{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:UUGCKNOXHEEBKQALEGDMLXUYNK","short_pith_number":"pith:UUGCKNOX","canonical_record":{"source":{"id":"1602.00847","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-02-02T09:23:51Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"1b837291d99e7663069f69df70d3d190e7942fd1c22aa2e0eb59a6db69d7784e","abstract_canon_sha256":"787accea0d0151d176e7390cdb319707b3308428afb7e6bd0c045d8170ef0227"},"schema_version":"1.0"},"canonical_sha256":"a50c2535d7390815400b2186c5de986aa53c2047460cdf8d6ad2246efab28d84","source":{"kind":"arxiv","id":"1602.00847","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.00847","created_at":"2026-05-18T01:09:36Z"},{"alias_kind":"arxiv_version","alias_value":"1602.00847v2","created_at":"2026-05-18T01:09:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.00847","created_at":"2026-05-18T01:09:36Z"},{"alias_kind":"pith_short_12","alias_value":"UUGCKNOXHEEB","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_16","alias_value":"UUGCKNOXHEEBKQAL","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_8","alias_value":"UUGCKNOX","created_at":"2026-05-18T12:30:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:UUGCKNOXHEEBKQALEGDMLXUYNK","target":"record","payload":{"canonical_record":{"source":{"id":"1602.00847","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-02-02T09:23:51Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"1b837291d99e7663069f69df70d3d190e7942fd1c22aa2e0eb59a6db69d7784e","abstract_canon_sha256":"787accea0d0151d176e7390cdb319707b3308428afb7e6bd0c045d8170ef0227"},"schema_version":"1.0"},"canonical_sha256":"a50c2535d7390815400b2186c5de986aa53c2047460cdf8d6ad2246efab28d84","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:09:36.109118Z","signature_b64":"4IcPJ9rd7tlLxPbgNZnP6KZAiu8l44VeGn9jxI1jSDRg4Tl4Y6G+iho3frP95vQLMQEPLCZwOK9xdsxFy6rbBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a50c2535d7390815400b2186c5de986aa53c2047460cdf8d6ad2246efab28d84","last_reissued_at":"2026-05-18T01:09:36.108655Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:09:36.108655Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1602.00847","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":"2026-05-18T01:09:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3M7rEKfHPgU7vZiAIYSVNgcmRv20S79GuOdsil0FN7oJb+kUMnYlyndY37e+LNGPCsptr0DN0o/uAN8HLpBUDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T07:33:12.807547Z"},"content_sha256":"d5c1d4095865543b954e32d7c63817d37888544df89050ffa51193649a708c6b","schema_version":"1.0","event_id":"sha256:d5c1d4095865543b954e32d7c63817d37888544df89050ffa51193649a708c6b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:UUGCKNOXHEEBKQALEGDMLXUYNK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Riesz Transform Characterization and Fefferman-Stein Decomposition of Triebel-Lizorkin Spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.CA","authors_text":"Dachun Yang, Qixiang Yang, Xing Fu","submitted_at":"2016-02-02T09:23:51Z","abstract_excerpt":"Let $D\\in\\mathbb{N}$, $q\\in[2,\\infty)$ and $(\\mathbb{R}^D,|\\cdot|,dx)$ be the Euclidean space equipped with the $D$-dimensional Lebesgue measure. In this article, via an auxiliary function space $\\mathrm{WE}^{1,\\,q}(\\mathbb R^D)$ defined via wavelet expansions, the authors establish the Riesz transform characterization of Triebel-Lizorkin spaces $\\dot{F}^0_{1,\\,q}(\\mathbb{R}^D)$. As a consequence, the authors obtain the Fefferman-Stein decomposition of Triebel-Lizorkin spaces $\\dot{F}^0_{\\infty,\\,q'}(\\mathbb{R}^D)$. Finally, the authors give an explicit example to show that $\\dot{F}^0_{1,\\,q}("},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.00847","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":"2026-05-18T01:09:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"D7w6ldYVMsDInHQ4iOaoqJNkZbN+mbKRiNdmxaedtS/a8Z3kxrJS16lfudnCjJeMaDpN4/ywkbxbjdtnJGYwBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T07:33:12.807906Z"},"content_sha256":"a6956c1d8f1e216af1bb5fd82521de713394a4b97ae85858180d6718ed3e8344","schema_version":"1.0","event_id":"sha256:a6956c1d8f1e216af1bb5fd82521de713394a4b97ae85858180d6718ed3e8344"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UUGCKNOXHEEBKQALEGDMLXUYNK/bundle.json","state_url":"https://