{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:FMIQNKU2Q7ZY245QIXZFHW2K5M","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":"3d14a2cc0b624fe3ae5b4708a8c7e14914fe7adfe53d35084b40bbfbea347459","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2020-08-20T11:34:06Z","title_canon_sha256":"77c841d3cad016f2ef3a13c3f2788eb0154979302d33a47ef80e6b133e9974e7"},"schema_version":"1.0","source":{"id":"2008.08897","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2008.08897","created_at":"2026-07-05T05:52:49Z"},{"alias_kind":"arxiv_version","alias_value":"2008.08897v2","created_at":"2026-07-05T05:52:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2008.08897","created_at":"2026-07-05T05:52:49Z"},{"alias_kind":"pith_short_12","alias_value":"FMIQNKU2Q7ZY","created_at":"2026-07-05T05:52:49Z"},{"alias_kind":"pith_short_16","alias_value":"FMIQNKU2Q7ZY245Q","created_at":"2026-07-05T05:52:49Z"},{"alias_kind":"pith_short_8","alias_value":"FMIQNKU2","created_at":"2026-07-05T05:52:49Z"}],"graph_snapshots":[{"event_id":"sha256:21e99350c0fcfc6c8f089bbba7c0ab49ae96b02355941787199e23a73791b647","target":"graph","created_at":"2026-07-05T05:52:49Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2008.08897/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We establish a new scale of $p$-variation estimates for martingale paraproducts, martingale transforms, and It\\^o integrals, of relevance in rough paths theory, stochastic, and harmonic analysis. As an application, we introduce rough semimartingales, a common generalization of classical semimartingales and (controlled) rough paths, and their integration theory.","authors_text":"Pavel Zorin-Kranich, Peter Friz","cross_cats":["math.CA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2020-08-20T11:34:06Z","title":"Rough semimartingales and $p$-variation estimates for martingale transforms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2008.08897","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:a7e354f22c51ba6f86d27dfcdc68de8b8a0ba5a5c6aee82215d3f1ef8d323b01","target":"record","created_at":"2026-07-05T05:52:49Z","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":"3d14a2cc0b624fe3ae5b4708a8c7e14914fe7adfe53d35084b40bbfbea347459","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2020-08-20T11:34:06Z","title_canon_sha256":"77c841d3cad016f2ef3a13c3f2788eb0154979302d33a47ef80e6b133e9974e7"},"schema_version":"1.0","source":{"id":"2008.08897","kind":"arxiv","version":2}},"canonical_sha256":"2b1106aa9a87f38d73b045f253db4aeb20c7fcb42d0191dda6085677a4af84cb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2b1106aa9a87f38d73b045f253db4aeb20c7fcb42d0191dda6085677a4af84cb","first_computed_at":"2026-07-05T05:52:49.072782Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:52:49.072782Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"S4pj/hEEP5vpslmUMJcnv1aH1iTDXITXp6xmsaDP7s7WkTIHe31S/uFCslW3YoY8tpQGgLTJiHpac4ozbIY3DA==","signature_status":"signed_v1","signed_at":"2026-07-05T05:52:49.073176Z","signed_message":"canonical_sha256_bytes"},"source_id":"2008.08897","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a7e354f22c51ba6f86d27dfcdc68de8b8a0ba5a5c6aee82215d3f1ef8d323b01","sha256:21e99350c0fcfc6c8f089bbba7c0ab49ae96b02355941787199e23a73791b647"],"state_sha256":"efeb81fe45adc4c1ed674775842348365a1d351e679ec9d381a477af82131dc9"}