{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:CCCOUDV3FELS7YYIFAKYT3M7EL","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":"d9c23eeec6f9d8fbebd8e433d6473a826f7ed8b7f9feb127d137533055e71307","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2019-06-16T13:10:02Z","title_canon_sha256":"a632462ca74edf8d0ba088137abb131af0818c8c32579e48bee18f1f8170d243"},"schema_version":"1.0","source":{"id":"1906.06677","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1906.06677","created_at":"2026-07-05T02:21:49Z"},{"alias_kind":"arxiv_version","alias_value":"1906.06677v2","created_at":"2026-07-05T02:21:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1906.06677","created_at":"2026-07-05T02:21:49Z"},{"alias_kind":"pith_short_12","alias_value":"CCCOUDV3FELS","created_at":"2026-07-05T02:21:49Z"},{"alias_kind":"pith_short_16","alias_value":"CCCOUDV3FELS7YYI","created_at":"2026-07-05T02:21:49Z"},{"alias_kind":"pith_short_8","alias_value":"CCCOUDV3","created_at":"2026-07-05T02:21:49Z"}],"graph_snapshots":[{"event_id":"sha256:8b29fb1066040c8006a06a5c82b0d3b27389ecaa8ebcb2f2ec0676a96217be72","target":"graph","created_at":"2026-07-05T02:21:49Z","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/1906.06677/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We show that the Rochberg spaces induced by complex interpolation form themselves complex interpolation scales, obtain the interpolated spaces and associated derivations. We present our results in the context of analytic families of Banach spaces and study the problem of determining the Rochberg spaces induced by these new families.","authors_text":"F\\'elix Cabello S\\'anchez, Jes\\'us M. F. Castillo, Willian H. G. Correa","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2019-06-16T13:10:02Z","title":"Higher order derivatives of analytic families of Banach spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.06677","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:f6cb07bce10d6ec1f2089aed13ec3a55f15e7e48ebfffc6835c35cfecf0d9a3f","target":"record","created_at":"2026-07-05T02:21:49Z","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":"d9c23eeec6f9d8fbebd8e433d6473a826f7ed8b7f9feb127d137533055e71307","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2019-06-16T13:10:02Z","title_canon_sha256":"a632462ca74edf8d0ba088137abb131af0818c8c32579e48bee18f1f8170d243"},"schema_version":"1.0","source":{"id":"1906.06677","kind":"arxiv","version":2}},"canonical_sha256":"1084ea0ebb29172fe308281589ed9f22e0c3be20812b0eeab19bd9d6ac0544f9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1084ea0ebb29172fe308281589ed9f22e0c3be20812b0eeab19bd9d6ac0544f9","first_computed_at":"2026-07-05T02:21:49.483643Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:21:49.483643Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/kpo/IMs0BM2BjFhTw/Bv2qbW87SbXi6jZBJunkoJ0AGLyUlmaaHtNwX1Qslzab3L3RawcCY6YthBDFm7FYVAg==","signature_status":"signed_v1","signed_at":"2026-07-05T02:21:49.483993Z","signed_message":"canonical_sha256_bytes"},"source_id":"1906.06677","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f6cb07bce10d6ec1f2089aed13ec3a55f15e7e48ebfffc6835c35cfecf0d9a3f","sha256:8b29fb1066040c8006a06a5c82b0d3b27389ecaa8ebcb2f2ec0676a96217be72"],"state_sha256":"976637e475e1d57bad0cd12b6f17ec36cb427909feea967d4b9a82147e79802f"}