{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:HGRT33DOKJOVY5V633XHNW7Z24","short_pith_number":"pith:HGRT33DO","canonical_record":{"source":{"id":"2405.02531","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2024-05-04T01:14:34Z","cross_cats_sorted":[],"title_canon_sha256":"5518be04a5d58a4c19a225dc348e02e88091e9b6617f7feb6235015bb3af22a9","abstract_canon_sha256":"3488eb5efb403c07b239d616858234c09556a784ca10a226938f8d998ff047aa"},"schema_version":"1.0"},"canonical_sha256":"39a33dec6e525d5c76bedeee76dbf9d73074909e4e6976ee000ad34718e0d52a","source":{"kind":"arxiv","id":"2405.02531","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2405.02531","created_at":"2026-07-05T08:15:16Z"},{"alias_kind":"arxiv_version","alias_value":"2405.02531v1","created_at":"2026-07-05T08:15:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2405.02531","created_at":"2026-07-05T08:15:16Z"},{"alias_kind":"pith_short_12","alias_value":"HGRT33DOKJOV","created_at":"2026-07-05T08:15:16Z"},{"alias_kind":"pith_short_16","alias_value":"HGRT33DOKJOVY5V6","created_at":"2026-07-05T08:15:16Z"},{"alias_kind":"pith_short_8","alias_value":"HGRT33DO","created_at":"2026-07-05T08:15:16Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:HGRT33DOKJOVY5V633XHNW7Z24","target":"record","payload":{"canonical_record":{"source":{"id":"2405.02531","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2024-05-04T01:14:34Z","cross_cats_sorted":[],"title_canon_sha256":"5518be04a5d58a4c19a225dc348e02e88091e9b6617f7feb6235015bb3af22a9","abstract_canon_sha256":"3488eb5efb403c07b239d616858234c09556a784ca10a226938f8d998ff047aa"},"schema_version":"1.0"},"canonical_sha256":"39a33dec6e525d5c76bedeee76dbf9d73074909e4e6976ee000ad34718e0d52a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:15:16.781351Z","signature_b64":"XPOBWbd7bGnBRNdE+Ya1dTBhiqKz1y+IG0CZGSW9DiP/mcwsNY1u6q44Ip9DYuWkAhakfyfdTxbey8Dc/JY7Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"39a33dec6e525d5c76bedeee76dbf9d73074909e4e6976ee000ad34718e0d52a","last_reissued_at":"2026-07-05T08:15:16.780947Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:15:16.780947Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2405.02531","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":"2026-07-05T08:15:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1N9+3SGZcOAzLPVoClZJW/ANrlfT7ArK6ha+a+Oqzwq7NQ64YzOOrpCt0tCskhXYAEV2lvgdXq7XrWHDW+NGDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-18T22:45:27.447740Z"},"content_sha256":"cf003ebbd5af27b01b08e221b1917a4f0666cbe0dbb0328af43e469b502fc26e","schema_version":"1.0","event_id":"sha256:cf003ebbd5af27b01b08e221b1917a4f0666cbe0dbb0328af43e469b502fc26e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:HGRT33DOKJOVY5V633XHNW7Z24","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Bochner-Riesz means for critical magnetic Schr\\\"odinger operators in ${\\mathbb R^2}$","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Changxing Miao, Junyong Zhang, Lixin Yan","submitted_at":"2024-05-04T01:14:34Z","abstract_excerpt":"We study $L^p$-boundedness of the Bochner-Riesz means for critical magnetic Schr\\\"odinger operators $\\mathcal{L}_{\\bf A}$ in ${\\mathbb{R}^2}$, which involve the physcial Aharonov-Bohm potential. We show that for $1\\leq p\\leq +\\infty$ and $p\\neq 2$, the Bochner-Riesz operator $S_{\\lambda}^\\delta(\\mathcal{L}_{\\bf A})$ of order $\\delta$ is bounded on $L^p(\\mathbb{R}^2)$ if and only if $\\delta>\\max\\big\\{0, 2\\big|1/2-1/p\\big|-1/2\\big\\}$. The new ingredient of the proof is to obtain the localized $L^4(\\mathbb R^2)$ estimate of $S_{\\lambda}^\\delta(\\mathcal{L}_{\\bf A})$, whose kernel is heavily affect"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2405.02531","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/2405.02531/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":"2026-07-05T08:15:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pK7Rlc6YEgtUDrVCpiC5OuECwl59dpUYsRRDancr1AQKyUjDGZ1yLb2rtphvnKbivoVTlF3e2TFawvYKD0sWCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-18T22:45:27.448245Z"},"content_sha256":"0f85c427bbb4742f499636f1618da1608e9421d52bbb374531f72affcdd2a721","schema_version":"1.0","event_id":"sha256:0f85c427bbb4742f499636f1618da1608e9421d52bbb374531f72affcdd2a721"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HGRT33DOKJOVY5V633XHNW7Z24/bundle.json","state_url":"https://pith.science