{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:QDLJQYHMWPCZA2BSN46H7IIWMZ","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":"f02636b76110bbe8ca47e4010c16b945d213abf05858de7c4f53ffe595f1c6f3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-11-08T19:02:31Z","title_canon_sha256":"beeae02a756152cd79999569f04a73af7f0b1f0742bb2ed5a4aa66ca74bda89f"},"schema_version":"1.0","source":{"id":"1611.02653","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.02653","created_at":"2026-05-18T00:59:51Z"},{"alias_kind":"arxiv_version","alias_value":"1611.02653v1","created_at":"2026-05-18T00:59:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.02653","created_at":"2026-05-18T00:59:51Z"},{"alias_kind":"pith_short_12","alias_value":"QDLJQYHMWPCZ","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_16","alias_value":"QDLJQYHMWPCZA2BS","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_8","alias_value":"QDLJQYHM","created_at":"2026-05-18T12:30:39Z"}],"graph_snapshots":[{"event_id":"sha256:fc4d81d521fdf83df9f1ce66753910fe678d024cdcf7280ca103b95f0261d3a2","target":"graph","created_at":"2026-05-18T00:59:51Z","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 prove that the $\\cal P$ norm estimate between a Hardy martingale and its cosine part are stable under dyadic perturbations, and show how dyadic stability of the $\\cal P$ norm estimate is used in the proof that $L^1$ embeds into $L^1/H^1$.","authors_text":"Paul F.X. M\\\"uller","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-11-08T19:02:31Z","title":"Conditional Square Functions, the Sine-Cosine Decomposition for Hardy Martingales and Dyadic Perturbation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.02653","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":"sha256:9fd3998791ebaf1be57115906ea9c50b8c90590a8ce773ed02d4b8ca2cdbf636","target":"record","created_at":"2026-05-18T00:59:51Z","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":"f02636b76110bbe8ca47e4010c16b945d213abf05858de7c4f53ffe595f1c6f3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-11-08T19:02:31Z","title_canon_sha256":"beeae02a756152cd79999569f04a73af7f0b1f0742bb2ed5a4aa66ca74bda89f"},"schema_version":"1.0","source":{"id":"1611.02653","kind":"arxiv","version":1}},"canonical_sha256":"80d69860ecb3c59068326f3c7fa116665ce71eeb1ce5c921b809ce8fbe6f1b7f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"80d69860ecb3c59068326f3c7fa116665ce71eeb1ce5c921b809ce8fbe6f1b7f","first_computed_at":"2026-05-18T00:59:51.319094Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:59:51.319094Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qN93sN6Q7v72dD/8ZR6rhLiF8p6Bj34iNRWTTWbkVE2m28Kqtq1aE4oik1Uy24zi8XgpGcmlVwk87Nd/JWIaCw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:59:51.319702Z","signed_message":"canonical_sha256_bytes"},"source_id":"1611.02653","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9fd3998791ebaf1be57115906ea9c50b8c90590a8ce773ed02d4b8ca2cdbf636","sha256:fc4d81d521fdf83df9f1ce66753910fe678d024cdcf7280ca103b95f0261d3a2"],"state_sha256":"c4fe0404bbff9aee5301006c60e8f465722ecb622a8b7db01a53d0cd071ec4ca"}