{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:ML3YEQVOOFSJYPMWZB4NUNZG3Z","short_pith_number":"pith:ML3YEQVO","schema_version":"1.0","canonical_sha256":"62f78242ae71649c3d96c878da3726de54cbf8b46ed58caeea498dbe61cb4241","source":{"kind":"arxiv","id":"1210.8090","version":1},"attestation_state":"computed","paper":{"title":"$L^p$ spectral multipliers on the free group $N_{3,2}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.AP","authors_text":"Alessio Martini, Detlef M\\\"uller","submitted_at":"2012-10-30T17:26:02Z","abstract_excerpt":"Let $L$ be the homogeneous sublaplacian on the 6-dimensional free 2-step nilpotent group $N_{3,2}$ on 3 generators. We prove a theorem of Mihlin-H\\\"ormander type for the functional calculus of $L$, where the order of differentiability $s > 6/2$ is required on the multiplier."},"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":"1210.8090","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-10-30T17:26:02Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"5169f325ea90b66ab2d33653f0acf24cfdedffee4aacd4c0e94dd51b9893cc96","abstract_canon_sha256":"90d7e62dd69e46d0b679e1537e429659a2b1fb93f1a7aa905706eaaa7a77b0b4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:08:59.658959Z","signature_b64":"8X5tQmoRNOlHyR9sqVQppJXkoDlGAqPZ+CA413n2zupFFlzD+GADRWQvUUJqz2Py0mjtHK/uIiVu2528ha7kDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"62f78242ae71649c3d96c878da3726de54cbf8b46ed58caeea498dbe61cb4241","last_reissued_at":"2026-05-18T03:08:59.658286Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:08:59.658286Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"$L^p$ spectral multipliers on the free group $N_{3,2}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.AP","authors_text":"Alessio Martini, Detlef M\\\"uller","submitted_at":"2012-10-30T17:26:02Z","abstract_excerpt":"Let $L$ be the homogeneous sublaplacian on the 6-dimensional free 2-step nilpotent group $N_{3,2}$ on 3 generators. We prove a theorem of Mihlin-H\\\"ormander type for the functional calculus of $L$, where the order of differentiability $s > 6/2$ is required on the multiplier."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.8090","kind":"arxiv","version":1},"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":"1210.8090","created_at":"2026-05-18T03:08:59.658401+00:00"},{"alias_kind":"arxiv_version","alias_value":"1210.8090v1","created_at":"2026-05-18T03:08:59.658401+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.8090","created_at":"2026-05-18T03:08:59.658401+00:00"},{"alias_kind":"pith_short_12","alias_value":"ML3YEQVOOFSJ","created_at":"2026-05-18T12:27:14.488303+00:00"},{"alias_kind":"pith_short_16","alias_value":"ML3YEQVOOFSJYPMW","created_at":"2026-05-18T12:27:14.488303+00:00"},{"alias_kind":"pith_short_8","alias_value":"ML3YEQVO","created_at":"2026-05-18T12:27:14.488303+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/ML3YEQVOOFSJYPMWZB4NUNZG3Z","json":"https://pith.science/pith/ML3YEQVOOFSJYPMWZB4NUNZG3Z.json","graph_json":"https://pith.science/api/pith-number/ML3YEQVOOFSJYPMWZB4NUNZG3Z/graph.json","events_json":"https://pith.science/api/pith-number/ML3YEQVOOFSJYPMWZB4NUNZG3Z/events.json","paper":"https://pith.science/paper/ML3YEQVO"},"agent_actions":{"view_html":"https://pith.science/pith/ML3YEQVOOFSJYPMWZB4NUNZG3Z","download_json":"https://pith.science/pith/ML3YEQVOOFSJYPMWZB4NUNZG3Z.json","view_paper":"https://pith.science/paper/ML3YEQVO","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1210.8090&json=true","fetch_graph":"https://pith.science/api/pith-number/ML3YEQVOOFSJYPMWZB4NUNZG3Z/graph.json","fetch_events":"https://pith.science/api/pith-number/ML3YEQVOOFSJYPMWZB4NUNZG3Z/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ML3YEQVOOFSJYPMWZB4NUNZG3Z/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ML3YEQVOOFSJYPMWZB4NUNZG3Z/action/storage_attestation","attest_author":"https://pith.science/pith/ML3YEQVOOFSJYPMWZB4NUNZG3Z/action/author_attestation","sign_citation":"https://pith.science/pith/ML3YEQVOOFSJYPMWZB4NUNZG3Z/action/citation_signature","submit_replication":"https://pith.science/pith/ML3YEQVOOFSJYPMWZB4NUNZG3Z/action/replication_record"}},"created_at":"2026-05-18T03:08:59.658401+00:00","updated_at":"2026-05-18T03:08:59.658401+00:00"}