{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:LVJM3RTGEDQQXRY7472CUJIU2W","short_pith_number":"pith:LVJM3RTG","canonical_record":{"source":{"id":"1507.02398","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2015-07-09T07:33:13Z","cross_cats_sorted":[],"title_canon_sha256":"48f649e81946e82e95d335d0fa245fe3e41450e7eb80827fc9745740fc59527c","abstract_canon_sha256":"d0c07d6aca71dd68d031c6f7572048b02790987082844c700ac9b1abe6d7aae0"},"schema_version":"1.0"},"canonical_sha256":"5d52cdc66620e10bc71fe7f42a2514d5b70342c738a7bb49271683ef78374941","source":{"kind":"arxiv","id":"1507.02398","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.02398","created_at":"2026-05-18T00:03:50Z"},{"alias_kind":"arxiv_version","alias_value":"1507.02398v2","created_at":"2026-05-18T00:03:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.02398","created_at":"2026-05-18T00:03:50Z"},{"alias_kind":"pith_short_12","alias_value":"LVJM3RTGEDQQ","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_16","alias_value":"LVJM3RTGEDQQXRY7","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_8","alias_value":"LVJM3RTG","created_at":"2026-05-18T12:29:29Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:LVJM3RTGEDQQXRY7472CUJIU2W","target":"record","payload":{"canonical_record":{"source":{"id":"1507.02398","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2015-07-09T07:33:13Z","cross_cats_sorted":[],"title_canon_sha256":"48f649e81946e82e95d335d0fa245fe3e41450e7eb80827fc9745740fc59527c","abstract_canon_sha256":"d0c07d6aca71dd68d031c6f7572048b02790987082844c700ac9b1abe6d7aae0"},"schema_version":"1.0"},"canonical_sha256":"5d52cdc66620e10bc71fe7f42a2514d5b70342c738a7bb49271683ef78374941","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:03:50.642114Z","signature_b64":"HWh21Tw96cGsczc+m0N9jOYaIUNvOoY4HXdgBpIl6Dj13/BmTSoPL6uOG/FBQGLJdFMd+TjCDVIDAMVv25DOAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5d52cdc66620e10bc71fe7f42a2514d5b70342c738a7bb49271683ef78374941","last_reissued_at":"2026-05-18T00:03:50.641473Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:03:50.641473Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1507.02398","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:03:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"W6Mqc0oDo+3xuuFa1WJPR8oIEHWa2yGo67sd/i4EvboxDfGGeZb1RtMxPx53avjzj9bX2SKpFII8JUD5I8hIDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T21:22:41.012393Z"},"content_sha256":"2baa627f194fb6d7f13efd1ac4ba37709ae21dd37030881ca86e11be1b1cecb5","schema_version":"1.0","event_id":"sha256:2baa627f194fb6d7f13efd1ac4ba37709ae21dd37030881ca86e11be1b1cecb5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:LVJM3RTGEDQQXRY7472CUJIU2W","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Oscillation estimates, self-improving results and good-$\\lambda$ inequalities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Jos\\'e Mar\\'ia Martell, Juha Kinnunen, Lauri Berkovits","submitted_at":"2015-07-09T07:33:13Z","abstract_excerpt":"Our main result is an abstract good-$\\lambda$ inequality that allows us to consider three self-improving properties related to oscillation estimates in a very general context. The novelty of our approach is that there is one principle behind these self-improving phenomena. First, we obtain higher integrability properties for functions belonging to the so-called John-Nirenberg spaces. Second, and as a consequence of the previous fact, we present very easy proofs of some of the self-improving properties of the generalized Poincar\\'e inequalities studied by B. Franchi, C. P\\'erez and R. Wheeden, "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.02398","kind":"arxiv","version":2},"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":"2026-05-18T00:03:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7sbiK706QkGC9VVxPIx+RgbwOMOxM0R+qz/mYWoaUbNlIVtWyTY7z1vtl4r2LLmMAO6jSeMphDMrKeFbtQVKAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T21:22:41.012757Z"},"content_sha256":"8a98102d8105f9662b25621deaad8f8bedf2266d78f49d9c8a9c1b45bad50d69","schema_version":"1.0","event_id":"sha256:8a98102d8105f9662b25621deaad8f8bedf2266d78f49d9c8a9c1b45bad50d69"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LVJM3RTGEDQQXRY7472CUJIU2W/bundle.json","state_url":"https://pith.science/pith/LVJM3RTGEDQQXRY7472CUJIU2W/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LVJM3RTGEDQQXRY7472CUJIU2W/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":"2026-05-27T21:22:41Z","links":{"resolver":"https://pith.science/pith/LVJM3RTGEDQQXRY7472CUJIU2W","bundle":"https://pith.science/pith/LVJM3RTGEDQQXRY7472CUJIU2W/bundle.json","state":"https://pith.science/pith/LVJM3RTGEDQQXRY7472CUJIU2W/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LVJM3RTGEDQQXRY7472CUJIU2W/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:LVJM3RTGEDQQXRY7472CUJIU2W","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":"d0c07d6aca71dd68d031c6f7572048b02790987082844c700ac9b1abe6d7aae0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2015-07-09T07:33:13Z","title_canon_sha256":"48f649e81946e82e95d335d0fa245fe3e41450e7eb80827fc9745740fc59527c"},"schema_version":"1.0","source":{"id":"1507.02398","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.02398","created_at":"2026-05-18T00:03:50Z"},{"alias_kind":"arxiv_version","alias_value":"1507.02398v2","created_at":"2026-05-18T00:03:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.02398","created_at":"2026-05-18T00:03:50Z"},{"alias_kind":"pith_short_12","alias_value":"LVJM3RTGEDQQ","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_16","alias_value":"LVJM3RTGEDQQXRY7","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_8","alias_value":"LVJM3RTG","created_at":"2026-05-18T12:29:29Z"}],"graph_snapshots":[{"event_id":"sha256:8a98102d8105f9662b25621deaad8f8bedf2266d78f49d9c8a9c1b45bad50d69","target":"graph","created_at":"2026-05-18T00:03:50Z","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":"Our main result is an abstract good-$\\lambda$ inequality that allows us to consider three self-improving properties related to oscillation estimates in a very general context. The novelty of our approach is that there is one principle behind these self-improving phenomena. First, we obtain higher integrability properties for functions belonging to the so-called John-Nirenberg spaces. Second, and as a consequence of the previous fact, we present very easy proofs of some of the self-improving properties of the generalized Poincar\\'e inequalities studied by B. Franchi, C. P\\'erez and R. Wheeden, ","authors_text":"Jos\\'e Mar\\'ia Martell, Juha Kinnunen, Lauri Berkovits","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2015-07-09T07:33:13Z","title":"Oscillation estimates, self-improving results and good-$\\lambda$ inequalities"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.02398","kind":"arxiv","version":2},"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":"sha256:2baa627f194fb6d7f13efd1ac4ba37709ae21dd37030881ca86e11be1b1cecb5","target":"record","created_at":"2026-05-18T00:03:50Z","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":"d0c07d6aca71dd68d031c6f7572048b02790987082844c700ac9b1abe6d7aae0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2015-07-09T07:33:13Z","title_canon_sha256":"48f649e81946e82e95d335d0fa245fe3e41450e7eb80827fc9745740fc59527c"},"schema_version":"1.0","source":{"id":"1507.02398","kind":"arxiv","version":2}},"canonical_sha256":"5d52cdc66620e10bc71fe7f42a2514d5b70342c738a7bb49271683ef78374941","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5d52cdc66620e10bc71fe7f42a2514d5b70342c738a7bb49271683ef78374941","first_computed_at":"2026-05-18T00:03:50.641473Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:03:50.641473Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HWh21Tw96cGsczc+m0N9jOYaIUNvOoY4HXdgBpIl6Dj13/BmTSoPL6uOG/FBQGLJdFMd+TjCDVIDAMVv25DOAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:03:50.642114Z","signed_message":"canonical_sha256_bytes"},"source_id":"1507.02398","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2baa627f194fb6d7f13efd1ac4ba37709ae21dd37030881ca86e11be1b1cecb5","sha256:8a98102d8105f9662b25621deaad8f8bedf2266d78f49d9c8a9c1b45bad50d69"],"state_sha256":"cb9453de22d4ee01ea2930827090a900101dc4307abdd17d3ffb31bdd2c78ba5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dVLKPXtPouEmwP57qrwRXLIOenS5zHwSqoSjKgIgEMZqzBiA/CXBoKlM1Ha1K9woCLxrklthzSPE0Ji+txLIAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T21:22:41.014983Z","bundle_sha256":"94cf84b9e21bd191c326a2b0ae6471e9c792ec45bf456e39a9f03bb89fe9f910"}}