{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:IVDEACM4H7EMWC2RZIRJCFONPR","short_pith_number":"pith:IVDEACM4","canonical_record":{"source":{"id":"2605.19438","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-05-19T06:48:37Z","cross_cats_sorted":[],"title_canon_sha256":"0e9b45d6610835443b8e47e95c7f204c71fbd4430ecb472cef9b392298fafa22","abstract_canon_sha256":"df81b2b1ae6ba46fb1b15ae79953cb766a60eb76c715666729270d349842156f"},"schema_version":"1.0"},"canonical_sha256":"454640099c3fc8cb0b51ca229115cd7c64752d5caaff30b50f4b6bd69f4ad93a","source":{"kind":"arxiv","id":"2605.19438","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.19438","created_at":"2026-05-20T01:05:45Z"},{"alias_kind":"arxiv_version","alias_value":"2605.19438v1","created_at":"2026-05-20T01:05:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.19438","created_at":"2026-05-20T01:05:45Z"},{"alias_kind":"pith_short_12","alias_value":"IVDEACM4H7EM","created_at":"2026-05-20T01:05:45Z"},{"alias_kind":"pith_short_16","alias_value":"IVDEACM4H7EMWC2R","created_at":"2026-05-20T01:05:45Z"},{"alias_kind":"pith_short_8","alias_value":"IVDEACM4","created_at":"2026-05-20T01:05:45Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:IVDEACM4H7EMWC2RZIRJCFONPR","target":"record","payload":{"canonical_record":{"source":{"id":"2605.19438","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-05-19T06:48:37Z","cross_cats_sorted":[],"title_canon_sha256":"0e9b45d6610835443b8e47e95c7f204c71fbd4430ecb472cef9b392298fafa22","abstract_canon_sha256":"df81b2b1ae6ba46fb1b15ae79953cb766a60eb76c715666729270d349842156f"},"schema_version":"1.0"},"canonical_sha256":"454640099c3fc8cb0b51ca229115cd7c64752d5caaff30b50f4b6bd69f4ad93a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-20T01:05:45.870731Z","signature_b64":"YMf0TpsZfli0NJtryDaNmkDZ6zN9O5fGa3rUkwDj9Qvu1P/Hql9GLbJDacGnM7YNS45jrpfeqfR0l6s0K8mBDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"454640099c3fc8cb0b51ca229115cd7c64752d5caaff30b50f4b6bd69f4ad93a","last_reissued_at":"2026-05-20T01:05:45.869887Z","signature_status":"signed_v1","first_computed_at":"2026-05-20T01:05:45.869887Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2605.19438","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":"2026-05-20T01:05:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sc/tCLIsAUwd6rSLp3IjJqeNl77J4btUubqYIo7IXuz+gggPlJkMzOw4crc/CrcPNpRfXsuRkmUr8x25vIPMBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T14:31:41.700752Z"},"content_sha256":"77b9a48da5fe32295f6948f76884db90187a35bf6d9ffe3179abf3e41e18ccf8","schema_version":"1.0","event_id":"sha256:77b9a48da5fe32295f6948f76884db90187a35bf6d9ffe3179abf3e41e18ccf8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:IVDEACM4H7EMWC2RZIRJCFONPR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Maximal inequalities and Riesz transforms for vector-valued magnetic Schr\\\"odinger operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Abdelaziz Rhandi, Davide Addona, Luca Lorenzi. El Maati Ouhabaz, Vincenzo Leone","submitted_at":"2026-05-19T06:48:37Z","abstract_excerpt":"We consider vector-valued magnetic Schr\\\"odinger operators $-\\bm \\Delta_{\\bm a}+V$ with magnetic potential $\\bm a \\in L^2_{\\mathrm{loc}}(\\mathbb{R}^d;\\mathbb{R}^d)$ and electric potential $V$ given by a matrix-valued function whose entries belong to $L^1_{\\mathrm{loc}}(\\mathbb{R}^d)$. We prove maximal inequalities in $L^p(\\mathbb{R}^d;\\mathbb{C}^m)$, $p\\in[1,\\infty)$ and the boundedness of the Riesz transforms $(\\nabla - i\\bm a)(-\\bm \\Delta_{\\bm a}+V)^{-\\frac{1}{2}}$ and $V^{\\alpha}(-\\bm \\Delta_{\\bm a}+V)^{-\\alpha}$ on $L^p(\\mathbb{R}^d;\\mathbb{C}^m)$ for every $p \\in (1,2]$ and every $\\alpha\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.19438","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/2605.19438/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":"2026-05-20T01:05:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"t2vddgFD1V/2pWSWsc4+5BwP6p/zu7y1ZwnVxbAkq+AYtXt2gTeRudtbw6ORMdOEGQHVtE4jJws9KcrXLDzjBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T14:31:41.701141Z"},"content_sha256":"4e0d5ee2340d4c27d19ef600c481b72e8ae2aed0474c174bef0bc7806e305319","schema_version":"1.0","event_id":"sha256:4e0d5ee2340d4c27d19ef600c481b72e8ae2aed0474c174bef0bc7806e305319"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IVDEACM4H7EMWC2RZIRJCFONPR/bundle.json","state_url":"https://pith.