{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:OA6EHDGKPH44PMK3KLIWUEEKU3","short_pith_number":"pith:OA6EHDGK","canonical_record":{"source":{"id":"1004.5507","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2010-04-30T11:45:42Z","cross_cats_sorted":["math.AP","math.FA"],"title_canon_sha256":"a7f86c907fed98c891c1fb21eec6c956bb59d7a2da5817546b52baafb2167661","abstract_canon_sha256":"5a9c1f3c0fc1038863e4e4ca85631dd84c99b483551af63059dc993109149419"},"schema_version":"1.0"},"canonical_sha256":"703c438cca79f9c7b15b52d16a108aa6cbfc36af6ed94e9616697ca7462ff442","source":{"kind":"arxiv","id":"1004.5507","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1004.5507","created_at":"2026-05-18T02:24:09Z"},{"alias_kind":"arxiv_version","alias_value":"1004.5507v1","created_at":"2026-05-18T02:24:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1004.5507","created_at":"2026-05-18T02:24:09Z"},{"alias_kind":"pith_short_12","alias_value":"OA6EHDGKPH44","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_16","alias_value":"OA6EHDGKPH44PMK3","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_8","alias_value":"OA6EHDGK","created_at":"2026-05-18T12:26:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:OA6EHDGKPH44PMK3KLIWUEEKU3","target":"record","payload":{"canonical_record":{"source":{"id":"1004.5507","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2010-04-30T11:45:42Z","cross_cats_sorted":["math.AP","math.FA"],"title_canon_sha256":"a7f86c907fed98c891c1fb21eec6c956bb59d7a2da5817546b52baafb2167661","abstract_canon_sha256":"5a9c1f3c0fc1038863e4e4ca85631dd84c99b483551af63059dc993109149419"},"schema_version":"1.0"},"canonical_sha256":"703c438cca79f9c7b15b52d16a108aa6cbfc36af6ed94e9616697ca7462ff442","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:24:09.899266Z","signature_b64":"4LeHE658oJjx0ivLr7BvCNfD98N02QNtUkiJkxLnV79G3+cJi3Z3y/rThzmTgrhr9BsnC9hc053dDdWLKy7VCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"703c438cca79f9c7b15b52d16a108aa6cbfc36af6ed94e9616697ca7462ff442","last_reissued_at":"2026-05-18T02:24:09.898530Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:24:09.898530Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1004.5507","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":"2026-05-18T02:24:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DlMxUzlfJSCSW2bt/vc0KKD12N0oy4BD4w7S6pVVBjWqKN9PRT+Kv6KTR8lI00rBdxWxLGkdCEx1IA766o/oCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T19:56:06.363184Z"},"content_sha256":"c65a457da9240aa23a8e26d9b5951d70f3c6f588856ce6f3916f38d4093ee43c","schema_version":"1.0","event_id":"sha256:c65a457da9240aa23a8e26d9b5951d70f3c6f588856ce6f3916f38d4093ee43c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:OA6EHDGKPH44PMK3KLIWUEEKU3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Pointwise Characterizations of Besov and Triebel-Lizorkin Spaces and Quasiconformal Mappings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.FA"],"primary_cat":"math.CA","authors_text":"Dachun Yang, Pekka Koskela, Yuan Zhou","submitted_at":"2010-04-30T11:45:42Z","abstract_excerpt":"In this paper, the authors characterize, in terms of pointwise inequalities, the classical Besov spaces $\\dot B^s_{p,\\,q}$ and Triebel-Lizorkin spaces $\\dot F^s_{p,\\,q}$ for all $s\\in(0,\\,1)$ and $p,\\,q\\in(n/(n+s),\\,\\infty],$ both in ${\\mathbb R}^n$ and in the metric measure spaces enjoying the doubling and reverse doubling properties. Applying this characterization, the authors prove that quasiconformal mappings preserve $\\dot F^s_{n/s,\\,q}$ on $\\rn$ for all $s\\in(0,\\,1)$ and $q\\in(n/(n+s),\\,\\infty]$. A metric measure space version of the above morphism property is also established."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1004.5507","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":"2026-05-18T02:24:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TgteYUrPUqqBcx+B9CgWB4Y23pHulT4ZZ22iMTxmTU8t2JUMp8/3h5hH8QrsLaP+6qY82Zasv3Ao8ZnYRmeeBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T19:56:06.363910Z"},"content_sha256":"f5446abaa4843f58022b7b349096110c58a968c610acd12941f89e4ae41604ba","schema_version":"1.0","event_id":"sha256:f5446abaa4843f58022b7b349096110c58a968c610acd12941f89e4ae41604ba"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OA6EHDGKPH44PMK3KLIWUEEKU3/bundle.json","state_url":"https://pith.science