{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:6LVEPCY44OZYY4WUB26C6E5QPX","short_pith_number":"pith:6LVEPCY4","canonical_record":{"source":{"id":"1502.07494","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-02-26T10:31:00Z","cross_cats_sorted":[],"title_canon_sha256":"10470925f10e81952b6232f2c728a4d7a267bfac6f75927540872473c772c027","abstract_canon_sha256":"fdaebd51bf649210b1afac9650c29f30f1890eb79ef6d26efee35fe183617f4e"},"schema_version":"1.0"},"canonical_sha256":"f2ea478b1ce3b38c72d40ebc2f13b07dcc61df696b0ce090aba8cf55ceee231c","source":{"kind":"arxiv","id":"1502.07494","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1502.07494","created_at":"2026-05-18T02:26:03Z"},{"alias_kind":"arxiv_version","alias_value":"1502.07494v1","created_at":"2026-05-18T02:26:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.07494","created_at":"2026-05-18T02:26:03Z"},{"alias_kind":"pith_short_12","alias_value":"6LVEPCY44OZY","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_16","alias_value":"6LVEPCY44OZYY4WU","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_8","alias_value":"6LVEPCY4","created_at":"2026-05-18T12:29:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:6LVEPCY44OZYY4WUB26C6E5QPX","target":"record","payload":{"canonical_record":{"source":{"id":"1502.07494","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-02-26T10:31:00Z","cross_cats_sorted":[],"title_canon_sha256":"10470925f10e81952b6232f2c728a4d7a267bfac6f75927540872473c772c027","abstract_canon_sha256":"fdaebd51bf649210b1afac9650c29f30f1890eb79ef6d26efee35fe183617f4e"},"schema_version":"1.0"},"canonical_sha256":"f2ea478b1ce3b38c72d40ebc2f13b07dcc61df696b0ce090aba8cf55ceee231c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:26:03.542079Z","signature_b64":"afhmqv6qbg4RjZmY6tH7hqAeBL1n7ZS4k+nl4kagA+WD3ynLbtAUyzdM4wkixfmXbYOyAkuFPe4hIR2ce1T1Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f2ea478b1ce3b38c72d40ebc2f13b07dcc61df696b0ce090aba8cf55ceee231c","last_reissued_at":"2026-05-18T02:26:03.541572Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:26:03.541572Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1502.07494","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":"2026-05-18T02:26:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WlgeF2I+JrKcUJLQOhYV8MAsMj+l81Fzs7kMxKqAdJ9Jcu7LTL2QQ6xHgzL1Ccl8K5eDhJuV6n4IggX3k2DlDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-03T13:30:57.005474Z"},"content_sha256":"c66bd5987c6bf1ff68122b7a3f46a65ba809d4fb7cfc5090344272604191119e","schema_version":"1.0","event_id":"sha256:c66bd5987c6bf1ff68122b7a3f46a65ba809d4fb7cfc5090344272604191119e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:6LVEPCY44OZYY4WUB26C6E5QPX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Riesz Means and Beurling Moving Averages","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"N. H. Bingham","submitted_at":"2015-02-26T10:31:00Z","abstract_excerpt":"We survey the interplay between the Riesz means and Beurling moving averages of the title, obtaining Abelian and Tauberian results relating different Riesz means (or Beurling moving averages) whose defining functions have comparable growth. The motivation includes strong limit theorems in probability theory."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.07494","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":"2026-05-18T02:26:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NykXcBm2VJPcsA3Qh26XpynN89LxAx83WRm8Si1m1F3mQDGqIZRWqFsJ41beyA5lPt+W9AohSGAyn//iEyDCCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-03T13:30:57.005837Z"},"content_sha256":"605885e958acbaaadf2563c4759ae3fafc19d9c19aed85693a9ea648dc351b3b","schema_version":"1.0","event_id":"sha256:605885e958acbaaadf2563c4759ae3fafc19d9c19aed85693a9ea648dc351b3b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6LVEPCY44OZYY4WUB26C6E5QPX/bundle.json","state_url":"https://pith