{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:5F7UBFGGAJPQGCYH5ZGH76Y3NC","short_pith_number":"pith:5F7UBFGG","canonical_record":{"source":{"id":"1604.08695","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-04-29T05:44:28Z","cross_cats_sorted":[],"title_canon_sha256":"b5a61f8c2ea1e1312edfcd9d28e2911ab431050db4fd3f03e8984fdd666d1c62","abstract_canon_sha256":"be6801a6111fdf66478d8250731f908e849efafa89e976ea8dc7e60ffb3e570c"},"schema_version":"1.0"},"canonical_sha256":"e97f4094c6025f030b07ee4c7ffb1b68bf7a5a9a436dc18e2e5ef7ed9e0b3620","source":{"kind":"arxiv","id":"1604.08695","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1604.08695","created_at":"2026-05-18T01:16:02Z"},{"alias_kind":"arxiv_version","alias_value":"1604.08695v1","created_at":"2026-05-18T01:16:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.08695","created_at":"2026-05-18T01:16:02Z"},{"alias_kind":"pith_short_12","alias_value":"5F7UBFGGAJPQ","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_16","alias_value":"5F7UBFGGAJPQGCYH","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_8","alias_value":"5F7UBFGG","created_at":"2026-05-18T12:30:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:5F7UBFGGAJPQGCYH5ZGH76Y3NC","target":"record","payload":{"canonical_record":{"source":{"id":"1604.08695","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-04-29T05:44:28Z","cross_cats_sorted":[],"title_canon_sha256":"b5a61f8c2ea1e1312edfcd9d28e2911ab431050db4fd3f03e8984fdd666d1c62","abstract_canon_sha256":"be6801a6111fdf66478d8250731f908e849efafa89e976ea8dc7e60ffb3e570c"},"schema_version":"1.0"},"canonical_sha256":"e97f4094c6025f030b07ee4c7ffb1b68bf7a5a9a436dc18e2e5ef7ed9e0b3620","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:16:02.155378Z","signature_b64":"VDLDvMEpdLQSoFGVXKaZhfrvxu/9S5s5OKnbljvQzVB9eMciftdAdccrHNBdb44RcH1g+nsMrYNNvPixz9FqDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e97f4094c6025f030b07ee4c7ffb1b68bf7a5a9a436dc18e2e5ef7ed9e0b3620","last_reissued_at":"2026-05-18T01:16:02.154565Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:16:02.154565Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1604.08695","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":"2026-05-18T01:16:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QQUPJngbFzFmHfSQvz2z4w6J0E+ujE0cWdou2i9mD+8lbMNQORon1O2PHbMnwtUiMVNt8iW8cnO9u0ZQlWIfCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T16:27:56.850187Z"},"content_sha256":"cef9f99ceb3b8261747e36016ddf298efccf06b5957f11c4b1c804622704e9a0","schema_version":"1.0","event_id":"sha256:cef9f99ceb3b8261747e36016ddf298efccf06b5957f11c4b1c804622704e9a0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:5F7UBFGGAJPQGCYH5ZGH76Y3NC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Discrete Carleson Theorem Along the Primes with a Restricted Supremum","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Ben Krause, Izabella Laba, Kevin Henriot, Laura Cladek, Malabika Pramanik","submitted_at":"2016-04-29T05:44:28Z","abstract_excerpt":"Consider the discrete maximal function acting on finitely supported functions on the integers, \\[ \\mathcal{C}_\\Lambda f(n) := \\sup_{\\lambda \\in \\Lambda} | \\sum_{p \\in \\pm \\mathbb{P}} f(n-p) \\log |p| \\frac{e^{2\\pi i \\lambda p}}{p} |,\\] where $\\pm \\mathbb{P} := \\{ \\pm p : p \\text{ is a prime} \\}$, and $\\Lambda \\subset [0,1]$. We give sufficient conditions on $\\Lambda$, met by (finite unions of) lacunary sets, for this to be a bounded sublinear operator on $\\ell^p(\\mathbb{Z})$ for $\\frac{3}{2} < p < 4$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.08695","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":"2026-05-18T01:16:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"k7/Bv0eGkuykyIKuyrUteHYxri5nIBSsgPPL/1KRSWWId+s06/BLkB/gDaeKZweKnd9rqJfN8Yjv38fU0+B+BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T16:27:56.850546Z"},"content_sha256":"37ffcfd608c4a184f52aca432b23a416de16c30b29893412d981e96547ce49ec","schema_version":"1.0","event_id":"sha256:37ffcfd608c4a184f52aca432b23a416de16c30b29893412d981e96547ce49ec"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5F7UBFGGAJPQGCYH5ZGH76Y3NC/bundle.json","state_url":"https://pith.science