{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:SCVZK5JEJPGXUOHBIV6TPXXVCW","short_pith_number":"pith:SCVZK5JE","canonical_record":{"source":{"id":"2505.24568","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2025-05-30T13:21:18Z","cross_cats_sorted":[],"title_canon_sha256":"3ed27a36456b9f70284c75be9350c210af8961de094a44f45dca74a7cea176ed","abstract_canon_sha256":"c967811283dc6fe38c6ce24a15f986ea87b7b302361740a774261d65c9b31264"},"schema_version":"1.0"},"canonical_sha256":"90ab9575244bcd7a38e1457d37def515b2a34c465ea0afb680c7975e7a8cbf57","source":{"kind":"arxiv","id":"2505.24568","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2505.24568","created_at":"2026-07-05T11:12:52Z"},{"alias_kind":"arxiv_version","alias_value":"2505.24568v1","created_at":"2026-07-05T11:12:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.24568","created_at":"2026-07-05T11:12:52Z"},{"alias_kind":"pith_short_12","alias_value":"SCVZK5JEJPGX","created_at":"2026-07-05T11:12:52Z"},{"alias_kind":"pith_short_16","alias_value":"SCVZK5JEJPGXUOHB","created_at":"2026-07-05T11:12:52Z"},{"alias_kind":"pith_short_8","alias_value":"SCVZK5JE","created_at":"2026-07-05T11:12:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:SCVZK5JEJPGXUOHBIV6TPXXVCW","target":"record","payload":{"canonical_record":{"source":{"id":"2505.24568","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2025-05-30T13:21:18Z","cross_cats_sorted":[],"title_canon_sha256":"3ed27a36456b9f70284c75be9350c210af8961de094a44f45dca74a7cea176ed","abstract_canon_sha256":"c967811283dc6fe38c6ce24a15f986ea87b7b302361740a774261d65c9b31264"},"schema_version":"1.0"},"canonical_sha256":"90ab9575244bcd7a38e1457d37def515b2a34c465ea0afb680c7975e7a8cbf57","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:12:52.419571Z","signature_b64":"3dsqbHLIjKxixFJoN47ShoUvkJwkmG8qcz3Ti4/ckzYVghHbayGE990HRUlcTwlYH5sFeI4u/a9rfdWXBJOABQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"90ab9575244bcd7a38e1457d37def515b2a34c465ea0afb680c7975e7a8cbf57","last_reissued_at":"2026-07-05T11:12:52.419050Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:12:52.419050Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2505.24568","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":"2026-07-05T11:12:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3tSf6hZw2rrH7mXuEUAbLGROHd4v99+C0PfDB6qYJq4pO0XYsOnwTn0tHR4YA2mvGsW1dUiXw4NPW96J0oWMAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T19:29:00.883801Z"},"content_sha256":"b040036c4efae01ca4586f6badcfea3866b1fc99f68548c5018b0fc9e54e4170","schema_version":"1.0","event_id":"sha256:b040036c4efae01ca4586f6badcfea3866b1fc99f68548c5018b0fc9e54e4170"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:SCVZK5JEJPGXUOHBIV6TPXXVCW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the rate of convergence for Landau type Schr\\\"odinger Operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Wenchang Sun, Yucheng Pan","submitted_at":"2025-05-30T13:21:18Z","abstract_excerpt":"We study the pointwise convergence of Landau type Schr\\\"odinger operators within the fractional Sobolev space $W^{s,p}(\\mathbb R)$. Our results extend those established by Bailey (Rev. Mat. Iberoam., 29 (2): 531-546, 2013) and Yuan, Zhao and Zheng (Nonlinear Anal., 208: Paper No. 112312, 28, 2021). Furthermore, we also analyze the convergence rate of Landau type Schr\\\"odinger operators along curves and derive a sharp result for the case of convergence along vertical lines."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.24568","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/2505.24568/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":"2026-07-05T11:12:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HO598e+slMQDM7wtVkiwUDY8HmD32lusvTKqrvrcIHYULe+7cHR+svjLkIsvA0b9vHK5nPByvCsZIn5hYKzdDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T19:29:00.884314Z"},"content_sha256":"19d0fb90832fe11ce6f16ebbeb15fd97167439005865a63786e2a171dbc2a91a","schema_version":"1.0","event_id":"sha256:19d0fb90832fe11ce6f16ebbeb15fd97167439005865a63786e2a171dbc2a91a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SCVZK5JEJPGXUOHBIV6TPXXVCW/bundle.json","state_url":"https://pith.science/pith