{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:6NJNH5SCER726ZS4GCVZ223SNE","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":"624b4a2cd2f50032c2ee700a6ab935c30b5da6dc2dd5c108d39e759216801d74","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2011-07-31T14:21:37Z","title_canon_sha256":"8454577c12f6b5b687e681b1373add40a24cb55c528119ff56596c944a3f2dad"},"schema_version":"1.0","source":{"id":"1108.0177","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1108.0177","created_at":"2026-05-18T04:16:31Z"},{"alias_kind":"arxiv_version","alias_value":"1108.0177v1","created_at":"2026-05-18T04:16:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1108.0177","created_at":"2026-05-18T04:16:31Z"},{"alias_kind":"pith_short_12","alias_value":"6NJNH5SCER72","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_16","alias_value":"6NJNH5SCER726ZS4","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_8","alias_value":"6NJNH5SC","created_at":"2026-05-18T12:26:22Z"}],"graph_snapshots":[{"event_id":"sha256:04d90d45de483a430be41d2ec238446bac57176a071f08eed1134b4a4c991939","target":"graph","created_at":"2026-05-18T04:16:31Z","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 $\\mathcal K$ be a flag kernel on a homogeneous nilpotent Lie group $G$. We prove that operators $T$ of the form $T(f)= f*\\mathcal K$ form an algebra under composition, and that such operators are bounded on $L^{p}(G)$ for $1<p<\\infty$.","authors_text":"Alexander Nagel, Elias M. Stein, Fulvio Ricci, Stephen Wainger","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2011-07-31T14:21:37Z","title":"Singular Integrals with Flag Kernels on Homogeneous Groups: I"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.0177","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":"sha256:6d89afefeaccf82f95b45a37a05fe67f053f9eb8af704b452245e91501e5b886","target":"record","created_at":"2026-05-18T04:16:31Z","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":"624b4a2cd2f50032c2ee700a6ab935c30b5da6dc2dd5c108d39e759216801d74","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2011-07-31T14:21:37Z","title_canon_sha256":"8454577c12f6b5b687e681b1373add40a24cb55c528119ff56596c944a3f2dad"},"schema_version":"1.0","source":{"id":"1108.0177","kind":"arxiv","version":1}},"canonical_sha256":"f352d3f642247faf665c30ab9d6b72690e4d3ecba17d08343c3ed4961a4bee34","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f352d3f642247faf665c30ab9d6b72690e4d3ecba17d08343c3ed4961a4bee34","first_computed_at":"2026-05-18T04:16:31.561715Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:16:31.561715Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"L1ht7iBUfrZjYGwF2EajYZsYD3mgeUNY2EFgoDdtps4aE17/o5SSdgG1XytdnZieakdvleInDpNCaM3MpI+iBw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:16:31.562103Z","signed_message":"canonical_sha256_bytes"},"source_id":"1108.0177","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6d89afefeaccf82f95b45a37a05fe67f053f9eb8af704b452245e91501e5b886","sha256:04d90d45de483a430be41d2ec238446bac57176a071f08eed1134b4a4c991939"],"state_sha256":"181468d417020777380342f08a5fab713863e0eab302ed554b97940aef29ac99"}