{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:5KXTGSVK75SDUCAZMCHKY6MVUK","short_pith_number":"pith:5KXTGSVK","canonical_record":{"source":{"id":"1506.08013","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-06-26T09:52:20Z","cross_cats_sorted":[],"title_canon_sha256":"4efe9646b465da29607fb35e674ade81ddfe25ce69fd119156954d00740c3891","abstract_canon_sha256":"d70805eec2c49d78efc7ab7f4ba3ddc6687e2ad3bbdf47f6f672d3a786227fb1"},"schema_version":"1.0"},"canonical_sha256":"eaaf334aaaff643a0819608eac7995a2a57183e1d9d3819897171dd9c103aeff","source":{"kind":"arxiv","id":"1506.08013","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.08013","created_at":"2026-05-18T01:32:00Z"},{"alias_kind":"arxiv_version","alias_value":"1506.08013v2","created_at":"2026-05-18T01:32:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.08013","created_at":"2026-05-18T01:32:00Z"},{"alias_kind":"pith_short_12","alias_value":"5KXTGSVK75SD","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_16","alias_value":"5KXTGSVK75SDUCAZ","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_8","alias_value":"5KXTGSVK","created_at":"2026-05-18T12:29:05Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:5KXTGSVK75SDUCAZMCHKY6MVUK","target":"record","payload":{"canonical_record":{"source":{"id":"1506.08013","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-06-26T09:52:20Z","cross_cats_sorted":[],"title_canon_sha256":"4efe9646b465da29607fb35e674ade81ddfe25ce69fd119156954d00740c3891","abstract_canon_sha256":"d70805eec2c49d78efc7ab7f4ba3ddc6687e2ad3bbdf47f6f672d3a786227fb1"},"schema_version":"1.0"},"canonical_sha256":"eaaf334aaaff643a0819608eac7995a2a57183e1d9d3819897171dd9c103aeff","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:32:00.287469Z","signature_b64":"R3ty0AwHNX9BOMfwp3sCQKLE1tKRpy07LwNPDnr9On9YJWJVUlogBgT5+WWU7Y8UjDX2rvxhx0LMB4hxMyXqCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"eaaf334aaaff643a0819608eac7995a2a57183e1d9d3819897171dd9c103aeff","last_reissued_at":"2026-05-18T01:32:00.287026Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:32:00.287026Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1506.08013","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":"2026-05-18T01:32:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"f5O5jdH7NnrWUoY+g/4L/tTV3VuSwgjVkhpgh2703vKKHkK1VrXGr2LELXbVrYaxl35lqlE8XUICeFjWQNJDBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T15:45:40.238258Z"},"content_sha256":"fb02e370ccf4db966ed96c479515aa90d52a91b3980025c00d5ddcb6a200ead0","schema_version":"1.0","event_id":"sha256:fb02e370ccf4db966ed96c479515aa90d52a91b3980025c00d5ddcb6a200ead0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:5KXTGSVK75SDUCAZMCHKY6MVUK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Estimates for vector-valued holomorphic functions and Littlewood-Paley-Stein theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Lutz Weis, Mark Veraar","submitted_at":"2015-06-26T09:52:20Z","abstract_excerpt":"In this paper we consider generalized square function norms of holomorphic functions with values in a Banach space. One of the main results is a characterization of embeddings of the form \\[L^p(X)\\subseteq \\gamma(X) \\subseteq L^q(X),\\] in terms of the type $p$ and cotype $q$ for the Banach space $X$. As an application we prove $L^p$-estimates for vector-valued Littlewood-Paley-Stein $g$-functions and derive an embedding result for real and complex interpolation spaces under type and cotype conditions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.08013","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":"2026-05-18T01:32:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1uHCA1j0W5S61SLn5jDCPo/tZi7XfuCqDyRV5qTVwcHR0mD4VYFnw9gX9RdpYwLdmWxEDx5BSKA7sKspRuvODA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T15:45:40.238627Z"},"content_sha256":"1a9e60033a3f35d891de963618b315f59c10ed765241631142aaac0ed5ef8f2d","schema_version":"1.0","event_id":"sha256:1a9e60033a3f35d891de963618b315f59c10ed765241631142aaac0ed5ef8f2d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5KXTGSVK75SDUCAZMCHKY6MVUK/bundle.json","state_url":"https://pith.science