{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:L54AOOPIRZOBWEHLEXVUWWVNLX","short_pith_number":"pith:L54AOOPI","canonical_record":{"source":{"id":"1409.6101","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-09-22T08:10:06Z","cross_cats_sorted":["math.OA"],"title_canon_sha256":"854f1cb1f30213955d05c3e6309fc558fab80e22bf6301948b2c50921fff6488","abstract_canon_sha256":"1fea7c1b98a4d4b8522f60ded98d3cbdd74bd7aca400f5c90f673920275f4e6d"},"schema_version":"1.0"},"canonical_sha256":"5f780739e88e5c1b10eb25eb4b5aad5de19524c5219054aceb13a2731a9df353","source":{"kind":"arxiv","id":"1409.6101","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.6101","created_at":"2026-05-18T01:16:33Z"},{"alias_kind":"arxiv_version","alias_value":"1409.6101v2","created_at":"2026-05-18T01:16:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.6101","created_at":"2026-05-18T01:16:33Z"},{"alias_kind":"pith_short_12","alias_value":"L54AOOPIRZOB","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_16","alias_value":"L54AOOPIRZOBWEHL","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_8","alias_value":"L54AOOPI","created_at":"2026-05-18T12:28:35Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:L54AOOPIRZOBWEHLEXVUWWVNLX","target":"record","payload":{"canonical_record":{"source":{"id":"1409.6101","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-09-22T08:10:06Z","cross_cats_sorted":["math.OA"],"title_canon_sha256":"854f1cb1f30213955d05c3e6309fc558fab80e22bf6301948b2c50921fff6488","abstract_canon_sha256":"1fea7c1b98a4d4b8522f60ded98d3cbdd74bd7aca400f5c90f673920275f4e6d"},"schema_version":"1.0"},"canonical_sha256":"5f780739e88e5c1b10eb25eb4b5aad5de19524c5219054aceb13a2731a9df353","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:16:33.519816Z","signature_b64":"hmjz5DhbCBuFZhl6vFeVt9wMDfERCDwzltnQBfEXAOYckbLzCPcofDl+CrK+QEXtnXGmJshs3L2/OHkkMYGyAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5f780739e88e5c1b10eb25eb4b5aad5de19524c5219054aceb13a2731a9df353","last_reissued_at":"2026-05-18T01:16:33.519014Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:16:33.519014Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1409.6101","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:16:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UyD1RQd4tWcDGcrETdgg7yWy1J99wf5+rHEZ60X3jCt6/jRs+WUQbzrHmgsc1q4WcjFFnR72eEK7kjxl4N9lCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T08:58:46.118021Z"},"content_sha256":"e5aab48bd62879fb277ba6a1a71076efe9bc6ac76f4b232a16635bd504882669","schema_version":"1.0","event_id":"sha256:e5aab48bd62879fb277ba6a1a71076efe9bc6ac76f4b232a16635bd504882669"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:L54AOOPIRZOBWEHLEXVUWWVNLX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Functional calculus on real interpolation spaces for generators of $C_{0}$-groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OA"],"primary_cat":"math.FA","authors_text":"Jan Rozendaal, Markus Haase","submitted_at":"2014-09-22T08:10:06Z","abstract_excerpt":"We study functional calculus properties of $C_{0}$-groups on real interpolation spaces, using transference principles. We obtain interpolation versions of the classical transference principle for bounded groups and of a recent transference principle for unbounded groups. Then we show that each group generator on a Banach space has a bounded $H^{\\infty}_{1}$-calculus on real interpolation spaces. Additional results are derived from this."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.6101","kind":"arxiv","version":2},"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":"2026-05-18T01:16:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LoYCc91iwyimrbhsIQPzvExjoJaux88ugAPTT8CGqiC0m3lSpnYtnWAWOox3tyL1czKvQESR97uhUOXZ6DdHAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T08:58:46.118391Z"},"content_sha256":"89b079f2d3d55e9b835953f96001838c8901ec632cec44bf8e144af7e156df23","schema_version":"1.0","event_id":"sha256:89b079f2d3d55e9b835953f96001838c8901ec632cec44bf8e144af7e156df23"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/L54AOOPIRZOBWEHLEXVUWWVNLX/bundle.json","state_url":"https://pith.science