{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:JEHU524G3YOHJHN5B5NYTVOJCK","short_pith_number":"pith:JEHU524G","canonical_record":{"source":{"id":"1510.02532","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2015-10-09T00:19:47Z","cross_cats_sorted":[],"title_canon_sha256":"af24608a1353ecdd315e0701dc26e92f2dac0887f4ab200ff1b2af1fb64eac6a","abstract_canon_sha256":"fa3fc765cd64a0d3b3d2469a8586e4c26267d20ea9a552c690be671ad9e30ddc"},"schema_version":"1.0"},"canonical_sha256":"490f4eeb86de1c749dbd0f5b89d5c912a567143d4ff65b0a63e2730790f16bd0","source":{"kind":"arxiv","id":"1510.02532","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.02532","created_at":"2026-05-18T01:30:42Z"},{"alias_kind":"arxiv_version","alias_value":"1510.02532v1","created_at":"2026-05-18T01:30:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.02532","created_at":"2026-05-18T01:30:42Z"},{"alias_kind":"pith_short_12","alias_value":"JEHU524G3YOH","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_16","alias_value":"JEHU524G3YOHJHN5","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_8","alias_value":"JEHU524G","created_at":"2026-05-18T12:29:27Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:JEHU524G3YOHJHN5B5NYTVOJCK","target":"record","payload":{"canonical_record":{"source":{"id":"1510.02532","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2015-10-09T00:19:47Z","cross_cats_sorted":[],"title_canon_sha256":"af24608a1353ecdd315e0701dc26e92f2dac0887f4ab200ff1b2af1fb64eac6a","abstract_canon_sha256":"fa3fc765cd64a0d3b3d2469a8586e4c26267d20ea9a552c690be671ad9e30ddc"},"schema_version":"1.0"},"canonical_sha256":"490f4eeb86de1c749dbd0f5b89d5c912a567143d4ff65b0a63e2730790f16bd0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:30:42.160175Z","signature_b64":"HVPe06qHJi6KEgmmCerX0r8jxUzkJbw9RB/6wCFCjh+W39JTjjKQLS5JD7Yh5NibMWJ38KqeHEN4Ra5LnaQ9DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"490f4eeb86de1c749dbd0f5b89d5c912a567143d4ff65b0a63e2730790f16bd0","last_reissued_at":"2026-05-18T01:30:42.159337Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:30:42.159337Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1510.02532","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":"2026-05-18T01:30:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1X7Am1tVxDT/e5mv9Amo1gCdutRcu2A2+QTWkSrRljQ+X0ggAxfCGegzXwqvnl3C6aKycWzRb2ysAH67oxu5Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T22:59:34.291117Z"},"content_sha256":"1859276ffcceaef2e7cf626ea8d64f9f940419ed6ab58f8c5eb2629a2e336caf","schema_version":"1.0","event_id":"sha256:1859276ffcceaef2e7cf626ea8d64f9f940419ed6ab58f8c5eb2629a2e336caf"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:JEHU524G3YOHJHN5B5NYTVOJCK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"New real variable methods in H summability of Fourier series","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"A. Susana Cor\\'e, Calixto P. Calder\\'on, Wilfredo Urbina","submitted_at":"2015-10-09T00:19:47Z","abstract_excerpt":"In this paper we shall be concerned with $H_\\alpha$ summability, for $0 < \\alpha \\leq 2$ of the Fourier series of arbitrary $L^1([-\\pi,\\pi]) $ functions. The methods to be employed here are a refinement of the real variable methods introduced by Marcinkiewicz in \\cite{Marcin1}. In addition, we introduce maximal theorems with respect to the Lebesgue measure and $A_1$ weights."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.02532","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":"2026-05-18T01:30:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DOTV3feElNcIjT2/4g9MOMDjxtbgordBeylb9ANbS/klQFYxVh4ekEHaiJJqFWKO+zLVIn4Q3UZJJiEnfxmRAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T22:59:34.291471Z"},"content_sha256":"727839902e61ba8c8e6f1da0e45486fe6dd3da9421c6c0c0b21ffce4f59039d2","schema_version":"1.0","event_id":"sha256:727839902e61ba8c8e6f1da0e45486fe6dd3da9421c6c0c0b21ffce4f59039d2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JEHU524G3YOHJHN5B5NYTVOJCK/bundle.json","state_url":"https://pith.science