{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:4KKNXHZVCQCSTPIKCWP67BA4C2","short_pith_number":"pith:4KKNXHZV","canonical_record":{"source":{"id":"1110.1771","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2011-10-08T21:40:28Z","cross_cats_sorted":[],"title_canon_sha256":"4d5feafeb44fcc65a46c420fcd913d9630dfebbdba961e243b48ca5817b6d9b8","abstract_canon_sha256":"8fd0cc4a997fa73badc1796860823e2240d0a6ab401b7f6efe220ab4830bd490"},"schema_version":"1.0"},"canonical_sha256":"e294db9f35140529bd0a159fef841c1695890d9cbde343e83faef80276b09e33","source":{"kind":"arxiv","id":"1110.1771","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.1771","created_at":"2026-05-18T04:11:19Z"},{"alias_kind":"arxiv_version","alias_value":"1110.1771v1","created_at":"2026-05-18T04:11:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.1771","created_at":"2026-05-18T04:11:19Z"},{"alias_kind":"pith_short_12","alias_value":"4KKNXHZVCQCS","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_16","alias_value":"4KKNXHZVCQCSTPIK","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_8","alias_value":"4KKNXHZV","created_at":"2026-05-18T12:26:20Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:4KKNXHZVCQCSTPIKCWP67BA4C2","target":"record","payload":{"canonical_record":{"source":{"id":"1110.1771","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2011-10-08T21:40:28Z","cross_cats_sorted":[],"title_canon_sha256":"4d5feafeb44fcc65a46c420fcd913d9630dfebbdba961e243b48ca5817b6d9b8","abstract_canon_sha256":"8fd0cc4a997fa73badc1796860823e2240d0a6ab401b7f6efe220ab4830bd490"},"schema_version":"1.0"},"canonical_sha256":"e294db9f35140529bd0a159fef841c1695890d9cbde343e83faef80276b09e33","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:11:19.653521Z","signature_b64":"pYAjqrDbznjkCrvl+6FxfAjVU70B9PJw4zKhO6o6K/Rd0rlz0ql0a55uQtJKT3VugN8VFQmGp55r/PozFqimCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e294db9f35140529bd0a159fef841c1695890d9cbde343e83faef80276b09e33","last_reissued_at":"2026-05-18T04:11:19.653023Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:11:19.653023Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1110.1771","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":"2026-05-18T04:11:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pA1YWEmH0EWsRX9pPGt0Laufpb7WD0StWkzqOwiaAQziV1IXKZEnQS5Ylh53vbCuZVXlp8VVoDVZPUeSEIUaAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T12:38:52.087983Z"},"content_sha256":"73a787a03b9b89d33b464cdb729083cf3469bf0fa86d7dd7fc27ee5f61336b6d","schema_version":"1.0","event_id":"sha256:73a787a03b9b89d33b464cdb729083cf3469bf0fa86d7dd7fc27ee5f61336b6d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:4KKNXHZVCQCSTPIKCWP67BA4C2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Sharp L^p estimates on BMO","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Leonid Slavin, Vasily Vasyunin","submitted_at":"2011-10-08T21:40:28Z","abstract_excerpt":"We construct the upper and lower Bellman functions for the $L^p$ (quasi)-norms of BMO functions. These appear as solutions to a series of Monge--Amp\\`ere boundary value problems on a non-convex plane domain. The knowledge of the Bellman functions leads to sharp constants in inequalities relating average oscillations of BMO functions and various BMO norms."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.1771","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":"2026-05-18T04:11:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Gf4Fa0PTNqIVZeNU6vn3Try+QG4jclm9kfnW3rWGafL6Zx9sdMDRahAZFK/K3hiFEvClwub1jDiXnNZ9J2zlDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T12:38:52.088581Z"},"content_sha256":"a3dc128d0a48963fd1110d22e435083aaa9f90a6aac054d1b297e82b66982742","schema_version":"1.0","event_id":"sha256:a3dc128d0a48963fd1110d22e435083aaa9f90a6aac054d1b297e82b66982742"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4KKNXHZVCQCSTPIKCWP67BA4C2/bundle.json","state_url":"https://pith.science