/SCVZK5JEJPGXUOHBIV6TPXXVCW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SCVZK5JEJPGXUOHBIV6TPXXVCW/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":"2026-08-09T19:29:00Z","links":{"resolver":"https://pith.science/pith/SCVZK5JEJPGXUOHBIV6TPXXVCW","bundle":"https://pith.science/pith/SCVZK5JEJPGXUOHBIV6TPXXVCW/bundle.json","state":"https://pith.science/pith/SCVZK5JEJPGXUOHBIV6TPXXVCW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SCVZK5JEJPGXUOHBIV6TPXXVCW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:SCVZK5JEJPGXUOHBIV6TPXXVCW","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":"c967811283dc6fe38c6ce24a15f986ea87b7b302361740a774261d65c9b31264","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2025-05-30T13:21:18Z","title_canon_sha256":"3ed27a36456b9f70284c75be9350c210af8961de094a44f45dca74a7cea176ed"},"schema_version":"1.0","source":{"id":"2505.24568","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2505.24568","created_at":"2026-07-05T11:12:52Z"},{"alias_kind":"arxiv_version","alias_value":"2505.24568v1","created_at":"2026-07-05T11:12:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.24568","created_at":"2026-07-05T11:12:52Z"},{"alias_kind":"pith_short_12","alias_value":"SCVZK5JEJPGX","created_at":"2026-07-05T11:12:52Z"},{"alias_kind":"pith_short_16","alias_value":"SCVZK5JEJPGXUOHB","created_at":"2026-07-05T11:12:52Z"},{"alias_kind":"pith_short_8","alias_value":"SCVZK5JE","created_at":"2026-07-05T11:12:52Z"}],"graph_snapshots":[{"event_id":"sha256:19d0fb90832fe11ce6f16ebbeb15fd97167439005865a63786e2a171dbc2a91a","target":"graph","created_at":"2026-07-05T11:12:52Z","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/2505.24568/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study the pointwise convergence of Landau type Schr\\\"odinger operators within the fractional Sobolev space $W^{s,p}(\\mathbb R)$. Our results extend those established by Bailey (Rev. Mat. Iberoam., 29 (2): 531-546, 2013) and Yuan, Zhao and Zheng (Nonlinear Anal., 208: Paper No. 112312, 28, 2021). Furthermore, we also analyze the convergence rate of Landau type Schr\\\"odinger operators along curves and derive a sharp result for the case of convergence along vertical lines.","authors_text":"Wenchang Sun, Yucheng Pan","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2025-05-30T13:21:18Z","title":"On the rate of convergence for Landau type Schr\\\"odinger Operators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.24568","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:b040036c4efae01ca4586f6badcfea3866b1fc99f68548c5018b0fc9e54e4170","target":"record","created_at":"2026-07-05T11:12:52Z","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":"c967811283dc6fe38c6ce24a15f986ea87b7b302361740a774261d65c9b31264","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2025-05-30T13:21:18Z","title_canon_sha256":"3ed27a36456b9f70284c75be9350c210af8961de094a44f45dca74a7cea176ed"},"schema_version":"1.0","source":{"id":"2505.24568","kind":"arxiv","version":1}},"canonical_sha256":"90ab9575244bcd7a38e1457d37def515b2a34c465ea0afb680c7975e7a8cbf57","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"90ab9575244bcd7a38e1457d37def515b2a34c465ea0afb680c7975e7a8cbf57","first_computed_at":"2026-07-05T11:12:52.419050Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:12:52.419050Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3dsqbHLIjKxixFJoN47ShoUvkJwkmG8qcz3Ti4/ckzYVghHbayGE990HRUlcTwlYH5sFeI4u/a9rfdWXBJOABQ==","signature_status":"signed_v1","signed_at":"2026-07-05T11:12:52.419571Z","signed_message":"canonical_sha256_bytes"},"source_id":"2505.24568","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b040036c4efae01ca4586f6badcfea3866b1fc99f68548c5018b0fc9e54e4170","sha256:19d0fb90832fe11ce6f16ebbeb15fd97167439005865a63786e2a171dbc2a91a"],"state_sha256":"4c5613792d83f67408542137246d7800240654a642e088added52a9f4896b0e3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"U6/iUxotROtLkGEAD1HoAQ14ZRRngWcIuohdoyBC/y6QOz6LPBz2Q3xFuxDupr5VLiy7JtZWek3f9tc7UevaDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-09T19:29:00.890099Z","bundle_sha256":"e769d217d0fc70a3534a3bbf42676274b2d0647b361d8dcf28e6d95f68f95274"}}