{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:7QI3SPH3LJJQBV7Y2UNGD3FNOP","short_pith_number":"pith:7QI3SPH3","canonical_record":{"source":{"id":"0910.1228","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2009-10-07T12:05:57Z","cross_cats_sorted":["math.MG"],"title_canon_sha256":"1445e22c0cf31fdab3f019291bbafd356927ecf7412a01ce07ccc19a0419d50c","abstract_canon_sha256":"0ae17d8e1cb79440e18373935bd2f8f5dfe5cdeac533c4965b947c26a587182e"},"schema_version":"1.0"},"canonical_sha256":"fc11b93cfb5a5300d7f8d51a61ecad73c3871a188cf3ebac24970d7122534158","source":{"kind":"arxiv","id":"0910.1228","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0910.1228","created_at":"2026-05-18T02:28:12Z"},{"alias_kind":"arxiv_version","alias_value":"0910.1228v2","created_at":"2026-05-18T02:28:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0910.1228","created_at":"2026-05-18T02:28:12Z"},{"alias_kind":"pith_short_12","alias_value":"7QI3SPH3LJJQ","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"7QI3SPH3LJJQBV7Y","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"7QI3SPH3","created_at":"2026-05-18T12:25:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:7QI3SPH3LJJQBV7Y2UNGD3FNOP","target":"record","payload":{"canonical_record":{"source":{"id":"0910.1228","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2009-10-07T12:05:57Z","cross_cats_sorted":["math.MG"],"title_canon_sha256":"1445e22c0cf31fdab3f019291bbafd356927ecf7412a01ce07ccc19a0419d50c","abstract_canon_sha256":"0ae17d8e1cb79440e18373935bd2f8f5dfe5cdeac533c4965b947c26a587182e"},"schema_version":"1.0"},"canonical_sha256":"fc11b93cfb5a5300d7f8d51a61ecad73c3871a188cf3ebac24970d7122534158","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:28:12.429899Z","signature_b64":"Pq+8J/H9QWu27THgwWP9w+EyVTJJ3KrdSw+sqfC5eMQ/RUMWtGL7PcX0u4lkFvf3mORfQUpfOkM6Pi1qNDVlBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fc11b93cfb5a5300d7f8d51a61ecad73c3871a188cf3ebac24970d7122534158","last_reissued_at":"2026-05-18T02:28:12.429428Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:28:12.429428Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0910.1228","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":"2026-05-18T02:28:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cAjM1T4Ti9fPwZhGzEZTaawFFpuHWM9FQWDKW0ytFfOgADthPovwFF7Wdp+g5zqDBWT+0bxS5Ja//ZQvM0RkAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T23:51:44.847413Z"},"content_sha256":"a3e795482526923635daee4b2609b481d7088c4fc7292972aa2e11fb31cbca46","schema_version":"1.0","event_id":"sha256:a3e795482526923635daee4b2609b481d7088c4fc7292972aa2e11fb31cbca46"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:7QI3SPH3LJJQBV7Y2UNGD3FNOP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"John-Nirenberg lemmas for a doubling measure","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MG"],"primary_cat":"math.FA","authors_text":"Daniel Aalto, Hong Yue, Lauri Berkovits, Outi Elina Maasalo","submitted_at":"2009-10-07T12:05:57Z","abstract_excerpt":"We study, in the context of doubling metric measure spaces, a class of BMO type functions defined by John and Nirenberg. In particular, we present a new version of the Calderon-Zygmund decomposition in metric spaces and use it to prove the corresponding John-Nirenberg inequality."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0910.1228","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":"2026-05-18T02:28:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zv8ehtXr2unq3f9XFErR/iC2c6oX5LvoiOGMibCr23bZM2nAzSCjK9ByTGaw1rcbknNHwoJldNEml4vhve7BBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T23:51:44.847773Z"},"content_sha256":"7a5d1b32eaa805cb89b96eacb4325292ca0a9d0ac4b436f24abbea77ce1a118d","schema_version":"1.0","event_id":"sha256:7a5d1b32eaa805cb89b96eacb4325292ca0a9d0ac4b436f24abbea77ce1a118d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7QI3SPH3LJJQBV7Y2UNGD3FNOP/bundle.json","state_url":"https://pith.science