/pith/OA6EHDGKPH44PMK3KLIWUEEKU3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OA6EHDGKPH44PMK3KLIWUEEKU3/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":"2026-06-06T19:56:06Z","links":{"resolver":"https://pith.science/pith/OA6EHDGKPH44PMK3KLIWUEEKU3","bundle":"https://pith.science/pith/OA6EHDGKPH44PMK3KLIWUEEKU3/bundle.json","state":"https://pith.science/pith/OA6EHDGKPH44PMK3KLIWUEEKU3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OA6EHDGKPH44PMK3KLIWUEEKU3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:OA6EHDGKPH44PMK3KLIWUEEKU3","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":"5a9c1f3c0fc1038863e4e4ca85631dd84c99b483551af63059dc993109149419","cross_cats_sorted":["math.AP","math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2010-04-30T11:45:42Z","title_canon_sha256":"a7f86c907fed98c891c1fb21eec6c956bb59d7a2da5817546b52baafb2167661"},"schema_version":"1.0","source":{"id":"1004.5507","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1004.5507","created_at":"2026-05-18T02:24:09Z"},{"alias_kind":"arxiv_version","alias_value":"1004.5507v1","created_at":"2026-05-18T02:24:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1004.5507","created_at":"2026-05-18T02:24:09Z"},{"alias_kind":"pith_short_12","alias_value":"OA6EHDGKPH44","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_16","alias_value":"OA6EHDGKPH44PMK3","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_8","alias_value":"OA6EHDGK","created_at":"2026-05-18T12:26:12Z"}],"graph_snapshots":[{"event_id":"sha256:f5446abaa4843f58022b7b349096110c58a968c610acd12941f89e4ae41604ba","target":"graph","created_at":"2026-05-18T02:24:09Z","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, the authors characterize, in terms of pointwise inequalities, the classical Besov spaces $\\dot B^s_{p,\\,q}$ and Triebel-Lizorkin spaces $\\dot F^s_{p,\\,q}$ for all $s\\in(0,\\,1)$ and $p,\\,q\\in(n/(n+s),\\,\\infty],$ both in ${\\mathbb R}^n$ and in the metric measure spaces enjoying the doubling and reverse doubling properties. Applying this characterization, the authors prove that quasiconformal mappings preserve $\\dot F^s_{n/s,\\,q}$ on $\\rn$ for all $s\\in(0,\\,1)$ and $q\\in(n/(n+s),\\,\\infty]$. A metric measure space version of the above morphism property is also established.","authors_text":"Dachun Yang, Pekka Koskela, Yuan Zhou","cross_cats":["math.AP","math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2010-04-30T11:45:42Z","title":"Pointwise Characterizations of Besov and Triebel-Lizorkin Spaces and Quasiconformal Mappings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1004.5507","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:c65a457da9240aa23a8e26d9b5951d70f3c6f588856ce6f3916f38d4093ee43c","target":"record","created_at":"2026-05-18T02:24:09Z","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":"5a9c1f3c0fc1038863e4e4ca85631dd84c99b483551af63059dc993109149419","cross_cats_sorted":["math.AP","math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2010-04-30T11:45:42Z","title_canon_sha256":"a7f86c907fed98c891c1fb21eec6c956bb59d7a2da5817546b52baafb2167661"},"schema_version":"1.0","source":{"id":"1004.5507","kind":"arxiv","version":1}},"canonical_sha256":"703c438cca79f9c7b15b52d16a108aa6cbfc36af6ed94e9616697ca7462ff442","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"703c438cca79f9c7b15b52d16a108aa6cbfc36af6ed94e9616697ca7462ff442","first_computed_at":"2026-05-18T02:24:09.898530Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:24:09.898530Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4LeHE658oJjx0ivLr7BvCNfD98N02QNtUkiJkxLnV79G3+cJi3Z3y/rThzmTgrhr9BsnC9hc053dDdWLKy7VCg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:24:09.899266Z","signed_message":"canonical_sha256_bytes"},"source_id":"1004.5507","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c65a457da9240aa23a8e26d9b5951d70f3c6f588856ce6f3916f38d4093ee43c","sha256:f5446abaa4843f58022b7b349096110c58a968c610acd12941f89e4ae41604ba"],"state_sha256":"04ecd5cf2d4571456940cabdc1eeba2c3727a77652aa5b1daf9c7303bc459aa9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0haMrIAGB+yPbQegsElQKjnNsoAuEfg203NuFxlUn+cZ/859H+HeD+oRkUO5U0gvRXvr2TRR/A+UHkH+rEE+CQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T19:56:06.367146Z","bundle_sha256":"f72c12b6bdd6c8d0122c83ca8bc01effc756aa7cb6548cb5bad4dbf650aa221d"}}