{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:G4Y4YMSSE6R6XYXBTGFWRPSJ6K","short_pith_number":"pith:G4Y4YMSS","canonical_record":{"source":{"id":"1110.5826","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2011-10-26T15:55:05Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"1fb958fff52b4c35534ca31947cd36bdfb4382ac0c976c14739b44efd932801b","abstract_canon_sha256":"13cc55fd81739e6f51097dd7f99515f018d8aff20ad4d59a122fb33161bac0e5"},"schema_version":"1.0"},"canonical_sha256":"3731cc325227a3ebe2e1998b68be49f290bab3f0ed256961621e86c467b21889","source":{"kind":"arxiv","id":"1110.5826","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.5826","created_at":"2026-05-18T04:10:11Z"},{"alias_kind":"arxiv_version","alias_value":"1110.5826v1","created_at":"2026-05-18T04:10:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.5826","created_at":"2026-05-18T04:10:11Z"},{"alias_kind":"pith_short_12","alias_value":"G4Y4YMSSE6R6","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_16","alias_value":"G4Y4YMSSE6R6XYXB","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_8","alias_value":"G4Y4YMSS","created_at":"2026-05-18T12:26:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:G4Y4YMSSE6R6XYXBTGFWRPSJ6K","target":"record","payload":{"canonical_record":{"source":{"id":"1110.5826","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2011-10-26T15:55:05Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"1fb958fff52b4c35534ca31947cd36bdfb4382ac0c976c14739b44efd932801b","abstract_canon_sha256":"13cc55fd81739e6f51097dd7f99515f018d8aff20ad4d59a122fb33161bac0e5"},"schema_version":"1.0"},"canonical_sha256":"3731cc325227a3ebe2e1998b68be49f290bab3f0ed256961621e86c467b21889","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:10:11.156505Z","signature_b64":"vBYn4ATiWCtYp79ox7TFISxiyFd+qtSunxZusSNZkK+/fG1WEz9hpfJT0FQYdnOLbMT4vHhic4sUPyW4Od9gDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3731cc325227a3ebe2e1998b68be49f290bab3f0ed256961621e86c467b21889","last_reissued_at":"2026-05-18T04:10:11.155632Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:10:11.155632Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1110.5826","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:10:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"grQMxbjVrC0d5fSV5ZU8sACgGbJ+29Dslp/g+Nty42g8q69fTLbuVXwWrADyR7ZRiv6NySVAHGVb8Y2vcJutBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T03:40:12.756527Z"},"content_sha256":"6ace58f8b4b1e18a499c10e048a1c9a8502e4ce459452c41bdede0de3d053572","schema_version":"1.0","event_id":"sha256:6ace58f8b4b1e18a499c10e048a1c9a8502e4ce459452c41bdede0de3d053572"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:G4Y4YMSSE6R6XYXBTGFWRPSJ6K","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Foundations of vector-valued singular integrals revisited---with random dyadic cubes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.FA","authors_text":"Tuomas P. Hyt\\\"onen","submitted_at":"2011-10-26T15:55:05Z","abstract_excerpt":"The vector-valued $T(1)$ theorem due to Figiel, and a certain square function estimate of Bourgain for translations of functions with a limited frequency spectrum, are two cornerstones of harmonic analysis in UMD spaces. In this paper, a simplified approach to these results is presented, exploiting Nazarov, Treil and Volberg's method of random dyadic cubes, which allows to circumvent the most subtle parts of the original arguments."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.5826","kind":"arxiv","version":1},"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":"2026-05-18T04:10:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Jh/dOhOWDD9cf0cyPQ3S+Ad58qqjcrcdaHUqJ/kJ58vPsXpB5dEcbBIUcla3TQ2681Otrx8zSSWxFnBcS1NiDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T03:40:12.757228Z"},"content_sha256":"fcda7b09cabedba17a13b49ea6181dc1befda41a5a2fae7bcd4245de9c152ffa","schema_version":"1.0","event_id":"sha256:fcda7b09cabedba17a13b49ea6181dc1befda41a5a2fae7bcd4245de9c152ffa"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/G4Y4YMSSE6R6XYXBTGFWRPSJ6K/bundle.json","state_url":"https://pith.science