pith.science/pith/UUGCKNOXHEEBKQALEGDMLXUYNK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UUGCKNOXHEEBKQALEGDMLXUYNK/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":"2026-05-30T07:33:12Z","links":{"resolver":"https://pith.science/pith/UUGCKNOXHEEBKQALEGDMLXUYNK","bundle":"https://pith.science/pith/UUGCKNOXHEEBKQALEGDMLXUYNK/bundle.json","state":"https://pith.science/pith/UUGCKNOXHEEBKQALEGDMLXUYNK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UUGCKNOXHEEBKQALEGDMLXUYNK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:UUGCKNOXHEEBKQALEGDMLXUYNK","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":"787accea0d0151d176e7390cdb319707b3308428afb7e6bd0c045d8170ef0227","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-02-02T09:23:51Z","title_canon_sha256":"1b837291d99e7663069f69df70d3d190e7942fd1c22aa2e0eb59a6db69d7784e"},"schema_version":"1.0","source":{"id":"1602.00847","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.00847","created_at":"2026-05-18T01:09:36Z"},{"alias_kind":"arxiv_version","alias_value":"1602.00847v2","created_at":"2026-05-18T01:09:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.00847","created_at":"2026-05-18T01:09:36Z"},{"alias_kind":"pith_short_12","alias_value":"UUGCKNOXHEEB","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_16","alias_value":"UUGCKNOXHEEBKQAL","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_8","alias_value":"UUGCKNOX","created_at":"2026-05-18T12:30:46Z"}],"graph_snapshots":[{"event_id":"sha256:a6956c1d8f1e216af1bb5fd82521de713394a4b97ae85858180d6718ed3e8344","target":"graph","created_at":"2026-05-18T01:09:36Z","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":"Let $D\\in\\mathbb{N}$, $q\\in[2,\\infty)$ and $(\\mathbb{R}^D,|\\cdot|,dx)$ be the Euclidean space equipped with the $D$-dimensional Lebesgue measure. In this article, via an auxiliary function space $\\mathrm{WE}^{1,\\,q}(\\mathbb R^D)$ defined via wavelet expansions, the authors establish the Riesz transform characterization of Triebel-Lizorkin spaces $\\dot{F}^0_{1,\\,q}(\\mathbb{R}^D)$. As a consequence, the authors obtain the Fefferman-Stein decomposition of Triebel-Lizorkin spaces $\\dot{F}^0_{\\infty,\\,q'}(\\mathbb{R}^D)$. Finally, the authors give an explicit example to show that $\\dot{F}^0_{1,\\,q}(","authors_text":"Dachun Yang, Qixiang Yang, Xing Fu","cross_cats":["math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-02-02T09:23:51Z","title":"Riesz Transform Characterization and Fefferman-Stein Decomposition of Triebel-Lizorkin Spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.00847","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:d5c1d4095865543b954e32d7c63817d37888544df89050ffa51193649a708c6b","target":"record","created_at":"2026-05-18T01:09:36Z","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":"787accea0d0151d176e7390cdb319707b3308428afb7e6bd0c045d8170ef0227","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-02-02T09:23:51Z","title_canon_sha256":"1b837291d99e7663069f69df70d3d190e7942fd1c22aa2e0eb59a6db69d7784e"},"schema_version":"1.0","source":{"id":"1602.00847","kind":"arxiv","version":2}},"canonical_sha256":"a50c2535d7390815400b2186c5de986aa53c2047460cdf8d6ad2246efab28d84","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a50c2535d7390815400b2186c5de986aa53c2047460cdf8d6ad2246efab28d84","first_computed_at":"2026-05-18T01:09:36.108655Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:09:36.108655Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4IcPJ9rd7tlLxPbgNZnP6KZAiu8l44VeGn9jxI1jSDRg4Tl4Y6G+iho3frP95vQLMQEPLCZwOK9xdsxFy6rbBA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:09:36.109118Z","signed_message":"canonical_sha256_bytes"},"source_id":"1602.00847","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d5c1d4095865543b954e32d7c63817d37888544df89050ffa51193649a708c6b","sha256:a6956c1d8f1e216af1bb5fd82521de713394a4b97ae85858180d6718ed3e8344"],"state_sha256":"46aabb4a3b9bac5b6a4c09412ae7becd8a262a444362d1168bd761265a894e9e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HxpJAADk5OJgO+oNipuhXTGyj8XaekHtO3zvmUm1PeRFOZrWauV9IQwRknxLESG2RTk52QbLMBZi2TL3XrH8Dw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T07:33:12.810099Z","bundle_sha256":"c0abebf94c724a83db2714ec90177b3de4d1e2f4472478df41641caea1b54862"}}