.science/pith/6LVEPCY44OZYY4WUB26C6E5QPX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6LVEPCY44OZYY4WUB26C6E5QPX/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":"2026-07-03T13:30:57Z","links":{"resolver":"https://pith.science/pith/6LVEPCY44OZYY4WUB26C6E5QPX","bundle":"https://pith.science/pith/6LVEPCY44OZYY4WUB26C6E5QPX/bundle.json","state":"https://pith.science/pith/6LVEPCY44OZYY4WUB26C6E5QPX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6LVEPCY44OZYY4WUB26C6E5QPX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:6LVEPCY44OZYY4WUB26C6E5QPX","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":"fdaebd51bf649210b1afac9650c29f30f1890eb79ef6d26efee35fe183617f4e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-02-26T10:31:00Z","title_canon_sha256":"10470925f10e81952b6232f2c728a4d7a267bfac6f75927540872473c772c027"},"schema_version":"1.0","source":{"id":"1502.07494","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1502.07494","created_at":"2026-05-18T02:26:03Z"},{"alias_kind":"arxiv_version","alias_value":"1502.07494v1","created_at":"2026-05-18T02:26:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.07494","created_at":"2026-05-18T02:26:03Z"},{"alias_kind":"pith_short_12","alias_value":"6LVEPCY44OZY","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_16","alias_value":"6LVEPCY44OZYY4WU","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_8","alias_value":"6LVEPCY4","created_at":"2026-05-18T12:29:07Z"}],"graph_snapshots":[{"event_id":"sha256:605885e958acbaaadf2563c4759ae3fafc19d9c19aed85693a9ea648dc351b3b","target":"graph","created_at":"2026-05-18T02:26:03Z","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 survey the interplay between the Riesz means and Beurling moving averages of the title, obtaining Abelian and Tauberian results relating different Riesz means (or Beurling moving averages) whose defining functions have comparable growth. The motivation includes strong limit theorems in probability theory.","authors_text":"N. H. Bingham","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-02-26T10:31:00Z","title":"Riesz Means and Beurling Moving Averages"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.07494","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:c66bd5987c6bf1ff68122b7a3f46a65ba809d4fb7cfc5090344272604191119e","target":"record","created_at":"2026-05-18T02:26:03Z","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":"fdaebd51bf649210b1afac9650c29f30f1890eb79ef6d26efee35fe183617f4e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-02-26T10:31:00Z","title_canon_sha256":"10470925f10e81952b6232f2c728a4d7a267bfac6f75927540872473c772c027"},"schema_version":"1.0","source":{"id":"1502.07494","kind":"arxiv","version":1}},"canonical_sha256":"f2ea478b1ce3b38c72d40ebc2f13b07dcc61df696b0ce090aba8cf55ceee231c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f2ea478b1ce3b38c72d40ebc2f13b07dcc61df696b0ce090aba8cf55ceee231c","first_computed_at":"2026-05-18T02:26:03.541572Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:26:03.541572Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"afhmqv6qbg4RjZmY6tH7hqAeBL1n7ZS4k+nl4kagA+WD3ynLbtAUyzdM4wkixfmXbYOyAkuFPe4hIR2ce1T1Dw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:26:03.542079Z","signed_message":"canonical_sha256_bytes"},"source_id":"1502.07494","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c66bd5987c6bf1ff68122b7a3f46a65ba809d4fb7cfc5090344272604191119e","sha256:605885e958acbaaadf2563c4759ae3fafc19d9c19aed85693a9ea648dc351b3b"],"state_sha256":"05d74222821b13673277547ff3f4e8b3b792606a1bc3f8c4ff7f720a46643a98"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8FLvqgCFS4lyHaswJP6NOOEUikcmrJ/WrNbSEc3I29hkVBKSULWW1Z5AvU/H5eSGAU6dXVPXccCwDMJ3dDMmCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-03T13:30:57.007784Z","bundle_sha256":"3dddbcdf07277426b56a347c00618855f05359136ebf33eadf05e1faf0198173"}}