/pith/HGRT33DOKJOVY5V633XHNW7Z24/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HGRT33DOKJOVY5V633XHNW7Z24/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":"2026-08-18T22:45:27Z","links":{"resolver":"https://pith.science/pith/HGRT33DOKJOVY5V633XHNW7Z24","bundle":"https://pith.science/pith/HGRT33DOKJOVY5V633XHNW7Z24/bundle.json","state":"https://pith.science/pith/HGRT33DOKJOVY5V633XHNW7Z24/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HGRT33DOKJOVY5V633XHNW7Z24/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:HGRT33DOKJOVY5V633XHNW7Z24","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":"3488eb5efb403c07b239d616858234c09556a784ca10a226938f8d998ff047aa","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2024-05-04T01:14:34Z","title_canon_sha256":"5518be04a5d58a4c19a225dc348e02e88091e9b6617f7feb6235015bb3af22a9"},"schema_version":"1.0","source":{"id":"2405.02531","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2405.02531","created_at":"2026-07-05T08:15:16Z"},{"alias_kind":"arxiv_version","alias_value":"2405.02531v1","created_at":"2026-07-05T08:15:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2405.02531","created_at":"2026-07-05T08:15:16Z"},{"alias_kind":"pith_short_12","alias_value":"HGRT33DOKJOV","created_at":"2026-07-05T08:15:16Z"},{"alias_kind":"pith_short_16","alias_value":"HGRT33DOKJOVY5V6","created_at":"2026-07-05T08:15:16Z"},{"alias_kind":"pith_short_8","alias_value":"HGRT33DO","created_at":"2026-07-05T08:15:16Z"}],"graph_snapshots":[{"event_id":"sha256:0f85c427bbb4742f499636f1618da1608e9421d52bbb374531f72affcdd2a721","target":"graph","created_at":"2026-07-05T08:15:16Z","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/2405.02531/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study $L^p$-boundedness of the Bochner-Riesz means for critical magnetic Schr\\\"odinger operators $\\mathcal{L}_{\\bf A}$ in ${\\mathbb{R}^2}$, which involve the physcial Aharonov-Bohm potential. We show that for $1\\leq p\\leq +\\infty$ and $p\\neq 2$, the Bochner-Riesz operator $S_{\\lambda}^\\delta(\\mathcal{L}_{\\bf A})$ of order $\\delta$ is bounded on $L^p(\\mathbb{R}^2)$ if and only if $\\delta>\\max\\big\\{0, 2\\big|1/2-1/p\\big|-1/2\\big\\}$. The new ingredient of the proof is to obtain the localized $L^4(\\mathbb R^2)$ estimate of $S_{\\lambda}^\\delta(\\mathcal{L}_{\\bf A})$, whose kernel is heavily affect","authors_text":"Changxing Miao, Junyong Zhang, Lixin Yan","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2024-05-04T01:14:34Z","title":"Bochner-Riesz means for critical magnetic Schr\\\"odinger operators in ${\\mathbb R^2}$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2405.02531","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:cf003ebbd5af27b01b08e221b1917a4f0666cbe0dbb0328af43e469b502fc26e","target":"record","created_at":"2026-07-05T08:15:16Z","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":"3488eb5efb403c07b239d616858234c09556a784ca10a226938f8d998ff047aa","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2024-05-04T01:14:34Z","title_canon_sha256":"5518be04a5d58a4c19a225dc348e02e88091e9b6617f7feb6235015bb3af22a9"},"schema_version":"1.0","source":{"id":"2405.02531","kind":"arxiv","version":1}},"canonical_sha256":"39a33dec6e525d5c76bedeee76dbf9d73074909e4e6976ee000ad34718e0d52a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"39a33dec6e525d5c76bedeee76dbf9d73074909e4e6976ee000ad34718e0d52a","first_computed_at":"2026-07-05T08:15:16.780947Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:15:16.780947Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XPOBWbd7bGnBRNdE+Ya1dTBhiqKz1y+IG0CZGSW9DiP/mcwsNY1u6q44Ip9DYuWkAhakfyfdTxbey8Dc/JY7Cg==","signature_status":"signed_v1","signed_at":"2026-07-05T08:15:16.781351Z","signed_message":"canonical_sha256_bytes"},"source_id":"2405.02531","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cf003ebbd5af27b01b08e221b1917a4f0666cbe0dbb0328af43e469b502fc26e","sha256:0f85c427bbb4742f499636f1618da1608e9421d52bbb374531f72affcdd2a721"],"state_sha256":"a5d2f0bb37c658ab72eed4a77e8536b3aabdaecd54b0e614f0cf4d0146eab91e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"b56hNPmnG8YXkE/l7Xjt7ebaXGoc4ax98DQdEHnESGU4z4/VPhgpxzMNc6c8owgma880AMuH9pOzkIwgFZIqDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-18T22:45:27.453649Z","bundle_sha256":"cb2850c3af0dc9ae90b15d2b069da1e7d169a83e48429c1dfde7d77aae7f7965"}}