/pith/5KXTGSVK75SDUCAZMCHKY6MVUK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5KXTGSVK75SDUCAZMCHKY6MVUK/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":"2026-06-25T15:45:40Z","links":{"resolver":"https://pith.science/pith/5KXTGSVK75SDUCAZMCHKY6MVUK","bundle":"https://pith.science/pith/5KXTGSVK75SDUCAZMCHKY6MVUK/bundle.json","state":"https://pith.science/pith/5KXTGSVK75SDUCAZMCHKY6MVUK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5KXTGSVK75SDUCAZMCHKY6MVUK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:5KXTGSVK75SDUCAZMCHKY6MVUK","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":"d70805eec2c49d78efc7ab7f4ba3ddc6687e2ad3bbdf47f6f672d3a786227fb1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-06-26T09:52:20Z","title_canon_sha256":"4efe9646b465da29607fb35e674ade81ddfe25ce69fd119156954d00740c3891"},"schema_version":"1.0","source":{"id":"1506.08013","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.08013","created_at":"2026-05-18T01:32:00Z"},{"alias_kind":"arxiv_version","alias_value":"1506.08013v2","created_at":"2026-05-18T01:32:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.08013","created_at":"2026-05-18T01:32:00Z"},{"alias_kind":"pith_short_12","alias_value":"5KXTGSVK75SD","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_16","alias_value":"5KXTGSVK75SDUCAZ","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_8","alias_value":"5KXTGSVK","created_at":"2026-05-18T12:29:05Z"}],"graph_snapshots":[{"event_id":"sha256:1a9e60033a3f35d891de963618b315f59c10ed765241631142aaac0ed5ef8f2d","target":"graph","created_at":"2026-05-18T01:32:00Z","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":"In this paper we consider generalized square function norms of holomorphic functions with values in a Banach space. One of the main results is a characterization of embeddings of the form \\[L^p(X)\\subseteq \\gamma(X) \\subseteq L^q(X),\\] in terms of the type $p$ and cotype $q$ for the Banach space $X$. As an application we prove $L^p$-estimates for vector-valued Littlewood-Paley-Stein $g$-functions and derive an embedding result for real and complex interpolation spaces under type and cotype conditions.","authors_text":"Lutz Weis, Mark Veraar","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-06-26T09:52:20Z","title":"Estimates for vector-valued holomorphic functions and Littlewood-Paley-Stein theory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.08013","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:fb02e370ccf4db966ed96c479515aa90d52a91b3980025c00d5ddcb6a200ead0","target":"record","created_at":"2026-05-18T01:32:00Z","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":"d70805eec2c49d78efc7ab7f4ba3ddc6687e2ad3bbdf47f6f672d3a786227fb1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-06-26T09:52:20Z","title_canon_sha256":"4efe9646b465da29607fb35e674ade81ddfe25ce69fd119156954d00740c3891"},"schema_version":"1.0","source":{"id":"1506.08013","kind":"arxiv","version":2}},"canonical_sha256":"eaaf334aaaff643a0819608eac7995a2a57183e1d9d3819897171dd9c103aeff","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"eaaf334aaaff643a0819608eac7995a2a57183e1d9d3819897171dd9c103aeff","first_computed_at":"2026-05-18T01:32:00.287026Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:32:00.287026Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"R3ty0AwHNX9BOMfwp3sCQKLE1tKRpy07LwNPDnr9On9YJWJVUlogBgT5+WWU7Y8UjDX2rvxhx0LMB4hxMyXqCA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:32:00.287469Z","signed_message":"canonical_sha256_bytes"},"source_id":"1506.08013","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fb02e370ccf4db966ed96c479515aa90d52a91b3980025c00d5ddcb6a200ead0","sha256:1a9e60033a3f35d891de963618b315f59c10ed765241631142aaac0ed5ef8f2d"],"state_sha256":"15755afb68c0e18a9e9854b5f074e266c7f0a8a306991ce7470f83a01780e702"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OV/A47yC1ZTE/v3DXeUoJWuU91xzYD1ReU17XUv+4sW8v68HAbBhmnahI+KOrfR50uW86gs9w2Kfx4khU/IhBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T15:45:40.240521Z","bundle_sha256":"7befd664c9fb4222e6baddf7e986c082e9c84b44f5608b6a72d55825c2fc475d"}}