{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:DM2SZAM3SKFMNBA3NMIQGPNBFH","short_pith_number":"pith:DM2SZAM3","canonical_record":{"source":{"id":"1210.5414","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-10-19T13:25:05Z","cross_cats_sorted":[],"title_canon_sha256":"12d1c61d4e994288799faa17acfb407c285da4b49add25021fccc160aa7ff29b","abstract_canon_sha256":"f42e164f28dc9279f27148d5f368cc187d8c6b6b15b7bbf583278e3b8dd4f18b"},"schema_version":"1.0"},"canonical_sha256":"1b352c819b928ac6841b6b11033da129f6ee26b5330b52f0cc4dab2b8dbf7c64","source":{"kind":"arxiv","id":"1210.5414","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.5414","created_at":"2026-05-18T03:42:45Z"},{"alias_kind":"arxiv_version","alias_value":"1210.5414v1","created_at":"2026-05-18T03:42:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.5414","created_at":"2026-05-18T03:42:45Z"},{"alias_kind":"pith_short_12","alias_value":"DM2SZAM3SKFM","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_16","alias_value":"DM2SZAM3SKFMNBA3","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_8","alias_value":"DM2SZAM3","created_at":"2026-05-18T12:27:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:DM2SZAM3SKFMNBA3NMIQGPNBFH","target":"record","payload":{"canonical_record":{"source":{"id":"1210.5414","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-10-19T13:25:05Z","cross_cats_sorted":[],"title_canon_sha256":"12d1c61d4e994288799faa17acfb407c285da4b49add25021fccc160aa7ff29b","abstract_canon_sha256":"f42e164f28dc9279f27148d5f368cc187d8c6b6b15b7bbf583278e3b8dd4f18b"},"schema_version":"1.0"},"canonical_sha256":"1b352c819b928ac6841b6b11033da129f6ee26b5330b52f0cc4dab2b8dbf7c64","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:42:45.329621Z","signature_b64":"TrroDsJm0YzjxL74S8N/4sHq+REVMSzuYIjrVkCPZqUrVcxXnfnvbYxAOPN3gNYQSoa7BaiYG+8hUYznxPbOCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1b352c819b928ac6841b6b11033da129f6ee26b5330b52f0cc4dab2b8dbf7c64","last_reissued_at":"2026-05-18T03:42:45.329143Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:42:45.329143Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1210.5414","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":"2026-05-18T03:42:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LanGnPgdizgUN6/AHPJEUA3Y8xuM71SKi05yH3JkAnROvM900PLQKRuQDRd6q4oyRGtbCXxA8eXH1znyeHwUCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T13:12:16.494295Z"},"content_sha256":"35d8de3cd79112285c9733db0d75edee20a178823accc298aa9ac4b554949d66","schema_version":"1.0","event_id":"sha256:35d8de3cd79112285c9733db0d75edee20a178823accc298aa9ac4b554949d66"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:DM2SZAM3SKFMNBA3NMIQGPNBFH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Weighted norm estimates for the Semyanistyi fractional integrals and Radon transforms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Boris Rubin","submitted_at":"2012-10-19T13:25:05Z","abstract_excerpt":"Semyanistyi's fractional integrals have come to analysis from integral geometry. They take functions on $R^n$ to functions on hyperplanes, commute with rotations, and have a nice behavior with respect to dilations. We obtain sharp inequalities for these integrals and the corresponding Radon transforms acting on $L^p$ spaces with a radial power weight. The operator norms are explicitly evaluated. Similar results are obtained for fractional integrals associated to $k$-plane transforms for any $1\\le k<n$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.5414","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":"2026-05-18T03:42:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ce/ZHqqRo88oycAxny0dzrVVnbH+9X5E0FJfnE40rujTWoVXf5TSWq7rMMJA1sEYma/3o80K02eQd44vusXyAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T13:12:16.494653Z"},"content_sha256":"e137108873dd92040f286a8f86168aa8075c6de7b864b1e33266eb8530b1543d","schema_version":"1.0","event_id":"sha256:e137108873dd92040f286a8f86168aa8075c6de7b864b1e33266eb8530b1543d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DM2SZAM3SKFMNBA3NMIQGPNBFH/bundle.json","state_url":"https://pith.science