{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:CRCTI4ISA5MAFJQJNQQFG7MVYE","short_pith_number":"pith:CRCTI4IS","schema_version":"1.0","canonical_sha256":"1445347112075802a6096c20537d95c1315d3197f4087ed968826b202d9ded0a","source":{"kind":"arxiv","id":"1510.06990","version":3},"attestation_state":"computed","paper":{"title":"Multilinear singular integral forms of Christ-Journ\\'e type","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.CA","authors_text":"Andreas Seeger, Brian Street, Charles K. Smart","submitted_at":"2015-10-23T16:55:30Z","abstract_excerpt":"We prove $L^{p_1}(\\mathbb R^d)\\times \\dots \\times L^{p_{n+2}}(\\mathbb R^{d})$ polynomial growth estimates for the Christ-Journ\\'e multilinear singular integral forms and suitable generalizations."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1510.06990","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2015-10-23T16:55:30Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"56609bf8206bf7f0704cde7d1f70394a1ac4e7dd5e0ebc088f7a77f97a28daa4","abstract_canon_sha256":"7d865c3d8382bce14bb97e788855bd69b745200ebe3ff0965cf1fbee090cf496"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:43:54.413048Z","signature_b64":"S7v+S3YfkxIsrtz2OuLvOzrBhguGyEgDRZLWq3MqK4SSyNfx9+XSjTBHc6ZxX1ysW6UzukTHmuS8nVfGhHeMDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1445347112075802a6096c20537d95c1315d3197f4087ed968826b202d9ded0a","last_reissued_at":"2026-05-17T23:43:54.412513Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:43:54.412513Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Multilinear singular integral forms of Christ-Journ\\'e type","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.CA","authors_text":"Andreas Seeger, Brian Street, Charles K. Smart","submitted_at":"2015-10-23T16:55:30Z","abstract_excerpt":"We prove $L^{p_1}(\\mathbb R^d)\\times \\dots \\times L^{p_{n+2}}(\\mathbb R^{d})$ polynomial growth estimates for the Christ-Journ\\'e multilinear singular integral forms and suitable generalizations."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.06990","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1510.06990","created_at":"2026-05-17T23:43:54.412598+00:00"},{"alias_kind":"arxiv_version","alias_value":"1510.06990v3","created_at":"2026-05-17T23:43:54.412598+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.06990","created_at":"2026-05-17T23:43:54.412598+00:00"},{"alias_kind":"pith_short_12","alias_value":"CRCTI4ISA5MA","created_at":"2026-05-18T12:29:17.054201+00:00"},{"alias_kind":"pith_short_16","alias_value":"CRCTI4ISA5MAFJQJ","created_at":"2026-05-18T12:29:17.054201+00:00"},{"alias_kind":"pith_short_8","alias_value":"CRCTI4IS","created_at":"2026-05-18T12:29:17.054201+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/CRCTI4ISA5MAFJQJNQQFG7MVYE","json":"https://pith.science/pith/CRCTI4ISA5MAFJQJNQQFG7MVYE.json","graph_json":"https://pith.science/api/pith-number/CRCTI4ISA5MAFJQJNQQFG7MVYE/graph.json","events_json":"https://pith.science/api/pith-number/CRCTI4ISA5MAFJQJNQQFG7MVYE/events.json","paper":"https://pith.science/paper/CRCTI4IS"},"agent_actions":{"view_html":"https://pith.science/pith/CRCTI4ISA5MAFJQJNQQFG7MVYE","download_json":"https://pith.science/pith/CRCTI4ISA5MAFJQJNQQFG7MVYE.json","view_paper":"https://pith.science/paper/CRCTI4IS","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1510.06990&json=true","fetch_graph":"https://pith.science/api/pith-number/CRCTI4ISA5MAFJQJNQQFG7MVYE/graph.json","fetch_events":"https://pith.science/api/pith-number/CRCTI4ISA5MAFJQJNQQFG7MVYE/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CRCTI4ISA5MAFJQJNQQFG7MVYE/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CRCTI4ISA5MAFJQJNQQFG7MVYE/action/storage_attestation","attest_author":"https://pith.science/pith/CRCTI4ISA5MAFJQJNQQFG7MVYE/action/author_attestation","sign_citation":"https://pith.science/pith/CRCTI4ISA5MAFJQJNQQFG7MVYE/action/citation_signature","submit_replication":"https://pith.science/pith/CRCTI4ISA5MAFJQJNQQFG7MVYE/action/replication_record"}},"created_at":"2026-05-17T23:43:54.412598+00:00","updated_at":"2026-05-17T23:43:54.412598+00:00"}