{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:INNLWBWQFLFPMIOOKQTBVAFEN6","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":"3dfce3cf26f8b470a79c6c8956b28d564df28b6de7e639eaa18a92d8d5140803","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2011-10-04T10:58:10Z","title_canon_sha256":"a0274464fd72f69db67bfb816e2cf336c51a53aa655cbd2d6c44b05d53136192"},"schema_version":"1.0","source":{"id":"1110.0633","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.0633","created_at":"2026-05-18T04:11:41Z"},{"alias_kind":"arxiv_version","alias_value":"1110.0633v1","created_at":"2026-05-18T04:11:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.0633","created_at":"2026-05-18T04:11:41Z"},{"alias_kind":"pith_short_12","alias_value":"INNLWBWQFLFP","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_16","alias_value":"INNLWBWQFLFPMIOO","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_8","alias_value":"INNLWBWQ","created_at":"2026-05-18T12:26:32Z"}],"graph_snapshots":[{"event_id":"sha256:08694a722e418f150791e4cf78ac17e1eb6b1b532ea3f3c7c31f88bcd15caf28","target":"graph","created_at":"2026-05-18T04:11:41Z","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":"Let 0<n<d be integers and let H denote the n-dimensional Hausdorff measure restricted to an n-dimensional Lipschitz graph in R^d with slope strictly less than 1. For r>2, we prove that the r-variation and oscillation for Calder\\'on-Zygmund singular integrals with odd kernel are bounded operators in L^p(H) for 1<p finite, from L^1(H) to weak-L^1(H), and from the space of bounded H-measurable functions to BMO(H). Concerning the first endpoint estimate, we actually show that such operators are bounded from the space of finite complex Radon measures in R^d to weak-L^1(H).","authors_text":"Albert Mas","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2011-10-04T10:58:10Z","title":"Variation for singular integrals on Lipschitz graphs: L^p and endpoint estimates"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.0633","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:afe4119634448d7fe6684bad352ae7f9097c5595acd19f65902bfc206b34529e","target":"record","created_at":"2026-05-18T04:11:41Z","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":"3dfce3cf26f8b470a79c6c8956b28d564df28b6de7e639eaa18a92d8d5140803","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2011-10-04T10:58:10Z","title_canon_sha256":"a0274464fd72f69db67bfb816e2cf336c51a53aa655cbd2d6c44b05d53136192"},"schema_version":"1.0","source":{"id":"1110.0633","kind":"arxiv","version":1}},"canonical_sha256":"435abb06d02acaf621ce54261a80a46f9ab36e49f6245f4cc35be027157a5323","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"435abb06d02acaf621ce54261a80a46f9ab36e49f6245f4cc35be027157a5323","first_computed_at":"2026-05-18T04:11:41.315650Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:11:41.315650Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TDkRFyBrQypXc4dz5rmiRMRBxOi7pullaBzTkgJY/fKnoqh53XEKi0fNedq+kFHOEFKUAOH1RX1xFe0xkqiKBw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:11:41.316344Z","signed_message":"canonical_sha256_bytes"},"source_id":"1110.0633","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:afe4119634448d7fe6684bad352ae7f9097c5595acd19f65902bfc206b34529e","sha256:08694a722e418f150791e4cf78ac17e1eb6b1b532ea3f3c7c31f88bcd15caf28"],"state_sha256":"fc3fbd43e7b41dbf4bfa70419bbff254e62588579484a525a0e96cf39130bbb4"}