/pith/DM2SZAM3SKFMNBA3NMIQGPNBFH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DM2SZAM3SKFMNBA3NMIQGPNBFH/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":"2026-05-28T13:12:16Z","links":{"resolver":"https://pith.science/pith/DM2SZAM3SKFMNBA3NMIQGPNBFH","bundle":"https://pith.science/pith/DM2SZAM3SKFMNBA3NMIQGPNBFH/bundle.json","state":"https://pith.science/pith/DM2SZAM3SKFMNBA3NMIQGPNBFH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DM2SZAM3SKFMNBA3NMIQGPNBFH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:DM2SZAM3SKFMNBA3NMIQGPNBFH","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":"f42e164f28dc9279f27148d5f368cc187d8c6b6b15b7bbf583278e3b8dd4f18b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-10-19T13:25:05Z","title_canon_sha256":"12d1c61d4e994288799faa17acfb407c285da4b49add25021fccc160aa7ff29b"},"schema_version":"1.0","source":{"id":"1210.5414","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.5414","created_at":"2026-05-18T03:42:45Z"},{"alias_kind":"arxiv_version","alias_value":"1210.5414v1","created_at":"2026-05-18T03:42:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.5414","created_at":"2026-05-18T03:42:45Z"},{"alias_kind":"pith_short_12","alias_value":"DM2SZAM3SKFM","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_16","alias_value":"DM2SZAM3SKFMNBA3","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_8","alias_value":"DM2SZAM3","created_at":"2026-05-18T12:27:04Z"}],"graph_snapshots":[{"event_id":"sha256:e137108873dd92040f286a8f86168aa8075c6de7b864b1e33266eb8530b1543d","target":"graph","created_at":"2026-05-18T03:42:45Z","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":"Semyanistyi's fractional integrals have come to analysis from integral geometry. They take functions on $R^n$ to functions on hyperplanes, commute with rotations, and have a nice behavior with respect to dilations. We obtain sharp inequalities for these integrals and the corresponding Radon transforms acting on $L^p$ spaces with a radial power weight. The operator norms are explicitly evaluated. Similar results are obtained for fractional integrals associated to $k$-plane transforms for any $1\\le k<n$.","authors_text":"Boris Rubin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-10-19T13:25:05Z","title":"Weighted norm estimates for the Semyanistyi fractional integrals and Radon transforms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.5414","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":"sha256:35d8de3cd79112285c9733db0d75edee20a178823accc298aa9ac4b554949d66","target":"record","created_at":"2026-05-18T03:42:45Z","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":"f42e164f28dc9279f27148d5f368cc187d8c6b6b15b7bbf583278e3b8dd4f18b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-10-19T13:25:05Z","title_canon_sha256":"12d1c61d4e994288799faa17acfb407c285da4b49add25021fccc160aa7ff29b"},"schema_version":"1.0","source":{"id":"1210.5414","kind":"arxiv","version":1}},"canonical_sha256":"1b352c819b928ac6841b6b11033da129f6ee26b5330b52f0cc4dab2b8dbf7c64","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1b352c819b928ac6841b6b11033da129f6ee26b5330b52f0cc4dab2b8dbf7c64","first_computed_at":"2026-05-18T03:42:45.329143Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:42:45.329143Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TrroDsJm0YzjxL74S8N/4sHq+REVMSzuYIjrVkCPZqUrVcxXnfnvbYxAOPN3gNYQSoa7BaiYG+8hUYznxPbOCA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:42:45.329621Z","signed_message":"canonical_sha256_bytes"},"source_id":"1210.5414","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:35d8de3cd79112285c9733db0d75edee20a178823accc298aa9ac4b554949d66","sha256:e137108873dd92040f286a8f86168aa8075c6de7b864b1e33266eb8530b1543d"],"state_sha256":"0c79cf6bd145d30c62d598278a019e1906fb250371bd1ab6f8932f74ad2c054f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nerlrTbTBoIGpr26562m2kn136QESvqKV+6g9pq0kldcD1HSQH7jt0dKeis3fGpLYEm4nNYpR83OR0I1lMSaAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T13:12:16.496609Z","bundle_sha256":"9cc6aa22e1e853ce1498724ce899ea44596a189e3ade10a590b6786fd3006b60"}}