{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:CNXER2JAJVDYHTDVHHRKITDAP3","short_pith_number":"pith:CNXER2JA","canonical_record":{"source":{"id":"1205.6328","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-05-29T11:07:57Z","cross_cats_sorted":["math.CV","math.FA"],"title_canon_sha256":"3696e9bf31555649e9f70e8dcdd5c6e7dd645f6b484fac9972d17b0eb01c0a19","abstract_canon_sha256":"5b41e6f402404a381999b2fe27d1bff4dd033965276e61f6a459613259744079"},"schema_version":"1.0"},"canonical_sha256":"136e48e9204d4783cc7539e2a44c607ecb6340b9a7315eb07d1f93d5d3ed9f89","source":{"kind":"arxiv","id":"1205.6328","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.6328","created_at":"2026-05-18T02:25:10Z"},{"alias_kind":"arxiv_version","alias_value":"1205.6328v2","created_at":"2026-05-18T02:25:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.6328","created_at":"2026-05-18T02:25:10Z"},{"alias_kind":"pith_short_12","alias_value":"CNXER2JAJVDY","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_16","alias_value":"CNXER2JAJVDYHTDV","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_8","alias_value":"CNXER2JA","created_at":"2026-05-18T12:27:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:CNXER2JAJVDYHTDVHHRKITDAP3","target":"record","payload":{"canonical_record":{"source":{"id":"1205.6328","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-05-29T11:07:57Z","cross_cats_sorted":["math.CV","math.FA"],"title_canon_sha256":"3696e9bf31555649e9f70e8dcdd5c6e7dd645f6b484fac9972d17b0eb01c0a19","abstract_canon_sha256":"5b41e6f402404a381999b2fe27d1bff4dd033965276e61f6a459613259744079"},"schema_version":"1.0"},"canonical_sha256":"136e48e9204d4783cc7539e2a44c607ecb6340b9a7315eb07d1f93d5d3ed9f89","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:25:10.828691Z","signature_b64":"PjaSpv8rwUFTG9LHEbgltebGur4FZwhStW7XYfLufXPj3C95YmkDZDkeSaA7QOUOLBuyHLu2ATmONWtCI/OKBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"136e48e9204d4783cc7539e2a44c607ecb6340b9a7315eb07d1f93d5d3ed9f89","last_reissued_at":"2026-05-18T02:25:10.828039Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:25:10.828039Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1205.6328","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":"2026-05-18T02:25:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NZz4t99VBQK3XlaM3IpgwXkgA5hMZFSYC27I15qpku2vWEoxip36NPpfmGgwvo4yFv0IIUcw1kwoZc/991agBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-29T14:48:45.815995Z"},"content_sha256":"a2026a4c53717d3e834a2e853ac681e4e530afa41a12d25b4adceac4f348d86b","schema_version":"1.0","event_id":"sha256:a2026a4c53717d3e834a2e853ac681e4e530afa41a12d25b4adceac4f348d86b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:CNXER2JAJVDYHTDVHHRKITDAP3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Logarithmic mean oscillation on the Polydisc, Multi-parameter paraproducts and iterated commutators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV","math.FA"],"primary_cat":"math.CA","authors_text":"Benoit F. Sehba","submitted_at":"2012-05-29T11:07:57Z","abstract_excerpt":"We introduce another notion of bounded logarithmic mean oscillation in the N-torus and give an equivalent definition in terms of boundedness of multi-parameter paraproducts from the dyadic little BMO of Cotlar-Sadosky to the product BMO of Chang-Fefferman. We also obtain a sufficient condition for the boundedness of iterated commutators with Hilbert transforms betweeen the strong notions of these two spaces."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.6328","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":"2026-05-18T02:25:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5At7XmRKzCfDLaM8rNHlqdOglVp+O+euI523OVbvQioL5RNLlxfTFzOkf08SVDSfR0wGQrOiVHQwDfN3udRyDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-29T14:48:45.816743Z"},"content_sha256":"e49397e4f66c2e0e2c517e7418e87b8c68d487e90fbd80fdb0f0a1cd92c224c8","schema_version":"1.0","event_id":"sha256:e49397e4f66c2e0e2c517e7418e87b8c68d487e90fbd80fdb0f0a1cd92c224c8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CNXER2JAJVDYHTDVHHRKITDAP3/bundle.json","state_url":"https://pith.science