05-17T23:52:08Z"},{"alias_kind":"arxiv_version","alias_value":"1701.06623v5","created_at":"2026-05-17T23:52:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.06623","created_at":"2026-05-17T23:52:08Z"},{"alias_kind":"pith_short_12","alias_value":"CAIXIAZEJDG3","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_16","alias_value":"CAIXIAZEJDG3GOCB","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_8","alias_value":"CAIXIAZE","created_at":"2026-05-18T12:31:10Z"}],"graph_snapshots":[{"event_id":"sha256:acc31b376bc8bb4189a727a38a66b6ac4a33f42def0e28f50a49db1c6d63c876","target":"graph","created_at":"2026-05-17T23:52:08Z","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":"We prove that the negative infinitesimal generator $L$ of a semigroup of positive contractions on $L^\\infty$ has a bounded $H^\\infty(S_\\eta^0)$-calculus on the associated Poisson semigroup-BMO space for any angle $\\eta>\\pi/2$, provided the semigroup satisfies Bakry-Emry's $\\Gamma_2 $ criterion. Our arguments only rely on the properties of the underlying semigroup and works well in the noncommutative setting. A key ingredient of our argument is a quasi monotone property for the subordinated semigroup $T_{t,\\alpha}=e^{-tL^\\alpha},0<\\alpha<1$, that is proved in the first half of the article.","authors_text":"Brian Simanek, Tao Mei, Tim Ferguson","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-01-23T20:38:11Z","title":"$H^\\infty$-calculus for semigroup generators on BMO"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.06623","kind":"arxiv","version":5},"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":"sha256:44942c511c8aab3c24e2aafb40194ea92e6accc0debe98999969fbfadf7d8d8a","target":"record","created_at":"2026-05-17T23:52:08Z","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":"c46ae06b8dec1b6e1490fd8b58e1365ec06c6fcc5d38dcd0e57ea37f84473637","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-01-23T20:38:11Z","title_canon_sha256":"ca2402afa4272b24fb5f34e42be6e5b891db0f66f65f99aa115223bff8a6dc61"},"schema_version":"1.0","source":{"id":"1701.06623","kind":"arxiv","version":5}},"canonical_sha256":"101174032448cdb3384139b24d08b6565746b46a35aa8171684220d21c95fa9a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"101174032448cdb3384139b24d08b6565746b46a35aa8171684220d21c95fa9a","first_computed_at":"2026-05-17T23:52:08.609063Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:52:08.609063Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CGFDVSAU52fCH0p4SzApm5rsqVaCZL4xAwRfNFgj7Udm270mgU9PsImgKio/7YIALH7fjNBVq+gnW6y6UI6FCg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:52:08.609524Z","signed_message":"canonical_sha256_bytes"},"source_id":"1701.06623","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:44942c511c8aab3c24e2aafb40194ea92e6accc0debe98999969fbfadf7d8d8a","sha256:acc31b376bc8bb4189a727a38a66b6ac4a33f42def0e28f50a49db1c6d63c876"],"state_sha256":"e4fa1228d19159abc942f2e04b581f1ebf112558cef13a0a3d447ca8f0ec0ebd"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KUhE4X4cjSY50SJHWVzwGxoiEc5b//ahq1hQ90uKv2gn3MgmmCwQiOo0T4gSLw7fqLCyerR5dj9IzQMoizH/AA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T09:22:36.542412Z","bundle_sha256":"893b3221fd57f1196330f61ce60882a8432ee93dda853275694f0b60abaec80a"}}