{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:JA7DKSBS35PC2RQLH32INT3ZMD","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":"957e55c75cd6a2b64bbd52289e768e5faad93aade69ce382f4da5e140428f359","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-10-03T12:13:10Z","title_canon_sha256":"4c477470bea88a53c706c10f844d832d8040e3e6e05a5e7be9540a7c016a93c5"},"schema_version":"1.0","source":{"id":"1110.0338","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.0338","created_at":"2026-05-18T04:11:50Z"},{"alias_kind":"arxiv_version","alias_value":"1110.0338v1","created_at":"2026-05-18T04:11:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.0338","created_at":"2026-05-18T04:11:50Z"},{"alias_kind":"pith_short_12","alias_value":"JA7DKSBS35PC","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_16","alias_value":"JA7DKSBS35PC2RQL","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_8","alias_value":"JA7DKSBS","created_at":"2026-05-18T12:26:32Z"}],"graph_snapshots":[{"event_id":"sha256:243eeac9aec4d7e2d50f9b1c3b6deaddef978dea05b79d97d727eb18e02bc11a","target":"graph","created_at":"2026-05-18T04:11:50Z","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":"Following \\cite{B2}, we introduce a notion of para-products associated to a semi-group. We do not use Fourier transform arguments and the background manifold is doubling, endowed with a sub-laplacian structure. Our main result is a paralinearization theorem in a non-euclidean framework, with an application to the propagation of regularity for some nonlinear PDEs.","authors_text":"Fr\\'ed\\'eric Bernicot, Yannick Sire","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-10-03T12:13:10Z","title":"Propagation of low regularity for solutions of nonlinear PDEs on a Riemannian manifold with a sub-Laplacian structure"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.0338","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:cb84ade8f8d1a265ea3f0def96dcf33eb2b4ac3da126ae6d7c320b213ef66d97","target":"record","created_at":"2026-05-18T04:11:50Z","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":"957e55c75cd6a2b64bbd52289e768e5faad93aade69ce382f4da5e140428f359","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-10-03T12:13:10Z","title_canon_sha256":"4c477470bea88a53c706c10f844d832d8040e3e6e05a5e7be9540a7c016a93c5"},"schema_version":"1.0","source":{"id":"1110.0338","kind":"arxiv","version":1}},"canonical_sha256":"483e354832df5e2d460b3ef486cf7960f9a2d85c4daa6876a20d724df65df533","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"483e354832df5e2d460b3ef486cf7960f9a2d85c4daa6876a20d724df65df533","first_computed_at":"2026-05-18T04:11:50.185626Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:11:50.185626Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/EJMsRD2gzJDhSQYxGwsGpyaT6MbxA8BGsD8lWht4rt2yXfHqNcN26ZsPTr54TDhX0kgrEaldNX0h4j85gymDg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:11:50.186332Z","signed_message":"canonical_sha256_bytes"},"source_id":"1110.0338","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cb84ade8f8d1a265ea3f0def96dcf33eb2b4ac3da126ae6d7c320b213ef66d97","sha256:243eeac9aec4d7e2d50f9b1c3b6deaddef978dea05b79d97d727eb18e02bc11a"],"state_sha256":"02027ed0e1d80586c993e81f7d6abad66e0d3ef0a4c874f4f75c3540db6d4a8b"}