{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:SKFUB7ZT55T2PPK4PQQIQVBSNC","short_pith_number":"pith:SKFUB7ZT","canonical_record":{"source":{"id":"1512.07518","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2015-12-23T15:36:19Z","cross_cats_sorted":[],"title_canon_sha256":"ec205b6f392108d49526feae7261446ee320c85cf4cd39921c7f81080bb366f4","abstract_canon_sha256":"3e8ba0b7c699c6eada8cbc2215b919c730063196ae13af8f6cd29ede5353dbee"},"schema_version":"1.0"},"canonical_sha256":"928b40ff33ef67a7bd5c7c2088543268af978ca10d9917fc25251df2decc3626","source":{"kind":"arxiv","id":"1512.07518","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.07518","created_at":"2026-05-18T00:02:03Z"},{"alias_kind":"arxiv_version","alias_value":"1512.07518v2","created_at":"2026-05-18T00:02:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.07518","created_at":"2026-05-18T00:02:03Z"},{"alias_kind":"pith_short_12","alias_value":"SKFUB7ZT55T2","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_16","alias_value":"SKFUB7ZT55T2PPK4","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_8","alias_value":"SKFUB7ZT","created_at":"2026-05-18T12:29:42Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:SKFUB7ZT55T2PPK4PQQIQVBSNC","target":"record","payload":{"canonical_record":{"source":{"id":"1512.07518","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2015-12-23T15:36:19Z","cross_cats_sorted":[],"title_canon_sha256":"ec205b6f392108d49526feae7261446ee320c85cf4cd39921c7f81080bb366f4","abstract_canon_sha256":"3e8ba0b7c699c6eada8cbc2215b919c730063196ae13af8f6cd29ede5353dbee"},"schema_version":"1.0"},"canonical_sha256":"928b40ff33ef67a7bd5c7c2088543268af978ca10d9917fc25251df2decc3626","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:02:03.638574Z","signature_b64":"MdLPyO0Pcqw0kyYpg2f9xF696yiW08e3F7/YoV9NzLBTLfEt4NUx6TQWYA74i68m8VUOMvDGqDPUsA6rbWh2Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"928b40ff33ef67a7bd5c7c2088543268af978ca10d9917fc25251df2decc3626","last_reissued_at":"2026-05-18T00:02:03.637915Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:02:03.637915Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1512.07518","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":"2026-05-18T00:02:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+c5OjcSMwT+qloQTm3D0+ZSbnaVo6DDkdjbPERRq3x4C7lGArOTC67SFl8R3w59jQF7W4HVMtGmuZMweYuX8BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T22:22:59.366233Z"},"content_sha256":"617308de58a062868ddf071ae110333c5843b1cf8154d7b84ddd1f1764729e64","schema_version":"1.0","event_id":"sha256:617308de58a062868ddf071ae110333c5843b1cf8154d7b84ddd1f1764729e64"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:SKFUB7ZT55T2PPK4PQQIQVBSNC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"$\\ell^p\\big(\\mathbb Z^d\\big)$-estimates for discrete operators of Radon type: Maximal functions and vector-valued estimates","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Bartosz Trojan, Elias M. Stein, Mariusz Mirek","submitted_at":"2015-12-23T15:36:19Z","abstract_excerpt":"We prove $\\ell^p\\big(\\mathbb Z^d\\big)$ bounds, for $p\\in(1, \\infty)$, of discrete maximal functions corresponding to averaging operators and truncated singular integrals of Radon type, and their applications to pointwise ergodic theory. Our new approach is based on a unified analysis of both types of operators, and also yields an extension to the vector-valued form of these results."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.07518","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":"2026-05-18T00:02:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vTooimc+ESjuV6zTPyIRQdEtzDEabQkjhQkj9fDnEDd1cpYpb5v7X5TtEJrT7S36YHIRMgsH/OqPVZyQaWKeDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T22:22:59.366940Z"},"content_sha256":"572ad93dd0e9155191366f73d6087ea9dc54883e5775cb43299bd9939f6beb3e","schema_version":"1.0","event_id":"sha256:572ad93dd0e9155191366f73d6087ea9dc54883e5775cb43299bd9939f6beb3e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SKFUB7ZT55T2PPK4PQQIQVBSNC/bundle.json","state_url":"https://pith.science