/pith/5F7UBFGGAJPQGCYH5ZGH76Y3NC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5F7UBFGGAJPQGCYH5ZGH76Y3NC/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":"2026-06-01T16:27:56Z","links":{"resolver":"https://pith.science/pith/5F7UBFGGAJPQGCYH5ZGH76Y3NC","bundle":"https://pith.science/pith/5F7UBFGGAJPQGCYH5ZGH76Y3NC/bundle.json","state":"https://pith.science/pith/5F7UBFGGAJPQGCYH5ZGH76Y3NC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5F7UBFGGAJPQGCYH5ZGH76Y3NC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:5F7UBFGGAJPQGCYH5ZGH76Y3NC","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":"be6801a6111fdf66478d8250731f908e849efafa89e976ea8dc7e60ffb3e570c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-04-29T05:44:28Z","title_canon_sha256":"b5a61f8c2ea1e1312edfcd9d28e2911ab431050db4fd3f03e8984fdd666d1c62"},"schema_version":"1.0","source":{"id":"1604.08695","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1604.08695","created_at":"2026-05-18T01:16:02Z"},{"alias_kind":"arxiv_version","alias_value":"1604.08695v1","created_at":"2026-05-18T01:16:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.08695","created_at":"2026-05-18T01:16:02Z"},{"alias_kind":"pith_short_12","alias_value":"5F7UBFGGAJPQ","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_16","alias_value":"5F7UBFGGAJPQGCYH","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_8","alias_value":"5F7UBFGG","created_at":"2026-05-18T12:30:01Z"}],"graph_snapshots":[{"event_id":"sha256:37ffcfd608c4a184f52aca432b23a416de16c30b29893412d981e96547ce49ec","target":"graph","created_at":"2026-05-18T01:16:02Z","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":"Consider the discrete maximal function acting on finitely supported functions on the integers, \\[ \\mathcal{C}_\\Lambda f(n) := \\sup_{\\lambda \\in \\Lambda} | \\sum_{p \\in \\pm \\mathbb{P}} f(n-p) \\log |p| \\frac{e^{2\\pi i \\lambda p}}{p} |,\\] where $\\pm \\mathbb{P} := \\{ \\pm p : p \\text{ is a prime} \\}$, and $\\Lambda \\subset [0,1]$. We give sufficient conditions on $\\Lambda$, met by (finite unions of) lacunary sets, for this to be a bounded sublinear operator on $\\ell^p(\\mathbb{Z})$ for $\\frac{3}{2} < p < 4$.","authors_text":"Ben Krause, Izabella Laba, Kevin Henriot, Laura Cladek, Malabika Pramanik","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-04-29T05:44:28Z","title":"A Discrete Carleson Theorem Along the Primes with a Restricted Supremum"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.08695","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:cef9f99ceb3b8261747e36016ddf298efccf06b5957f11c4b1c804622704e9a0","target":"record","created_at":"2026-05-18T01:16:02Z","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":"be6801a6111fdf66478d8250731f908e849efafa89e976ea8dc7e60ffb3e570c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-04-29T05:44:28Z","title_canon_sha256":"b5a61f8c2ea1e1312edfcd9d28e2911ab431050db4fd3f03e8984fdd666d1c62"},"schema_version":"1.0","source":{"id":"1604.08695","kind":"arxiv","version":1}},"canonical_sha256":"e97f4094c6025f030b07ee4c7ffb1b68bf7a5a9a436dc18e2e5ef7ed9e0b3620","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e97f4094c6025f030b07ee4c7ffb1b68bf7a5a9a436dc18e2e5ef7ed9e0b3620","first_computed_at":"2026-05-18T01:16:02.154565Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:16:02.154565Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VDLDvMEpdLQSoFGVXKaZhfrvxu/9S5s5OKnbljvQzVB9eMciftdAdccrHNBdb44RcH1g+nsMrYNNvPixz9FqDw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:16:02.155378Z","signed_message":"canonical_sha256_bytes"},"source_id":"1604.08695","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cef9f99ceb3b8261747e36016ddf298efccf06b5957f11c4b1c804622704e9a0","sha256:37ffcfd608c4a184f52aca432b23a416de16c30b29893412d981e96547ce49ec"],"state_sha256":"5baee20be4cf4dcc91a3358afa4406a255ea73d96c9cc73abe9ea94e399c82b9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"g7QGiyWR/FKToyvCiVvvhcKB8PSbkhRGVd/+hrnh85fNlPHZDtCOjKcXi3wi/sqwH1i/OkQhJ54RsdNQdvfjDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T16:27:56.852415Z","bundle_sha256":"33c44c32b6dc7a9384c9786a16858235742aeca7ca1c7751cfc74c760a8ed4ed"}}