/pith/G4Y4YMSSE6R6XYXBTGFWRPSJ6K/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/G4Y4YMSSE6R6XYXBTGFWRPSJ6K/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":"2026-05-26T03:40:12Z","links":{"resolver":"https://pith.science/pith/G4Y4YMSSE6R6XYXBTGFWRPSJ6K","bundle":"https://pith.science/pith/G4Y4YMSSE6R6XYXBTGFWRPSJ6K/bundle.json","state":"https://pith.science/pith/G4Y4YMSSE6R6XYXBTGFWRPSJ6K/state.json","well_known_bundle":"https://pith.science/.well-known/pith/G4Y4YMSSE6R6XYXBTGFWRPSJ6K/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:G4Y4YMSSE6R6XYXBTGFWRPSJ6K","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":"13cc55fd81739e6f51097dd7f99515f018d8aff20ad4d59a122fb33161bac0e5","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2011-10-26T15:55:05Z","title_canon_sha256":"1fb958fff52b4c35534ca31947cd36bdfb4382ac0c976c14739b44efd932801b"},"schema_version":"1.0","source":{"id":"1110.5826","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.5826","created_at":"2026-05-18T04:10:11Z"},{"alias_kind":"arxiv_version","alias_value":"1110.5826v1","created_at":"2026-05-18T04:10:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.5826","created_at":"2026-05-18T04:10:11Z"},{"alias_kind":"pith_short_12","alias_value":"G4Y4YMSSE6R6","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_16","alias_value":"G4Y4YMSSE6R6XYXB","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_8","alias_value":"G4Y4YMSS","created_at":"2026-05-18T12:26:28Z"}],"graph_snapshots":[{"event_id":"sha256:fcda7b09cabedba17a13b49ea6181dc1befda41a5a2fae7bcd4245de9c152ffa","target":"graph","created_at":"2026-05-18T04:10:11Z","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":"The vector-valued $T(1)$ theorem due to Figiel, and a certain square function estimate of Bourgain for translations of functions with a limited frequency spectrum, are two cornerstones of harmonic analysis in UMD spaces. In this paper, a simplified approach to these results is presented, exploiting Nazarov, Treil and Volberg's method of random dyadic cubes, which allows to circumvent the most subtle parts of the original arguments.","authors_text":"Tuomas P. Hyt\\\"onen","cross_cats":["math.CA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2011-10-26T15:55:05Z","title":"Foundations of vector-valued singular integrals revisited---with random dyadic cubes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.5826","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":"sha256:6ace58f8b4b1e18a499c10e048a1c9a8502e4ce459452c41bdede0de3d053572","target":"record","created_at":"2026-05-18T04:10:11Z","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":"13cc55fd81739e6f51097dd7f99515f018d8aff20ad4d59a122fb33161bac0e5","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2011-10-26T15:55:05Z","title_canon_sha256":"1fb958fff52b4c35534ca31947cd36bdfb4382ac0c976c14739b44efd932801b"},"schema_version":"1.0","source":{"id":"1110.5826","kind":"arxiv","version":1}},"canonical_sha256":"3731cc325227a3ebe2e1998b68be49f290bab3f0ed256961621e86c467b21889","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3731cc325227a3ebe2e1998b68be49f290bab3f0ed256961621e86c467b21889","first_computed_at":"2026-05-18T04:10:11.155632Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:10:11.155632Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vBYn4ATiWCtYp79ox7TFISxiyFd+qtSunxZusSNZkK+/fG1WEz9hpfJT0FQYdnOLbMT4vHhic4sUPyW4Od9gDw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:10:11.156505Z","signed_message":"canonical_sha256_bytes"},"source_id":"1110.5826","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6ace58f8b4b1e18a499c10e048a1c9a8502e4ce459452c41bdede0de3d053572","sha256:fcda7b09cabedba17a13b49ea6181dc1befda41a5a2fae7bcd4245de9c152ffa"],"state_sha256":"093858429d32f690b36daaeeeb2743ceaf4325868660f4f1710cb5364b4c773e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HYJ2+nGzFdOF6JbdYqzKfwQ14MAEuhCOQCBs2O1UHIhSnvpynmhHAzgHL/uNEOfnxz3nG5O16vGdVBrMjGWaCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T03:40:12.760828Z","bundle_sha256":"d7383296beed71512e146b69978b8ca023f4b6c570cc842bca5b40ac20d248b6"}}