/pith/SKFUB7ZT55T2PPK4PQQIQVBSNC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SKFUB7ZT55T2PPK4PQQIQVBSNC/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":"2026-05-27T22:22:59Z","links":{"resolver":"https://pith.science/pith/SKFUB7ZT55T2PPK4PQQIQVBSNC","bundle":"https://pith.science/pith/SKFUB7ZT55T2PPK4PQQIQVBSNC/bundle.json","state":"https://pith.science/pith/SKFUB7ZT55T2PPK4PQQIQVBSNC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SKFUB7ZT55T2PPK4PQQIQVBSNC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:SKFUB7ZT55T2PPK4PQQIQVBSNC","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":"3e8ba0b7c699c6eada8cbc2215b919c730063196ae13af8f6cd29ede5353dbee","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2015-12-23T15:36:19Z","title_canon_sha256":"ec205b6f392108d49526feae7261446ee320c85cf4cd39921c7f81080bb366f4"},"schema_version":"1.0","source":{"id":"1512.07518","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.07518","created_at":"2026-05-18T00:02:03Z"},{"alias_kind":"arxiv_version","alias_value":"1512.07518v2","created_at":"2026-05-18T00:02:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.07518","created_at":"2026-05-18T00:02:03Z"},{"alias_kind":"pith_short_12","alias_value":"SKFUB7ZT55T2","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_16","alias_value":"SKFUB7ZT55T2PPK4","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_8","alias_value":"SKFUB7ZT","created_at":"2026-05-18T12:29:42Z"}],"graph_snapshots":[{"event_id":"sha256:572ad93dd0e9155191366f73d6087ea9dc54883e5775cb43299bd9939f6beb3e","target":"graph","created_at":"2026-05-18T00:02:03Z","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 prove $\\ell^p\\big(\\mathbb Z^d\\big)$ bounds, for $p\\in(1, \\infty)$, of discrete maximal functions corresponding to averaging operators and truncated singular integrals of Radon type, and their applications to pointwise ergodic theory. Our new approach is based on a unified analysis of both types of operators, and also yields an extension to the vector-valued form of these results.","authors_text":"Bartosz Trojan, Elias M. Stein, Mariusz Mirek","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2015-12-23T15:36:19Z","title":"$\\ell^p\\big(\\mathbb Z^d\\big)$-estimates for discrete operators of Radon type: Maximal functions and vector-valued estimates"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.07518","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":"sha256:617308de58a062868ddf071ae110333c5843b1cf8154d7b84ddd1f1764729e64","target":"record","created_at":"2026-05-18T00:02:03Z","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":"3e8ba0b7c699c6eada8cbc2215b919c730063196ae13af8f6cd29ede5353dbee","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2015-12-23T15:36:19Z","title_canon_sha256":"ec205b6f392108d49526feae7261446ee320c85cf4cd39921c7f81080bb366f4"},"schema_version":"1.0","source":{"id":"1512.07518","kind":"arxiv","version":2}},"canonical_sha256":"928b40ff33ef67a7bd5c7c2088543268af978ca10d9917fc25251df2decc3626","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"928b40ff33ef67a7bd5c7c2088543268af978ca10d9917fc25251df2decc3626","first_computed_at":"2026-05-18T00:02:03.637915Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:02:03.637915Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MdLPyO0Pcqw0kyYpg2f9xF696yiW08e3F7/YoV9NzLBTLfEt4NUx6TQWYA74i68m8VUOMvDGqDPUsA6rbWh2Bg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:02:03.638574Z","signed_message":"canonical_sha256_bytes"},"source_id":"1512.07518","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:617308de58a062868ddf071ae110333c5843b1cf8154d7b84ddd1f1764729e64","sha256:572ad93dd0e9155191366f73d6087ea9dc54883e5775cb43299bd9939f6beb3e"],"state_sha256":"daa0c86d81d969d621b2a0a914bfc7440477c96cb955a524d343790baf8a224a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"o7ipMXHmuJcgMg578ANd5Uh7XXA5CxGl0PJHNa76gBrDyVBYHKES0W5yU8aw2Cbu0c/M2p/kXn2VCNhymlqqBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T22:22:59.370303Z","bundle_sha256":"ed965ef3d2a16ad6fea3664a4a0d88f7409082743ceee1e5de54aeb5318643f1"}}