/pith/4KKNXHZVCQCSTPIKCWP67BA4C2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4KKNXHZVCQCSTPIKCWP67BA4C2/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":"2026-06-08T12:38:52Z","links":{"resolver":"https://pith.science/pith/4KKNXHZVCQCSTPIKCWP67BA4C2","bundle":"https://pith.science/pith/4KKNXHZVCQCSTPIKCWP67BA4C2/bundle.json","state":"https://pith.science/pith/4KKNXHZVCQCSTPIKCWP67BA4C2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4KKNXHZVCQCSTPIKCWP67BA4C2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:4KKNXHZVCQCSTPIKCWP67BA4C2","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":"8fd0cc4a997fa73badc1796860823e2240d0a6ab401b7f6efe220ab4830bd490","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2011-10-08T21:40:28Z","title_canon_sha256":"4d5feafeb44fcc65a46c420fcd913d9630dfebbdba961e243b48ca5817b6d9b8"},"schema_version":"1.0","source":{"id":"1110.1771","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.1771","created_at":"2026-05-18T04:11:19Z"},{"alias_kind":"arxiv_version","alias_value":"1110.1771v1","created_at":"2026-05-18T04:11:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.1771","created_at":"2026-05-18T04:11:19Z"},{"alias_kind":"pith_short_12","alias_value":"4KKNXHZVCQCS","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_16","alias_value":"4KKNXHZVCQCSTPIK","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_8","alias_value":"4KKNXHZV","created_at":"2026-05-18T12:26:20Z"}],"graph_snapshots":[{"event_id":"sha256:a3dc128d0a48963fd1110d22e435083aaa9f90a6aac054d1b297e82b66982742","target":"graph","created_at":"2026-05-18T04:11:19Z","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 construct the upper and lower Bellman functions for the $L^p$ (quasi)-norms of BMO functions. These appear as solutions to a series of Monge--Amp\\`ere boundary value problems on a non-convex plane domain. The knowledge of the Bellman functions leads to sharp constants in inequalities relating average oscillations of BMO functions and various BMO norms.","authors_text":"Leonid Slavin, Vasily Vasyunin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2011-10-08T21:40:28Z","title":"Sharp L^p estimates on BMO"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.1771","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":"sha256:73a787a03b9b89d33b464cdb729083cf3469bf0fa86d7dd7fc27ee5f61336b6d","target":"record","created_at":"2026-05-18T04:11:19Z","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":"8fd0cc4a997fa73badc1796860823e2240d0a6ab401b7f6efe220ab4830bd490","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2011-10-08T21:40:28Z","title_canon_sha256":"4d5feafeb44fcc65a46c420fcd913d9630dfebbdba961e243b48ca5817b6d9b8"},"schema_version":"1.0","source":{"id":"1110.1771","kind":"arxiv","version":1}},"canonical_sha256":"e294db9f35140529bd0a159fef841c1695890d9cbde343e83faef80276b09e33","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e294db9f35140529bd0a159fef841c1695890d9cbde343e83faef80276b09e33","first_computed_at":"2026-05-18T04:11:19.653023Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:11:19.653023Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"pYAjqrDbznjkCrvl+6FxfAjVU70B9PJw4zKhO6o6K/Rd0rlz0ql0a55uQtJKT3VugN8VFQmGp55r/PozFqimCw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:11:19.653521Z","signed_message":"canonical_sha256_bytes"},"source_id":"1110.1771","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:73a787a03b9b89d33b464cdb729083cf3469bf0fa86d7dd7fc27ee5f61336b6d","sha256:a3dc128d0a48963fd1110d22e435083aaa9f90a6aac054d1b297e82b66982742"],"state_sha256":"98200c507af4a1b7a281ee68f7f35b301fa9e1d377af8c603f0edb60136908d1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7d8doS5IOl92uniLFx/YuOH4Yd520FDcw+N4o/vZrtPl7RuQtmNNYbZWsU576P6Uen54OXBPRLbxKSFk2BSJDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T12:38:52.091627Z","bundle_sha256":"f5c4bae1d4a220460ec396a08d1d625178d020eb4673b4dc6bc0628678a143d1"}}