/pith/L54AOOPIRZOBWEHLEXVUWWVNLX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/L54AOOPIRZOBWEHLEXVUWWVNLX/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":"2026-06-26T08:58:46Z","links":{"resolver":"https://pith.science/pith/L54AOOPIRZOBWEHLEXVUWWVNLX","bundle":"https://pith.science/pith/L54AOOPIRZOBWEHLEXVUWWVNLX/bundle.json","state":"https://pith.science/pith/L54AOOPIRZOBWEHLEXVUWWVNLX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/L54AOOPIRZOBWEHLEXVUWWVNLX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:L54AOOPIRZOBWEHLEXVUWWVNLX","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":"1fea7c1b98a4d4b8522f60ded98d3cbdd74bd7aca400f5c90f673920275f4e6d","cross_cats_sorted":["math.OA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-09-22T08:10:06Z","title_canon_sha256":"854f1cb1f30213955d05c3e6309fc558fab80e22bf6301948b2c50921fff6488"},"schema_version":"1.0","source":{"id":"1409.6101","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.6101","created_at":"2026-05-18T01:16:33Z"},{"alias_kind":"arxiv_version","alias_value":"1409.6101v2","created_at":"2026-05-18T01:16:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.6101","created_at":"2026-05-18T01:16:33Z"},{"alias_kind":"pith_short_12","alias_value":"L54AOOPIRZOB","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_16","alias_value":"L54AOOPIRZOBWEHL","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_8","alias_value":"L54AOOPI","created_at":"2026-05-18T12:28:35Z"}],"graph_snapshots":[{"event_id":"sha256:89b079f2d3d55e9b835953f96001838c8901ec632cec44bf8e144af7e156df23","target":"graph","created_at":"2026-05-18T01:16:33Z","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 study functional calculus properties of $C_{0}$-groups on real interpolation spaces, using transference principles. We obtain interpolation versions of the classical transference principle for bounded groups and of a recent transference principle for unbounded groups. Then we show that each group generator on a Banach space has a bounded $H^{\\infty}_{1}$-calculus on real interpolation spaces. Additional results are derived from this.","authors_text":"Jan Rozendaal, Markus Haase","cross_cats":["math.OA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-09-22T08:10:06Z","title":"Functional calculus on real interpolation spaces for generators of $C_{0}$-groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.6101","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:e5aab48bd62879fb277ba6a1a71076efe9bc6ac76f4b232a16635bd504882669","target":"record","created_at":"2026-05-18T01:16:33Z","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":"1fea7c1b98a4d4b8522f60ded98d3cbdd74bd7aca400f5c90f673920275f4e6d","cross_cats_sorted":["math.OA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-09-22T08:10:06Z","title_canon_sha256":"854f1cb1f30213955d05c3e6309fc558fab80e22bf6301948b2c50921fff6488"},"schema_version":"1.0","source":{"id":"1409.6101","kind":"arxiv","version":2}},"canonical_sha256":"5f780739e88e5c1b10eb25eb4b5aad5de19524c5219054aceb13a2731a9df353","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5f780739e88e5c1b10eb25eb4b5aad5de19524c5219054aceb13a2731a9df353","first_computed_at":"2026-05-18T01:16:33.519014Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:16:33.519014Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hmjz5DhbCBuFZhl6vFeVt9wMDfERCDwzltnQBfEXAOYckbLzCPcofDl+CrK+QEXtnXGmJshs3L2/OHkkMYGyAg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:16:33.519816Z","signed_message":"canonical_sha256_bytes"},"source_id":"1409.6101","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e5aab48bd62879fb277ba6a1a71076efe9bc6ac76f4b232a16635bd504882669","sha256:89b079f2d3d55e9b835953f96001838c8901ec632cec44bf8e144af7e156df23"],"state_sha256":"73cec4cecca6967d4cb264f5392783043263d64370a6350ce5ce34dba11434fd"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zZXvoYyEOJS+0JgCtSBlekrc/VWtkXCfgw42ImnxABPY9fnzJS+fVl5PHNJT1mZPYG+/QZ6zI8Ot4/jRyrg9Cg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T08:58:46.120401Z","bundle_sha256":"7c1db9065a3d9cdcfca500b1e4e45407fae50e3e0fd7c53be35b2c219ba408ff"}}