{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:YCHQWBHIK7MS3UM377DVM2DTYB","short_pith_number":"pith:YCHQWBHI","canonical_record":{"source":{"id":"1505.04042","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2015-05-15T12:04:24Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"8ecc407434e62aa04631d52bfa4aaca60ecaa8ec1acabb2e9fc99e62de311ce9","abstract_canon_sha256":"d1faa71eab9aaee6b9e066a1030adefa334f45a415b0e72c9e19a17eb468ea7f"},"schema_version":"1.0"},"canonical_sha256":"c08f0b04e857d92dd19bffc7566873c06aa4f099db661734fc6f5c10a6b946d9","source":{"kind":"arxiv","id":"1505.04042","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1505.04042","created_at":"2026-05-18T02:09:40Z"},{"alias_kind":"arxiv_version","alias_value":"1505.04042v1","created_at":"2026-05-18T02:09:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.04042","created_at":"2026-05-18T02:09:40Z"},{"alias_kind":"pith_short_12","alias_value":"YCHQWBHIK7MS","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_16","alias_value":"YCHQWBHIK7MS3UM3","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_8","alias_value":"YCHQWBHI","created_at":"2026-05-18T12:29:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:YCHQWBHIK7MS3UM377DVM2DTYB","target":"record","payload":{"canonical_record":{"source":{"id":"1505.04042","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2015-05-15T12:04:24Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"8ecc407434e62aa04631d52bfa4aaca60ecaa8ec1acabb2e9fc99e62de311ce9","abstract_canon_sha256":"d1faa71eab9aaee6b9e066a1030adefa334f45a415b0e72c9e19a17eb468ea7f"},"schema_version":"1.0"},"canonical_sha256":"c08f0b04e857d92dd19bffc7566873c06aa4f099db661734fc6f5c10a6b946d9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:09:40.347109Z","signature_b64":"y4SGaDx135ITn+m8TfnS+ZPVuzhjAsGY8r64Y9CBl3TkO1dxacGq8Hn5xCDEW3n6IYbdZWshd8lFBiLNdwZbBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c08f0b04e857d92dd19bffc7566873c06aa4f099db661734fc6f5c10a6b946d9","last_reissued_at":"2026-05-18T02:09:40.346249Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:09:40.346249Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1505.04042","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":"2026-05-18T02:09:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HL4IXIZ9KUidzdb/G+aaNJ5dVP41M5UWpRT/k9594iMViIAvBD0Csi459ajexhi/FxSb3rEyP4xpFfZRHh/7DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T09:24:59.699297Z"},"content_sha256":"4aa01290eda01efdbd11db356236016bf3ac7da3d97d109777b905169d1cf9f9","schema_version":"1.0","event_id":"sha256:4aa01290eda01efdbd11db356236016bf3ac7da3d97d109777b905169d1cf9f9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:YCHQWBHIK7MS3UM377DVM2DTYB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Beyond local maximal operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.CA","authors_text":"Antti V. V\\\"ah\\\"akangas, Hannes Luiro","submitted_at":"2015-05-15T12:04:24Z","abstract_excerpt":"We obtain (essentially sharp) boundedness results for certain generalized local maximal operators between fractional weighted Sobolev spaces and their modifications. Concrete boundedness results between well known fractional Sobolev spaces are derived as consequences of our main result. We also apply our boundedness results by studying both generalized neighbourhood capacities and the Lebesgue differentiation of fractional weighted Sobolev functions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.04042","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":"2026-05-18T02:09:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JnDyrA7zVewpVkbuqqYeSHqKN1uaxB4ovx2+Wlar55vAwl3vqxscZkjDo5r5tu8D0UQd2cVl3UshhyINZToQDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T09:24:59.699655Z"},"content_sha256":"20594742ca02d696b9d61aefa208bc2a306ad195d9cef32c216412e3880b1290","schema_version":"1.0","event_id":"sha256:20594742ca02d696b9d61aefa208bc2a306ad195d9cef32c216412e3880b1290"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YCHQWBHIK7MS3UM377DVM2DTYB/bundle.json","state_url":"https://pith.science