/pith/7QI3SPH3LJJQBV7Y2UNGD3FNOP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7QI3SPH3LJJQBV7Y2UNGD3FNOP/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":"2026-05-30T23:51:44Z","links":{"resolver":"https://pith.science/pith/7QI3SPH3LJJQBV7Y2UNGD3FNOP","bundle":"https://pith.science/pith/7QI3SPH3LJJQBV7Y2UNGD3FNOP/bundle.json","state":"https://pith.science/pith/7QI3SPH3LJJQBV7Y2UNGD3FNOP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7QI3SPH3LJJQBV7Y2UNGD3FNOP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:7QI3SPH3LJJQBV7Y2UNGD3FNOP","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":"0ae17d8e1cb79440e18373935bd2f8f5dfe5cdeac533c4965b947c26a587182e","cross_cats_sorted":["math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2009-10-07T12:05:57Z","title_canon_sha256":"1445e22c0cf31fdab3f019291bbafd356927ecf7412a01ce07ccc19a0419d50c"},"schema_version":"1.0","source":{"id":"0910.1228","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0910.1228","created_at":"2026-05-18T02:28:12Z"},{"alias_kind":"arxiv_version","alias_value":"0910.1228v2","created_at":"2026-05-18T02:28:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0910.1228","created_at":"2026-05-18T02:28:12Z"},{"alias_kind":"pith_short_12","alias_value":"7QI3SPH3LJJQ","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"7QI3SPH3LJJQBV7Y","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"7QI3SPH3","created_at":"2026-05-18T12:25:58Z"}],"graph_snapshots":[{"event_id":"sha256:7a5d1b32eaa805cb89b96eacb4325292ca0a9d0ac4b436f24abbea77ce1a118d","target":"graph","created_at":"2026-05-18T02:28:12Z","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 study, in the context of doubling metric measure spaces, a class of BMO type functions defined by John and Nirenberg. In particular, we present a new version of the Calderon-Zygmund decomposition in metric spaces and use it to prove the corresponding John-Nirenberg inequality.","authors_text":"Daniel Aalto, Hong Yue, Lauri Berkovits, Outi Elina Maasalo","cross_cats":["math.MG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2009-10-07T12:05:57Z","title":"John-Nirenberg lemmas for a doubling measure"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0910.1228","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:a3e795482526923635daee4b2609b481d7088c4fc7292972aa2e11fb31cbca46","target":"record","created_at":"2026-05-18T02:28:12Z","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":"0ae17d8e1cb79440e18373935bd2f8f5dfe5cdeac533c4965b947c26a587182e","cross_cats_sorted":["math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2009-10-07T12:05:57Z","title_canon_sha256":"1445e22c0cf31fdab3f019291bbafd356927ecf7412a01ce07ccc19a0419d50c"},"schema_version":"1.0","source":{"id":"0910.1228","kind":"arxiv","version":2}},"canonical_sha256":"fc11b93cfb5a5300d7f8d51a61ecad73c3871a188cf3ebac24970d7122534158","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fc11b93cfb5a5300d7f8d51a61ecad73c3871a188cf3ebac24970d7122534158","first_computed_at":"2026-05-18T02:28:12.429428Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:28:12.429428Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Pq+8J/H9QWu27THgwWP9w+EyVTJJ3KrdSw+sqfC5eMQ/RUMWtGL7PcX0u4lkFvf3mORfQUpfOkM6Pi1qNDVlBA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:28:12.429899Z","signed_message":"canonical_sha256_bytes"},"source_id":"0910.1228","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a3e795482526923635daee4b2609b481d7088c4fc7292972aa2e11fb31cbca46","sha256:7a5d1b32eaa805cb89b96eacb4325292ca0a9d0ac4b436f24abbea77ce1a118d"],"state_sha256":"b46cc5d2891c2991edca69337b2ad44fc277256912e3c3cff684b2270283ddff"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tf2P3NsOIgFGpG3+3tWR5N7jO7RMNFdWfAa6tyta851lUztNQveEop+jeQUbprP4n4Ec0txKrWeJu8I/mxlVBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T23:51:44.850951Z","bundle_sha256":"cfa8a5c3f59d4d2787a8a694e4f9f2d405223cab9933395996f3f0520093b739"}}