{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:WBTBDX74UJSNLC2N2SG62UJPGO","short_pith_number":"pith:WBTBDX74","schema_version":"1.0","canonical_sha256":"b06611dffca264d58b4dd48ded512f33b66be62957cc83231597a7a8b18a131f","source":{"kind":"arxiv","id":"1504.03862","version":2},"attestation_state":"computed","paper":{"title":"Spectral multipliers for sub-Laplacians on solvable extensions of stratified groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Alessandro Ottazzi, Alessio Martini, Maria Vallarino","submitted_at":"2015-04-15T11:24:28Z","abstract_excerpt":"Let $G = N \\rtimes A$, where $N$ is a stratified group and $A = \\mathbb{R}$ acts on $N$ via automorphic dilations. Homogeneous sub-Laplacians on $N$ and $A$ can be lifted to left-invariant operators on $G$ and their sum is a sub-Laplacian $\\Delta$ on $G$. We prove a theorem of Mihlin-H\\\"ormander type for spectral multipliers of $\\Delta$. The proof of the theorem hinges on a Calder\\'on-Zygmund theory adapted to a sub-Riemannian structure of $G$ and on $L^1$-estimates of the gradient of the heat kernel associated to the sub-Laplacian $\\Delta$."},"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":"1504.03862","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-04-15T11:24:28Z","cross_cats_sorted":[],"title_canon_sha256":"295dbc52606d3f968a141f00f9f6cadeca4f5fc8aa98d3711444860a571be80f","abstract_canon_sha256":"a49dbfa97949d37b2d75d7c3d557727b9e23a778289f33acaf09dec082b372c3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:58:15.326749Z","signature_b64":"CPBuwofNgnxJZ5aRDr/VQ1pn9nXy44L1YtQIh6TgJdD4xBbuW4esvG2FOUcKcmEIV0yVjDyPgYFHREyk+6QUCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b06611dffca264d58b4dd48ded512f33b66be62957cc83231597a7a8b18a131f","last_reissued_at":"2026-05-17T23:58:15.326133Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:58:15.326133Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Spectral multipliers for sub-Laplacians on solvable extensions of stratified groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Alessandro Ottazzi, Alessio Martini, Maria Vallarino","submitted_at":"2015-04-15T11:24:28Z","abstract_excerpt":"Let $G = N \\rtimes A$, where $N$ is a stratified group and $A = \\mathbb{R}$ acts on $N$ via automorphic dilations. Homogeneous sub-Laplacians on $N$ and $A$ can be lifted to left-invariant operators on $G$ and their sum is a sub-Laplacian $\\Delta$ on $G$. We prove a theorem of Mihlin-H\\\"ormander type for spectral multipliers of $\\Delta$. The proof of the theorem hinges on a Calder\\'on-Zygmund theory adapted to a sub-Riemannian structure of $G$ and on $L^1$-estimates of the gradient of the heat kernel associated to the sub-Laplacian $\\Delta$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.03862","kind":"arxiv","version":2},"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":"1504.03862","created_at":"2026-05-17T23:58:15.326228+00:00"},{"alias_kind":"arxiv_version","alias_value":"1504.03862v2","created_at":"2026-05-17T23:58:15.326228+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.03862","created_at":"2026-05-17T23:58:15.326228+00:00"},{"alias_kind":"pith_short_12","alias_value":"WBTBDX74UJSN","created_at":"2026-05-18T12:29:47.479230+00:00"},{"alias_kind":"pith_short_16","alias_value":"WBTBDX74UJSNLC2N","created_at":"2026-05-18T12:29:47.479230+00:00"},{"alias_kind":"pith_short_8","alias_value":"WBTBDX74","created_at":"2026-05-18T12:29:47.479230+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/WBTBDX74UJSNLC2N2SG62UJPGO","json":"https://pith.science/pith/WBTBDX74UJSNLC2N2SG62UJPGO.json","graph_json":"https://pith.science/api/pith-number/WBTBDX74UJSNLC2N2SG62UJPGO/graph.json","events_json":"https://pith.science/api/pith-number/WBTBDX74UJSNLC2N2SG62UJPGO/events.json","paper":"https://pith.science/paper/WBTBDX74"},"agent_actions":{"view_html":"https://pith.science/pith/WBTBDX74UJSNLC2N2SG62UJPGO","download_json":"https://pith.science/pith/WBTBDX74UJSNLC2N2SG62UJPGO.json","view_paper":"https://pith.science/paper/WBTBDX74","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1504.03862&json=true","fetch_graph":"https://pith.science/api/pith-number/WBTBDX74UJSNLC2N2SG62UJPGO/graph.json","fetch_events":"https://pith.science/api/pith-number/WBTBDX74UJSNLC2N2SG62UJPGO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WBTBDX74UJSNLC2N2SG62UJPGO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WBTBDX74UJSNLC2N2SG62UJPGO/action/storage_attestation","attest_author":"https://pith.science/pith/WBTBDX74UJSNLC2N2SG62UJPGO/action/author_attestation","sign_citation":"https://pith.science/pith/WBTBDX74UJSNLC2N2SG62UJPGO/action/citation_signature","submit_replication":"https://pith.science/pith/WBTBDX74UJSNLC2N2SG62UJPGO/action/replication_record"}},"created_at":"2026-05-17T23:58:15.326228+00:00","updated_at":"2026-05-17T23:58:15.326228+00:00"}