{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:F6XVGRS5B7I2OON2LPNGLU5EK3","short_pith_number":"pith:F6XVGRS5","canonical_record":{"source":{"id":"2302.12997","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CA","submitted_at":"2023-02-18T13:55:12Z","cross_cats_sorted":[],"title_canon_sha256":"a20677e430ec23fc0d846d8d3f6df3d2c43b22cbdb1ee8aa82809f8b68a2fdbd","abstract_canon_sha256":"2e9a1c2c73c34fb4509c0b3df0b1d941f197dd96129eeb34d2c2f977ebcf9e81"},"schema_version":"1.0"},"canonical_sha256":"2faf53465d0fd1a739ba5bda65d3a456f04f0fd7cbcea6d15b72838926edc923","source":{"kind":"arxiv","id":"2302.12997","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2302.12997","created_at":"2026-07-05T05:45:42Z"},{"alias_kind":"arxiv_version","alias_value":"2302.12997v1","created_at":"2026-07-05T05:45:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2302.12997","created_at":"2026-07-05T05:45:42Z"},{"alias_kind":"pith_short_12","alias_value":"F6XVGRS5B7I2","created_at":"2026-07-05T05:45:42Z"},{"alias_kind":"pith_short_16","alias_value":"F6XVGRS5B7I2OON2","created_at":"2026-07-05T05:45:42Z"},{"alias_kind":"pith_short_8","alias_value":"F6XVGRS5","created_at":"2026-07-05T05:45:42Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:F6XVGRS5B7I2OON2LPNGLU5EK3","target":"record","payload":{"canonical_record":{"source":{"id":"2302.12997","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CA","submitted_at":"2023-02-18T13:55:12Z","cross_cats_sorted":[],"title_canon_sha256":"a20677e430ec23fc0d846d8d3f6df3d2c43b22cbdb1ee8aa82809f8b68a2fdbd","abstract_canon_sha256":"2e9a1c2c73c34fb4509c0b3df0b1d941f197dd96129eeb34d2c2f977ebcf9e81"},"schema_version":"1.0"},"canonical_sha256":"2faf53465d0fd1a739ba5bda65d3a456f04f0fd7cbcea6d15b72838926edc923","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:45:42.072523Z","signature_b64":"IokuYe8nmbh7GzVq93ePm7vZluApt2GVfo1Kd7ibkzG30Q2dUJm61gGm9Cs/trKV9i99O4fpQtbKUcV6nSsQBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2faf53465d0fd1a739ba5bda65d3a456f04f0fd7cbcea6d15b72838926edc923","last_reissued_at":"2026-07-05T05:45:42.072085Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:45:42.072085Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2302.12997","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":"2026-07-05T05:45:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"d9UfyyjByD8xGAMucdt7VDbbaUDSpPxzHV5aAjpdoSp7Lc+2ZlNabJ9BEVsvdoysASrY0Ov4jg+++8nOgP9ODg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-20T00:00:25.300299Z"},"content_sha256":"5b055ee8268adc7dd775045f9232dd8361d14d90ca181c2f8844d714e9df475c","schema_version":"1.0","event_id":"sha256:5b055ee8268adc7dd775045f9232dd8361d14d90ca181c2f8844d714e9df475c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:F6XVGRS5B7I2OON2LPNGLU5EK3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Some new restricted maximal operators of Fej\\'er means of Walsh-Fourier series in the space $H_{1/2}$","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Davit Baramidze, George Tephnadze, Lars-Erik Persson","submitted_at":"2023-02-18T13:55:12Z","abstract_excerpt":"In this paper we derive the maximal subspace of natural numbers $\\left\\{n_{k}:k\\geq 0\\right\\}$, such that the restricted maximal operator, defined by $\\sup_{k\\in \\mathbb{N}}\\left\\vert \\sigma_{n_{k}}F \\right\\vert$ on this subspace of Fej\\'er means of Walsh-Fourier series is bounded from the martingale Hardy space $H_{1/2}$ to the Lebesgue space $L_{1/2}$. The sharpness of this result is also proved."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2302.12997","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2302.12997/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T05:45:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RvF2NMR53Fm+Y32TUXBRzqsxhu8H+qTknYCftw/lGR7RN2UaUyLoo0amkySJUGwWSS5rO73hhaMCjqf9VeyLDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-20T00:00:25.300667Z"},"content_sha256":"ff367f33a226ea22325e0eb934f715aa0a5644f4499d6861385e3ea2f4397195","schema_version":"1.0","event_id":"sha256:ff367f33a226ea22325e0eb934f715aa0a5644f4499d6861385e3ea2f4397195"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/F6XVGRS5B7I2OON2LPNGLU5EK3/bundle.json","state_url":"https://pith.science/pith/F6XVGRS5B7I2OON2LPNGLU5EK3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/F6XVGRS5B7I2OON2LPNGLU5EK3/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":"2026-07-20T00:00:25Z","links":{"resolver":"https://pith.science/pith/F6XVGRS5B7I2OON2LPNGLU5EK3","bundle":"https://pith.science/pith/F6XVGRS5B7I2OON2LPNGLU5EK3/bundle.json","state":"https://pith.science/pith/F6XVGRS5B7I2OON2LPNGLU5EK3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/F6XVGRS5B7I2OON2LPNGLU5EK3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:F6XVGRS5B7I2OON2LPNGLU5EK3","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":"2e9a1c2c73c34fb4509c0b3df0b1d941f197dd96129eeb34d2c2f977ebcf9e81","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CA","submitted_at":"2023-02-18T13:55:12Z","title_canon_sha256":"a20677e430ec23fc0d846d8d3f6df3d2c43b22cbdb1ee8aa82809f8b68a2fdbd"},"schema_version":"1.0","source":{"id":"2302.12997","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2302.12997","created_at":"2026-07-05T05:45:42Z"},{"alias_kind":"arxiv_version","alias_value":"2302.12997v1","created_at":"2026-07-05T05:45:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2302.12997","created_at":"2026-07-05T05:45:42Z"},{"alias_kind":"pith_short_12","alias_value":"F6XVGRS5B7I2","created_at":"2026-07-05T05:45:42Z"},{"alias_kind":"pith_short_16","alias_value":"F6XVGRS5B7I2OON2","created_at":"2026-07-05T05:45:42Z"},{"alias_kind":"pith_short_8","alias_value":"F6XVGRS5","created_at":"2026-07-05T05:45:42Z"}],"graph_snapshots":[{"event_id":"sha256:ff367f33a226ea22325e0eb934f715aa0a5644f4499d6861385e3ea2f4397195","target":"graph","created_at":"2026-07-05T05:45:42Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2302.12997/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper we derive the maximal subspace of natural numbers $\\left\\{n_{k}:k\\geq 0\\right\\}$, such that the restricted maximal operator, defined by $\\sup_{k\\in \\mathbb{N}}\\left\\vert \\sigma_{n_{k}}F \\right\\vert$ on this subspace of Fej\\'er means of Walsh-Fourier series is bounded from the martingale Hardy space $H_{1/2}$ to the Lebesgue space $L_{1/2}$. The sharpness of this result is also proved.","authors_text":"Davit Baramidze, George Tephnadze, Lars-Erik Persson","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CA","submitted_at":"2023-02-18T13:55:12Z","title":"Some new restricted maximal operators of Fej\\'er means of Walsh-Fourier series in the space $H_{1/2}$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2302.12997","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":"sha256:5b055ee8268adc7dd775045f9232dd8361d14d90ca181c2f8844d714e9df475c","target":"record","created_at":"2026-07-05T05:45:42Z","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":"2e9a1c2c73c34fb4509c0b3df0b1d941f197dd96129eeb34d2c2f977ebcf9e81","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CA","submitted_at":"2023-02-18T13:55:12Z","title_canon_sha256":"a20677e430ec23fc0d846d8d3f6df3d2c43b22cbdb1ee8aa82809f8b68a2fdbd"},"schema_version":"1.0","source":{"id":"2302.12997","kind":"arxiv","version":1}},"canonical_sha256":"2faf53465d0fd1a739ba5bda65d3a456f04f0fd7cbcea6d15b72838926edc923","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2faf53465d0fd1a739ba5bda65d3a456f04f0fd7cbcea6d15b72838926edc923","first_computed_at":"2026-07-05T05:45:42.072085Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:45:42.072085Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"IokuYe8nmbh7GzVq93ePm7vZluApt2GVfo1Kd7ibkzG30Q2dUJm61gGm9Cs/trKV9i99O4fpQtbKUcV6nSsQBQ==","signature_status":"signed_v1","signed_at":"2026-07-05T05:45:42.072523Z","signed_message":"canonical_sha256_bytes"},"source_id":"2302.12997","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5b055ee8268adc7dd775045f9232dd8361d14d90ca181c2f8844d714e9df475c","sha256:ff367f33a226ea22325e0eb934f715aa0a5644f4499d6861385e3ea2f4397195"],"state_sha256":"648fb125733f00dacebf1817f0c57612f882cfc08686a3d63cb5da775bb62d57"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qYXBDAoCNw4rpAbk2rqAtHooXEZAi0lxRZ66+y1ifErqWKVfm+L5eDGb0zPHZWk0/TckT5APVp+AIDscnyfdDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-20T00:00:25.302674Z","bundle_sha256":"a02654fe39290d0f06cc8d2265411ec52afbc13ce27514190b1583ebbd81d93a"}}