{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:LEMIYCB5HRR6IDXZ4AHDX3TQDP","short_pith_number":"pith:LEMIYCB5","canonical_record":{"source":{"id":"1810.11331","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-10-26T13:55:58Z","cross_cats_sorted":[],"title_canon_sha256":"10298dd9396bb89b7eec9c41a5e5be4ad6caf045e1c9a4833903224f0c8f3580","abstract_canon_sha256":"d23a4526844f19ca8672471b06b019779a794f18eee3b40881ad9e82bc74d447"},"schema_version":"1.0"},"canonical_sha256":"59188c083d3c63e40ef9e00e3bee701bce94d06568b9738356859b17fef0427e","source":{"kind":"arxiv","id":"1810.11331","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.11331","created_at":"2026-05-18T00:02:14Z"},{"alias_kind":"arxiv_version","alias_value":"1810.11331v1","created_at":"2026-05-18T00:02:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.11331","created_at":"2026-05-18T00:02:14Z"},{"alias_kind":"pith_short_12","alias_value":"LEMIYCB5HRR6","created_at":"2026-05-18T12:32:37Z"},{"alias_kind":"pith_short_16","alias_value":"LEMIYCB5HRR6IDXZ","created_at":"2026-05-18T12:32:37Z"},{"alias_kind":"pith_short_8","alias_value":"LEMIYCB5","created_at":"2026-05-18T12:32:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:LEMIYCB5HRR6IDXZ4AHDX3TQDP","target":"record","payload":{"canonical_record":{"source":{"id":"1810.11331","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-10-26T13:55:58Z","cross_cats_sorted":[],"title_canon_sha256":"10298dd9396bb89b7eec9c41a5e5be4ad6caf045e1c9a4833903224f0c8f3580","abstract_canon_sha256":"d23a4526844f19ca8672471b06b019779a794f18eee3b40881ad9e82bc74d447"},"schema_version":"1.0"},"canonical_sha256":"59188c083d3c63e40ef9e00e3bee701bce94d06568b9738356859b17fef0427e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:02:14.462803Z","signature_b64":"mx5WOX0pJ1YfzEHyfQ1oaaMgiWJChWYwzr4I5H42yLmAYy3AmFnEQXjXMbnURXbuh1PqWg3So3TB+ftMdYoRCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"59188c083d3c63e40ef9e00e3bee701bce94d06568b9738356859b17fef0427e","last_reissued_at":"2026-05-18T00:02:14.462103Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:02:14.462103Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1810.11331","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":"2026-05-18T00:02:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DSl1r4fkrWI34wBO2vV6nkCJ77nmHs2RUXMsNF5pXcV/6E4c8DkvhIyPIC8Qe0jjYWQ0rJ71Y4K18Hy7MLnMBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T02:38:35.441192Z"},"content_sha256":"a72867389d00bc4f67117b87b4cc4a88b8b2bc35aa9be2a79d3429f5c179b2b5","schema_version":"1.0","event_id":"sha256:a72867389d00bc4f67117b87b4cc4a88b8b2bc35aa9be2a79d3429f5c179b2b5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:LEMIYCB5HRR6IDXZ4AHDX3TQDP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Weighted inequalities of Fefferman-Stein type for Riesz-Schr\\\"odinger Transforms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Bruno Bongioanni, Eleonor Harboure, Pablo Quijano","submitted_at":"2018-10-26T13:55:58Z","abstract_excerpt":"In this work we are concerned with Fefferman-Stein type inequalities. More precisely, given an operator $T$ and some $p$, $1<p<\\infty$, we look for operators $\\mathcal{M}$ such that the inequality $$\\int |Tf|^pw\\leq C\\int |f|^p \\mathcal{M}w$$ holds true for any weight $w$. Specifically, we are interested in the case of $T$ being any first or second order Riesz transform associated to the Schr\\\"odinger operator $L=-\\Delta + V$, with $V$ a non-negative function satisfying an appropriate reverse-H\\\"older condition. For the Riesz-Schr\\\"odinger transforms $\\nabla L^{-1/2}$ and $\\nabla^2 L^{-1}$ we "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.11331","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":"2026-05-18T00:02:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vWJLTSASZVoVd6PiV4iE7WvrkgI2uWSJFL8q6cufKd92hzJ7yRb0UlnyOkcZBLkvPI032cRj0A/T53Y4yhyyCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T02:38:35.441906Z"},"content_sha256":"c82a607f339ec12bc3a3081b35995ebd3b7ba5670054549edf000dc78e7db902","schema_version":"1.0","event_id":"sha256:c82a607f339ec12bc3a3081b35995ebd3b7ba5670054549edf000dc78e7db902"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LEMIYCB5HRR6IDXZ4AHDX3TQDP/bundle.json","state_url":"https://pith