/pith/YCHQWBHIK7MS3UM377DVM2DTYB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YCHQWBHIK7MS3UM377DVM2DTYB/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":"2026-06-29T09:24:59Z","links":{"resolver":"https://pith.science/pith/YCHQWBHIK7MS3UM377DVM2DTYB","bundle":"https://pith.science/pith/YCHQWBHIK7MS3UM377DVM2DTYB/bundle.json","state":"https://pith.science/pith/YCHQWBHIK7MS3UM377DVM2DTYB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YCHQWBHIK7MS3UM377DVM2DTYB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:YCHQWBHIK7MS3UM377DVM2DTYB","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":"d1faa71eab9aaee6b9e066a1030adefa334f45a415b0e72c9e19a17eb468ea7f","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2015-05-15T12:04:24Z","title_canon_sha256":"8ecc407434e62aa04631d52bfa4aaca60ecaa8ec1acabb2e9fc99e62de311ce9"},"schema_version":"1.0","source":{"id":"1505.04042","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1505.04042","created_at":"2026-05-18T02:09:40Z"},{"alias_kind":"arxiv_version","alias_value":"1505.04042v1","created_at":"2026-05-18T02:09:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.04042","created_at":"2026-05-18T02:09:40Z"},{"alias_kind":"pith_short_12","alias_value":"YCHQWBHIK7MS","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_16","alias_value":"YCHQWBHIK7MS3UM3","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_8","alias_value":"YCHQWBHI","created_at":"2026-05-18T12:29:50Z"}],"graph_snapshots":[{"event_id":"sha256:20594742ca02d696b9d61aefa208bc2a306ad195d9cef32c216412e3880b1290","target":"graph","created_at":"2026-05-18T02:09:40Z","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 obtain (essentially sharp) boundedness results for certain generalized local maximal operators between fractional weighted Sobolev spaces and their modifications. Concrete boundedness results between well known fractional Sobolev spaces are derived as consequences of our main result. We also apply our boundedness results by studying both generalized neighbourhood capacities and the Lebesgue differentiation of fractional weighted Sobolev functions.","authors_text":"Antti V. V\\\"ah\\\"akangas, Hannes Luiro","cross_cats":["math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2015-05-15T12:04:24Z","title":"Beyond local maximal operators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.04042","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":"sha256:4aa01290eda01efdbd11db356236016bf3ac7da3d97d109777b905169d1cf9f9","target":"record","created_at":"2026-05-18T02:09:40Z","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":"d1faa71eab9aaee6b9e066a1030adefa334f45a415b0e72c9e19a17eb468ea7f","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2015-05-15T12:04:24Z","title_canon_sha256":"8ecc407434e62aa04631d52bfa4aaca60ecaa8ec1acabb2e9fc99e62de311ce9"},"schema_version":"1.0","source":{"id":"1505.04042","kind":"arxiv","version":1}},"canonical_sha256":"c08f0b04e857d92dd19bffc7566873c06aa4f099db661734fc6f5c10a6b946d9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c08f0b04e857d92dd19bffc7566873c06aa4f099db661734fc6f5c10a6b946d9","first_computed_at":"2026-05-18T02:09:40.346249Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:09:40.346249Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"y4SGaDx135ITn+m8TfnS+ZPVuzhjAsGY8r64Y9CBl3TkO1dxacGq8Hn5xCDEW3n6IYbdZWshd8lFBiLNdwZbBA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:09:40.347109Z","signed_message":"canonical_sha256_bytes"},"source_id":"1505.04042","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4aa01290eda01efdbd11db356236016bf3ac7da3d97d109777b905169d1cf9f9","sha256:20594742ca02d696b9d61aefa208bc2a306ad195d9cef32c216412e3880b1290"],"state_sha256":"46b0fc4e324705b32bbde1c04f3c0dadc196f610cb101c88ceae4843eb9e6e70"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"G3oi+TQVX/tGl/bJLLo8ZZkyS0zMtUMdcqn7Jc0iaknb4IOq6qU6DDhF8O8daeWHZjChFWiWXGYrP0R0ojpdBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-29T09:24:59.702520Z","bundle_sha256":"abe49fd8e44d4a95d09abc7639347c572f62b2f1e79ea9fe8b6a8e25237b766b"}}