/pith/JEHU524G3YOHJHN5B5NYTVOJCK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JEHU524G3YOHJHN5B5NYTVOJCK/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":"2026-06-29T22:59:34Z","links":{"resolver":"https://pith.science/pith/JEHU524G3YOHJHN5B5NYTVOJCK","bundle":"https://pith.science/pith/JEHU524G3YOHJHN5B5NYTVOJCK/bundle.json","state":"https://pith.science/pith/JEHU524G3YOHJHN5B5NYTVOJCK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JEHU524G3YOHJHN5B5NYTVOJCK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:JEHU524G3YOHJHN5B5NYTVOJCK","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":"fa3fc765cd64a0d3b3d2469a8586e4c26267d20ea9a552c690be671ad9e30ddc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2015-10-09T00:19:47Z","title_canon_sha256":"af24608a1353ecdd315e0701dc26e92f2dac0887f4ab200ff1b2af1fb64eac6a"},"schema_version":"1.0","source":{"id":"1510.02532","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.02532","created_at":"2026-05-18T01:30:42Z"},{"alias_kind":"arxiv_version","alias_value":"1510.02532v1","created_at":"2026-05-18T01:30:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.02532","created_at":"2026-05-18T01:30:42Z"},{"alias_kind":"pith_short_12","alias_value":"JEHU524G3YOH","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_16","alias_value":"JEHU524G3YOHJHN5","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_8","alias_value":"JEHU524G","created_at":"2026-05-18T12:29:27Z"}],"graph_snapshots":[{"event_id":"sha256:727839902e61ba8c8e6f1da0e45486fe6dd3da9421c6c0c0b21ffce4f59039d2","target":"graph","created_at":"2026-05-18T01:30:42Z","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":"In this paper we shall be concerned with $H_\\alpha$ summability, for $0 < \\alpha \\leq 2$ of the Fourier series of arbitrary $L^1([-\\pi,\\pi]) $ functions. The methods to be employed here are a refinement of the real variable methods introduced by Marcinkiewicz in \\cite{Marcin1}. In addition, we introduce maximal theorems with respect to the Lebesgue measure and $A_1$ weights.","authors_text":"A. Susana Cor\\'e, Calixto P. Calder\\'on, Wilfredo Urbina","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2015-10-09T00:19:47Z","title":"New real variable methods in H summability of Fourier series"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.02532","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":"sha256:1859276ffcceaef2e7cf626ea8d64f9f940419ed6ab58f8c5eb2629a2e336caf","target":"record","created_at":"2026-05-18T01:30:42Z","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":"fa3fc765cd64a0d3b3d2469a8586e4c26267d20ea9a552c690be671ad9e30ddc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2015-10-09T00:19:47Z","title_canon_sha256":"af24608a1353ecdd315e0701dc26e92f2dac0887f4ab200ff1b2af1fb64eac6a"},"schema_version":"1.0","source":{"id":"1510.02532","kind":"arxiv","version":1}},"canonical_sha256":"490f4eeb86de1c749dbd0f5b89d5c912a567143d4ff65b0a63e2730790f16bd0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"490f4eeb86de1c749dbd0f5b89d5c912a567143d4ff65b0a63e2730790f16bd0","first_computed_at":"2026-05-18T01:30:42.159337Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:30:42.159337Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HVPe06qHJi6KEgmmCerX0r8jxUzkJbw9RB/6wCFCjh+W39JTjjKQLS5JD7Yh5NibMWJ38KqeHEN4Ra5LnaQ9DA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:30:42.160175Z","signed_message":"canonical_sha256_bytes"},"source_id":"1510.02532","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1859276ffcceaef2e7cf626ea8d64f9f940419ed6ab58f8c5eb2629a2e336caf","sha256:727839902e61ba8c8e6f1da0e45486fe6dd3da9421c6c0c0b21ffce4f59039d2"],"state_sha256":"cd63e9d267cf849e36d757e1a8cc548adb1c84e58b8e14b9d75030d16cbb6ca3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ceb/CoPed1PLICF28/fDcbg+pkUjqObX4EY5hdlGk8N03lPIrFNyWboLSsFMPsix4e11PBhaojiBY5JA4UjrAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-29T22:59:34.293338Z","bundle_sha256":"4c784c8f6416a7bb1281c162ba383288c3700f725f56a0696428d70b2579e8d0"}}