{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:VFINDCXNJDHJFHOI4I6CGOYH5F","short_pith_number":"pith:VFINDCXN","canonical_record":{"source":{"id":"1003.4092","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2010-03-22T08:31:14Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"1be78ee6c00121d1e6292145d1e693a772a6a3f8e3345d30425f9e12f9184f9b","abstract_canon_sha256":"4c2c1da3786318706b6e61bb51970a326ca7da63fdf2dc8a1d231bbcdf5787e0"},"schema_version":"1.0"},"canonical_sha256":"a950d18aed48ce929dc8e23c233b07e97c54d2f1fe8b2b7437c1f3c3bd609469","source":{"kind":"arxiv","id":"1003.4092","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1003.4092","created_at":"2026-05-18T04:34:38Z"},{"alias_kind":"arxiv_version","alias_value":"1003.4092v2","created_at":"2026-05-18T04:34:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1003.4092","created_at":"2026-05-18T04:34:38Z"},{"alias_kind":"pith_short_12","alias_value":"VFINDCXNJDHJ","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_16","alias_value":"VFINDCXNJDHJFHOI","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_8","alias_value":"VFINDCXN","created_at":"2026-05-18T12:26:15Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:VFINDCXNJDHJFHOI4I6CGOYH5F","target":"record","payload":{"canonical_record":{"source":{"id":"1003.4092","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2010-03-22T08:31:14Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"1be78ee6c00121d1e6292145d1e693a772a6a3f8e3345d30425f9e12f9184f9b","abstract_canon_sha256":"4c2c1da3786318706b6e61bb51970a326ca7da63fdf2dc8a1d231bbcdf5787e0"},"schema_version":"1.0"},"canonical_sha256":"a950d18aed48ce929dc8e23c233b07e97c54d2f1fe8b2b7437c1f3c3bd609469","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:34:38.120144Z","signature_b64":"4T9i3uw0Sero3Ac0KogqJH/u8ctBNiVszzsZZ1qhbMC7zpbwOz4CfoB8ddAnIFotM5I+etmGAjhnROxXX/fWBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a950d18aed48ce929dc8e23c233b07e97c54d2f1fe8b2b7437c1f3c3bd609469","last_reissued_at":"2026-05-18T04:34:38.119618Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:34:38.119618Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1003.4092","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":"2026-05-18T04:34:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uaBvQ+taSpMY49gBXwKFVSLF+RgEJ0f3+7rmGKMxGiwJcRex+m0j96g4uE4BgYqyILp7EOmVzfckxqJCnfN0Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T09:40:12.237202Z"},"content_sha256":"594bf429bcca38836161e256ab812cd247e880dc1e58c995cd062aa99e121880","schema_version":"1.0","event_id":"sha256:594bf429bcca38836161e256ab812cd247e880dc1e58c995cd062aa99e121880"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:VFINDCXNJDHJFHOI4I6CGOYH5F","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Non-tangential maximal functions and conical square functions with respect to the Gaussian measure","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.FA","authors_text":"Jan Maas, Jan van Neerven, Pierre Portal","submitted_at":"2010-03-22T08:31:14Z","abstract_excerpt":"We study, in $L^{1}(\\R^n;\\gamma)$ with respect to the gaussian measure, non-tangential maximal functions and conical square functions associated with the Ornstein-Uhlenbeck operator by developing a set of techniques which allow us, to some extent, to compensate for the non-doubling character of the gaussian measure. The main result asserts that conical square functions can be controlled in $L^1$-norm by non-tangential maximal functions. Along the way we prove a change of aperture result for the latter. This complements recent results on gaussian Hardy spaces due to Mauceri and Meda."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1003.4092","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":"2026-05-18T04:34:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"g3IDg75SxNZ24aEQVwm34AafSZSvjmlsBd2pONC1HbEkrkXC0MAmi6bqv0YQXrjJTm6p+jju0Rlep1bFdeDuBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T09:40:12.237909Z"},"content_sha256":"cba6850c357caf8a00543b3b032dd2b8e29bd16d7273cdca612e66b239627a59","schema_version":"1.0","event_id":"sha256:cba6850c357caf8a00543b3b032dd2b8e29bd16d7273cdca612e66b239627a59"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VFINDCXNJDHJFHOI4I6CGOYH5F/bundle.json","state_url":"https://pith.