science/pith/IVDEACM4H7EMWC2RZIRJCFONPR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IVDEACM4H7EMWC2RZIRJCFONPR/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":"2026-06-02T14:31:41Z","links":{"resolver":"https://pith.science/pith/IVDEACM4H7EMWC2RZIRJCFONPR","bundle":"https://pith.science/pith/IVDEACM4H7EMWC2RZIRJCFONPR/bundle.json","state":"https://pith.science/pith/IVDEACM4H7EMWC2RZIRJCFONPR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IVDEACM4H7EMWC2RZIRJCFONPR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:IVDEACM4H7EMWC2RZIRJCFONPR","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":"df81b2b1ae6ba46fb1b15ae79953cb766a60eb76c715666729270d349842156f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-05-19T06:48:37Z","title_canon_sha256":"0e9b45d6610835443b8e47e95c7f204c71fbd4430ecb472cef9b392298fafa22"},"schema_version":"1.0","source":{"id":"2605.19438","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.19438","created_at":"2026-05-20T01:05:45Z"},{"alias_kind":"arxiv_version","alias_value":"2605.19438v1","created_at":"2026-05-20T01:05:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.19438","created_at":"2026-05-20T01:05:45Z"},{"alias_kind":"pith_short_12","alias_value":"IVDEACM4H7EM","created_at":"2026-05-20T01:05:45Z"},{"alias_kind":"pith_short_16","alias_value":"IVDEACM4H7EMWC2R","created_at":"2026-05-20T01:05:45Z"},{"alias_kind":"pith_short_8","alias_value":"IVDEACM4","created_at":"2026-05-20T01:05:45Z"}],"graph_snapshots":[{"event_id":"sha256:4e0d5ee2340d4c27d19ef600c481b72e8ae2aed0474c174bef0bc7806e305319","target":"graph","created_at":"2026-05-20T01:05:45Z","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/2605.19438/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We consider vector-valued magnetic Schr\\\"odinger operators $-\\bm \\Delta_{\\bm a}+V$ with magnetic potential $\\bm a \\in L^2_{\\mathrm{loc}}(\\mathbb{R}^d;\\mathbb{R}^d)$ and electric potential $V$ given by a matrix-valued function whose entries belong to $L^1_{\\mathrm{loc}}(\\mathbb{R}^d)$. We prove maximal inequalities in $L^p(\\mathbb{R}^d;\\mathbb{C}^m)$, $p\\in[1,\\infty)$ and the boundedness of the Riesz transforms $(\\nabla - i\\bm a)(-\\bm \\Delta_{\\bm a}+V)^{-\\frac{1}{2}}$ and $V^{\\alpha}(-\\bm \\Delta_{\\bm a}+V)^{-\\alpha}$ on $L^p(\\mathbb{R}^d;\\mathbb{C}^m)$ for every $p \\in (1,2]$ and every $\\alpha\\","authors_text":"Abdelaziz Rhandi, Davide Addona, Luca Lorenzi. El Maati Ouhabaz, Vincenzo Leone","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-05-19T06:48:37Z","title":"Maximal inequalities and Riesz transforms for vector-valued magnetic Schr\\\"odinger operators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.19438","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":"sha256:77b9a48da5fe32295f6948f76884db90187a35bf6d9ffe3179abf3e41e18ccf8","target":"record","created_at":"2026-05-20T01:05:45Z","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":"df81b2b1ae6ba46fb1b15ae79953cb766a60eb76c715666729270d349842156f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-05-19T06:48:37Z","title_canon_sha256":"0e9b45d6610835443b8e47e95c7f204c71fbd4430ecb472cef9b392298fafa22"},"schema_version":"1.0","source":{"id":"2605.19438","kind":"arxiv","version":1}},"canonical_sha256":"454640099c3fc8cb0b51ca229115cd7c64752d5caaff30b50f4b6bd69f4ad93a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"454640099c3fc8cb0b51ca229115cd7c64752d5caaff30b50f4b6bd69f4ad93a","first_computed_at":"2026-05-20T01:05:45.869887Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-20T01:05:45.869887Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YMf0TpsZfli0NJtryDaNmkDZ6zN9O5fGa3rUkwDj9Qvu1P/Hql9GLbJDacGnM7YNS45jrpfeqfR0l6s0K8mBDw==","signature_status":"signed_v1","signed_at":"2026-05-20T01:05:45.870731Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.19438","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:77b9a48da5fe32295f6948f76884db90187a35bf6d9ffe3179abf3e41e18ccf8","sha256:4e0d5ee2340d4c27d19ef600c481b72e8ae2aed0474c174bef0bc7806e305319"],"state_sha256":"65fcc7738a3c4c7f5a1d1580ddf734408ab3e2d643f4763825abaa9057ddcf18"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VD+qDCz5p77OC7VT5tCvdMJimuZdMuuEc6sAq8O6Lir6iZRRNnWj5Vn7vFbl8wI4olCF+Afm0Xv3EARBrtc7Ag==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T14:31:41.703384Z","bundle_sha256":"cc78a8502a8172b94de638cb52c924a9434ce8f309a435de9031dd7fc9eae2fa"}}