{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:BX7G5ESZANZ5ZKHLNEKIMQ4NCS","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":"09806124cccb245ae90891d1386f318f10bf96079d17d3e6338a9cec86c7d471","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2012-02-22T19:05:11Z","title_canon_sha256":"b1a4638ea6de2b7a0321c026da51c234e0109091e6fed028370c515e549b8317"},"schema_version":"1.0","source":{"id":"1202.5007","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1202.5007","created_at":"2026-05-18T04:01:40Z"},{"alias_kind":"arxiv_version","alias_value":"1202.5007v1","created_at":"2026-05-18T04:01:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.5007","created_at":"2026-05-18T04:01:40Z"},{"alias_kind":"pith_short_12","alias_value":"BX7G5ESZANZ5","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_16","alias_value":"BX7G5ESZANZ5ZKHL","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_8","alias_value":"BX7G5ESZ","created_at":"2026-05-18T12:27:01Z"}],"graph_snapshots":[{"event_id":"sha256:7d81ffd9ada6b6bc9423dfb40910eb6286d22576b4710be67dff88c117d4891a","target":"graph","created_at":"2026-05-18T04:01:40Z","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 $G$ be an exponential solvable Lie group. By definition $G$ is $\\ast$-regular if $ker_{L^1(G)}\\pi$ is dense in $ker_{C^\\ast(G)}\\pi$ for all unitary representations $\\pi$ of $G$. Boidol characterized the $\\ast$-regular exponential Lie groups by a purely algebraic condition. In this article we will focus on non-$\\ast$-regular groups. We say that $G$ is primitive $\\ast$-regular if the above density condition is satisfied for all irreducible representations. Our goal is to develop appropriate tools to verify this weaker property. To this end we will introduce Duflo pairs $(W,p)$ and central Fo","authors_text":"Oliver Ungermann","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2012-02-22T19:05:11Z","title":"Invariant differential operators and central Fourier multipliers on exponential Lie groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.5007","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:c26fb5bff6c23b099ba9867d7ca008bfea638b2adb97ade6ccf41d7a62e64f54","target":"record","created_at":"2026-05-18T04:01:40Z","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":"09806124cccb245ae90891d1386f318f10bf96079d17d3e6338a9cec86c7d471","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2012-02-22T19:05:11Z","title_canon_sha256":"b1a4638ea6de2b7a0321c026da51c234e0109091e6fed028370c515e549b8317"},"schema_version":"1.0","source":{"id":"1202.5007","kind":"arxiv","version":1}},"canonical_sha256":"0dfe6e92590373dca8eb691486438d148acfa6bc5e9f27fe6c2247a1b5c8b068","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0dfe6e92590373dca8eb691486438d148acfa6bc5e9f27fe6c2247a1b5c8b068","first_computed_at":"2026-05-18T04:01:40.046813Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:01:40.046813Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"pD434PMeebGS+dslezVHVNG79oQYQRhycOywm9JA0sHyY5XDTrFRIp5NyuMDlR7ul6ue2hMCjNXWvpkEQBg+Cw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:01:40.047779Z","signed_message":"canonical_sha256_bytes"},"source_id":"1202.5007","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c26fb5bff6c23b099ba9867d7ca008bfea638b2adb97ade6ccf41d7a62e64f54","sha256:7d81ffd9ada6b6bc9423dfb40910eb6286d22576b4710be67dff88c117d4891a"],"state_sha256":"3664c7b3b210112c47499a1e51cf910c5d370d1dc45b6968c92435ace35b4cf6"}