science/pith/VFINDCXNJDHJFHOI4I6CGOYH5F/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VFINDCXNJDHJFHOI4I6CGOYH5F/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":"2026-05-31T09:40:12Z","links":{"resolver":"https://pith.science/pith/VFINDCXNJDHJFHOI4I6CGOYH5F","bundle":"https://pith.science/pith/VFINDCXNJDHJFHOI4I6CGOYH5F/bundle.json","state":"https://pith.science/pith/VFINDCXNJDHJFHOI4I6CGOYH5F/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VFINDCXNJDHJFHOI4I6CGOYH5F/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:VFINDCXNJDHJFHOI4I6CGOYH5F","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":"4c2c1da3786318706b6e61bb51970a326ca7da63fdf2dc8a1d231bbcdf5787e0","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2010-03-22T08:31:14Z","title_canon_sha256":"1be78ee6c00121d1e6292145d1e693a772a6a3f8e3345d30425f9e12f9184f9b"},"schema_version":"1.0","source":{"id":"1003.4092","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1003.4092","created_at":"2026-05-18T04:34:38Z"},{"alias_kind":"arxiv_version","alias_value":"1003.4092v2","created_at":"2026-05-18T04:34:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1003.4092","created_at":"2026-05-18T04:34:38Z"},{"alias_kind":"pith_short_12","alias_value":"VFINDCXNJDHJ","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_16","alias_value":"VFINDCXNJDHJFHOI","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_8","alias_value":"VFINDCXN","created_at":"2026-05-18T12:26:15Z"}],"graph_snapshots":[{"event_id":"sha256:cba6850c357caf8a00543b3b032dd2b8e29bd16d7273cdca612e66b239627a59","target":"graph","created_at":"2026-05-18T04:34:38Z","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 study, in $L^{1}(\\R^n;\\gamma)$ with respect to the gaussian measure, non-tangential maximal functions and conical square functions associated with the Ornstein-Uhlenbeck operator by developing a set of techniques which allow us, to some extent, to compensate for the non-doubling character of the gaussian measure. The main result asserts that conical square functions can be controlled in $L^1$-norm by non-tangential maximal functions. Along the way we prove a change of aperture result for the latter. This complements recent results on gaussian Hardy spaces due to Mauceri and Meda.","authors_text":"Jan Maas, Jan van Neerven, Pierre Portal","cross_cats":["math.CA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2010-03-22T08:31:14Z","title":"Non-tangential maximal functions and conical square functions with respect to the Gaussian measure"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1003.4092","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":"sha256:594bf429bcca38836161e256ab812cd247e880dc1e58c995cd062aa99e121880","target":"record","created_at":"2026-05-18T04:34:38Z","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":"4c2c1da3786318706b6e61bb51970a326ca7da63fdf2dc8a1d231bbcdf5787e0","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2010-03-22T08:31:14Z","title_canon_sha256":"1be78ee6c00121d1e6292145d1e693a772a6a3f8e3345d30425f9e12f9184f9b"},"schema_version":"1.0","source":{"id":"1003.4092","kind":"arxiv","version":2}},"canonical_sha256":"a950d18aed48ce929dc8e23c233b07e97c54d2f1fe8b2b7437c1f3c3bd609469","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a950d18aed48ce929dc8e23c233b07e97c54d2f1fe8b2b7437c1f3c3bd609469","first_computed_at":"2026-05-18T04:34:38.119618Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:34:38.119618Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4T9i3uw0Sero3Ac0KogqJH/u8ctBNiVszzsZZ1qhbMC7zpbwOz4CfoB8ddAnIFotM5I+etmGAjhnROxXX/fWBg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:34:38.120144Z","signed_message":"canonical_sha256_bytes"},"source_id":"1003.4092","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:594bf429bcca38836161e256ab812cd247e880dc1e58c995cd062aa99e121880","sha256:cba6850c357caf8a00543b3b032dd2b8e29bd16d7273cdca612e66b239627a59"],"state_sha256":"ede8d715fe351dbea618cb3b3a6d6d8fc933ac642c273cac04c2ce8c08145295"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Xhd+/bMRWqGgUqlAQe7jq87AN6czAfNviZzqkhYq8uP09c+QykbJ8CTMuXIT1eTpn1YfTaBnDx+HhNWte3owDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T09:40:12.241783Z","bundle_sha256":"88baa5659ac780959a235dc8139d4bf967c426917191a29da94076e548318df0"}}