{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:3372327GL2X66O6OFA3DDY24BT","short_pith_number":"pith:3372327G","canonical_record":{"source":{"id":"1110.3471","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2011-10-16T10:55:15Z","cross_cats_sorted":[],"title_canon_sha256":"1eb18a41b81936a6a95364e7a79d2fdc229f80ceba24a0e6daab7f87fea9664c","abstract_canon_sha256":"d432fb4549690ece3d8fb9fecbfbfcf73f6b9ef36383cc3cd5f920c20dfc778f"},"schema_version":"1.0"},"canonical_sha256":"deffadebe65eafef3bce283631e35c0ce07fabff727ca0223c4beb5ce48651db","source":{"kind":"arxiv","id":"1110.3471","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.3471","created_at":"2026-05-18T00:04:10Z"},{"alias_kind":"arxiv_version","alias_value":"1110.3471v2","created_at":"2026-05-18T00:04:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.3471","created_at":"2026-05-18T00:04:10Z"},{"alias_kind":"pith_short_12","alias_value":"3372327GL2X6","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_16","alias_value":"3372327GL2X66O6O","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_8","alias_value":"3372327G","created_at":"2026-05-18T12:26:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:3372327GL2X66O6OFA3DDY24BT","target":"record","payload":{"canonical_record":{"source":{"id":"1110.3471","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2011-10-16T10:55:15Z","cross_cats_sorted":[],"title_canon_sha256":"1eb18a41b81936a6a95364e7a79d2fdc229f80ceba24a0e6daab7f87fea9664c","abstract_canon_sha256":"d432fb4549690ece3d8fb9fecbfbfcf73f6b9ef36383cc3cd5f920c20dfc778f"},"schema_version":"1.0"},"canonical_sha256":"deffadebe65eafef3bce283631e35c0ce07fabff727ca0223c4beb5ce48651db","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:04:10.728444Z","signature_b64":"b7Snyrqx6NkHNEr46xKP6+CgG4qci2nrgiQTSad+/OJl2RZUVVPW2Wzk/DUCspid6m2uVzsjGT1AulEcCPjZBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"deffadebe65eafef3bce283631e35c0ce07fabff727ca0223c4beb5ce48651db","last_reissued_at":"2026-05-18T00:04:10.727714Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:04:10.727714Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1110.3471","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":"2026-05-18T00:04:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kjLkTXHggrU8HdZoJO1aSeokiXu6bFfy1TJrqmkLYcsR7KvFgTSZ+faLpY7VCPdRr8BOooIg+0Uk11low7Q3DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T18:32:35.007228Z"},"content_sha256":"f11bd376b63b7fb2ccac882b072663384550eac492bf8c2f47a4b8f6070d62cc","schema_version":"1.0","event_id":"sha256:f11bd376b63b7fb2ccac882b072663384550eac492bf8c2f47a4b8f6070d62cc"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:3372327GL2X66O6OFA3DDY24BT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A weighted inequality for potential type operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"A\\\"issata Adama, Ibrahim Fofana, Justin Feuto","submitted_at":"2011-10-16T10:55:15Z","abstract_excerpt":"We establish a weighted inequality for fractional maximal and convolution type operators, between weak Lebesgue spaces and Wiener amalgam type spaces on $ \\mathbb R $ endowed with a measure which needs not to be doubling."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.3471","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":"2026-05-18T00:04:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IofUq5vkTnOSrHCODbICbKWeGuYn30f/2apZeE3sCiJp6GWvi+kxn8cgSEr+LTQgHXifTvdu+AMATo61yMx1DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T18:32:35.007927Z"},"content_sha256":"5632e6452faa6ac4528cfaead3616bd1007f419922332170152a3c339521d673","schema_version":"1.0","event_id":"sha256:5632e6452faa6ac4528cfaead3616bd1007f419922332170152a3c339521d673"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3372327GL2X66O6OFA3DDY24BT/bundle.json","state_url":"https://pith.science