/pith/CNXER2JAJVDYHTDVHHRKITDAP3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CNXER2JAJVDYHTDVHHRKITDAP3/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":"2026-05-29T14:48:45Z","links":{"resolver":"https://pith.science/pith/CNXER2JAJVDYHTDVHHRKITDAP3","bundle":"https://pith.science/pith/CNXER2JAJVDYHTDVHHRKITDAP3/bundle.json","state":"https://pith.science/pith/CNXER2JAJVDYHTDVHHRKITDAP3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CNXER2JAJVDYHTDVHHRKITDAP3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:CNXER2JAJVDYHTDVHHRKITDAP3","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":"5b41e6f402404a381999b2fe27d1bff4dd033965276e61f6a459613259744079","cross_cats_sorted":["math.CV","math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-05-29T11:07:57Z","title_canon_sha256":"3696e9bf31555649e9f70e8dcdd5c6e7dd645f6b484fac9972d17b0eb01c0a19"},"schema_version":"1.0","source":{"id":"1205.6328","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.6328","created_at":"2026-05-18T02:25:10Z"},{"alias_kind":"arxiv_version","alias_value":"1205.6328v2","created_at":"2026-05-18T02:25:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.6328","created_at":"2026-05-18T02:25:10Z"},{"alias_kind":"pith_short_12","alias_value":"CNXER2JAJVDY","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_16","alias_value":"CNXER2JAJVDYHTDV","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_8","alias_value":"CNXER2JA","created_at":"2026-05-18T12:27:01Z"}],"graph_snapshots":[{"event_id":"sha256:e49397e4f66c2e0e2c517e7418e87b8c68d487e90fbd80fdb0f0a1cd92c224c8","target":"graph","created_at":"2026-05-18T02:25:10Z","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 introduce another notion of bounded logarithmic mean oscillation in the N-torus and give an equivalent definition in terms of boundedness of multi-parameter paraproducts from the dyadic little BMO of Cotlar-Sadosky to the product BMO of Chang-Fefferman. We also obtain a sufficient condition for the boundedness of iterated commutators with Hilbert transforms betweeen the strong notions of these two spaces.","authors_text":"Benoit F. Sehba","cross_cats":["math.CV","math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-05-29T11:07:57Z","title":"Logarithmic mean oscillation on the Polydisc, Multi-parameter paraproducts and iterated commutators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.6328","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:a2026a4c53717d3e834a2e853ac681e4e530afa41a12d25b4adceac4f348d86b","target":"record","created_at":"2026-05-18T02:25:10Z","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":"5b41e6f402404a381999b2fe27d1bff4dd033965276e61f6a459613259744079","cross_cats_sorted":["math.CV","math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-05-29T11:07:57Z","title_canon_sha256":"3696e9bf31555649e9f70e8dcdd5c6e7dd645f6b484fac9972d17b0eb01c0a19"},"schema_version":"1.0","source":{"id":"1205.6328","kind":"arxiv","version":2}},"canonical_sha256":"136e48e9204d4783cc7539e2a44c607ecb6340b9a7315eb07d1f93d5d3ed9f89","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"136e48e9204d4783cc7539e2a44c607ecb6340b9a7315eb07d1f93d5d3ed9f89","first_computed_at":"2026-05-18T02:25:10.828039Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:25:10.828039Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PjaSpv8rwUFTG9LHEbgltebGur4FZwhStW7XYfLufXPj3C95YmkDZDkeSaA7QOUOLBuyHLu2ATmONWtCI/OKBw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:25:10.828691Z","signed_message":"canonical_sha256_bytes"},"source_id":"1205.6328","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a2026a4c53717d3e834a2e853ac681e4e530afa41a12d25b4adceac4f348d86b","sha256:e49397e4f66c2e0e2c517e7418e87b8c68d487e90fbd80fdb0f0a1cd92c224c8"],"state_sha256":"286a1004da98c9c7fcddec0cb9c8fa9dbb80f4df50813fbb548e89ef3beddc8d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bZbOhs6gbEupM/6djo79AgXWHMhpIL7LXzrWaXfGSNSuRmZpgkJI5BhCh81vEePoZHY4+Y2czBlJwEOlFTrjCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-29T14:48:45.820589Z","bundle_sha256":"0f62153fdb5a7111b6de79e4ad640acaf7061451bd86a67ddefde40432a05d79"}}