.science/pith/LEMIYCB5HRR6IDXZ4AHDX3TQDP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LEMIYCB5HRR6IDXZ4AHDX3TQDP/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":"2026-06-11T02:38:35Z","links":{"resolver":"https://pith.science/pith/LEMIYCB5HRR6IDXZ4AHDX3TQDP","bundle":"https://pith.science/pith/LEMIYCB5HRR6IDXZ4AHDX3TQDP/bundle.json","state":"https://pith.science/pith/LEMIYCB5HRR6IDXZ4AHDX3TQDP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LEMIYCB5HRR6IDXZ4AHDX3TQDP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:LEMIYCB5HRR6IDXZ4AHDX3TQDP","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":"d23a4526844f19ca8672471b06b019779a794f18eee3b40881ad9e82bc74d447","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-10-26T13:55:58Z","title_canon_sha256":"10298dd9396bb89b7eec9c41a5e5be4ad6caf045e1c9a4833903224f0c8f3580"},"schema_version":"1.0","source":{"id":"1810.11331","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.11331","created_at":"2026-05-18T00:02:14Z"},{"alias_kind":"arxiv_version","alias_value":"1810.11331v1","created_at":"2026-05-18T00:02:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.11331","created_at":"2026-05-18T00:02:14Z"},{"alias_kind":"pith_short_12","alias_value":"LEMIYCB5HRR6","created_at":"2026-05-18T12:32:37Z"},{"alias_kind":"pith_short_16","alias_value":"LEMIYCB5HRR6IDXZ","created_at":"2026-05-18T12:32:37Z"},{"alias_kind":"pith_short_8","alias_value":"LEMIYCB5","created_at":"2026-05-18T12:32:37Z"}],"graph_snapshots":[{"event_id":"sha256:c82a607f339ec12bc3a3081b35995ebd3b7ba5670054549edf000dc78e7db902","target":"graph","created_at":"2026-05-18T00:02:14Z","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 work we are concerned with Fefferman-Stein type inequalities. More precisely, given an operator $T$ and some $p$, $1<p<\\infty$, we look for operators $\\mathcal{M}$ such that the inequality $$\\int |Tf|^pw\\leq C\\int |f|^p \\mathcal{M}w$$ holds true for any weight $w$. Specifically, we are interested in the case of $T$ being any first or second order Riesz transform associated to the Schr\\\"odinger operator $L=-\\Delta + V$, with $V$ a non-negative function satisfying an appropriate reverse-H\\\"older condition. For the Riesz-Schr\\\"odinger transforms $\\nabla L^{-1/2}$ and $\\nabla^2 L^{-1}$ we ","authors_text":"Bruno Bongioanni, Eleonor Harboure, Pablo Quijano","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-10-26T13:55:58Z","title":"Weighted inequalities of Fefferman-Stein type for Riesz-Schr\\\"odinger Transforms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.11331","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:a72867389d00bc4f67117b87b4cc4a88b8b2bc35aa9be2a79d3429f5c179b2b5","target":"record","created_at":"2026-05-18T00:02:14Z","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":"d23a4526844f19ca8672471b06b019779a794f18eee3b40881ad9e82bc74d447","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-10-26T13:55:58Z","title_canon_sha256":"10298dd9396bb89b7eec9c41a5e5be4ad6caf045e1c9a4833903224f0c8f3580"},"schema_version":"1.0","source":{"id":"1810.11331","kind":"arxiv","version":1}},"canonical_sha256":"59188c083d3c63e40ef9e00e3bee701bce94d06568b9738356859b17fef0427e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"59188c083d3c63e40ef9e00e3bee701bce94d06568b9738356859b17fef0427e","first_computed_at":"2026-05-18T00:02:14.462103Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:02:14.462103Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mx5WOX0pJ1YfzEHyfQ1oaaMgiWJChWYwzr4I5H42yLmAYy3AmFnEQXjXMbnURXbuh1PqWg3So3TB+ftMdYoRCw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:02:14.462803Z","signed_message":"canonical_sha256_bytes"},"source_id":"1810.11331","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a72867389d00bc4f67117b87b4cc4a88b8b2bc35aa9be2a79d3429f5c179b2b5","sha256:c82a607f339ec12bc3a3081b35995ebd3b7ba5670054549edf000dc78e7db902"],"state_sha256":"a26435a97f812473dd0054a48ee98de7a7daa6911397863b08edf97b06c3363a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cQLvZ7LI9TALaiiSoyoaTfx0zA9fodu30ZeU5urGCXdezw9k+U7GsxtkLOI+70g3vGZv1O5+ZLKhxkx0QHYqAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T02:38:35.445745Z","bundle_sha256":"834cace3d0dbe788caf5235ebdb17bd4e2dacce56dd524ee71eb110071c20537"}}