/pith/3372327GL2X66O6OFA3DDY24BT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3372327GL2X66O6OFA3DDY24BT/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":"2026-06-07T18:32:35Z","links":{"resolver":"https://pith.science/pith/3372327GL2X66O6OFA3DDY24BT","bundle":"https://pith.science/pith/3372327GL2X66O6OFA3DDY24BT/bundle.json","state":"https://pith.science/pith/3372327GL2X66O6OFA3DDY24BT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3372327GL2X66O6OFA3DDY24BT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:3372327GL2X66O6OFA3DDY24BT","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":"d432fb4549690ece3d8fb9fecbfbfcf73f6b9ef36383cc3cd5f920c20dfc778f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2011-10-16T10:55:15Z","title_canon_sha256":"1eb18a41b81936a6a95364e7a79d2fdc229f80ceba24a0e6daab7f87fea9664c"},"schema_version":"1.0","source":{"id":"1110.3471","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.3471","created_at":"2026-05-18T00:04:10Z"},{"alias_kind":"arxiv_version","alias_value":"1110.3471v2","created_at":"2026-05-18T00:04:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.3471","created_at":"2026-05-18T00:04:10Z"},{"alias_kind":"pith_short_12","alias_value":"3372327GL2X6","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_16","alias_value":"3372327GL2X66O6O","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_8","alias_value":"3372327G","created_at":"2026-05-18T12:26:18Z"}],"graph_snapshots":[{"event_id":"sha256:5632e6452faa6ac4528cfaead3616bd1007f419922332170152a3c339521d673","target":"graph","created_at":"2026-05-18T00:04:10Z","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":"We establish a weighted inequality for fractional maximal and convolution type operators, between weak Lebesgue spaces and Wiener amalgam type spaces on $ \\mathbb R $ endowed with a measure which needs not to be doubling.","authors_text":"A\\\"issata Adama, Ibrahim Fofana, Justin Feuto","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2011-10-16T10:55:15Z","title":"A weighted inequality for potential type operators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.3471","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:f11bd376b63b7fb2ccac882b072663384550eac492bf8c2f47a4b8f6070d62cc","target":"record","created_at":"2026-05-18T00:04:10Z","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":"d432fb4549690ece3d8fb9fecbfbfcf73f6b9ef36383cc3cd5f920c20dfc778f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2011-10-16T10:55:15Z","title_canon_sha256":"1eb18a41b81936a6a95364e7a79d2fdc229f80ceba24a0e6daab7f87fea9664c"},"schema_version":"1.0","source":{"id":"1110.3471","kind":"arxiv","version":2}},"canonical_sha256":"deffadebe65eafef3bce283631e35c0ce07fabff727ca0223c4beb5ce48651db","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"deffadebe65eafef3bce283631e35c0ce07fabff727ca0223c4beb5ce48651db","first_computed_at":"2026-05-18T00:04:10.727714Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:04:10.727714Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"b7Snyrqx6NkHNEr46xKP6+CgG4qci2nrgiQTSad+/OJl2RZUVVPW2Wzk/DUCspid6m2uVzsjGT1AulEcCPjZBg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:04:10.728444Z","signed_message":"canonical_sha256_bytes"},"source_id":"1110.3471","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f11bd376b63b7fb2ccac882b072663384550eac492bf8c2f47a4b8f6070d62cc","sha256:5632e6452faa6ac4528cfaead3616bd1007f419922332170152a3c339521d673"],"state_sha256":"1d22c59e69ab2e9a357ee2376943b59069aa201842d2bee67b7375aae75fd50d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"p0Cn18G/m05EGqRWTAsEVuZiKmTReroNvOGJRp+GPHFw0WV/+/P9MusdriYjK62UM42k3go0OAzLJkrwwv5bAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T18:32:35.011605Z","bundle_sha256":"46ed71aa4b1214ac3685f4f9c76bd4b509af16bd2be6711647959fc7a63365aa"}}