{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:O7UWHEYM4OEMUSWULEOFZ5OUD7","short_pith_number":"pith:O7UWHEYM","schema_version":"1.0","canonical_sha256":"77e963930ce388ca4ad4591c5cf5d41fcb9ab3156f6c660f5f186466ca6ae07d","source":{"kind":"arxiv","id":"1102.4475","version":1},"attestation_state":"computed","paper":{"title":"Harmonic analysis on Heisenberg--Clifford Lie supergroups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Alexander Alldridge, Joachim Hilgert, Martin Laubinger","submitted_at":"2011-02-22T11:53:48Z","abstract_excerpt":"We define a Fourier transform and a convolution product for functions and distributions on Heisenberg--Clifford Lie supergroups. The Fourier transform exchanges the convolution and a pointwise product, and is an intertwining operator for the left regular representation. We generalize various classical theorems, including the Paley--Wiener--Schwartz theorem, and define a convolution Banach algebra."},"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":"1102.4475","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2011-02-22T11:53:48Z","cross_cats_sorted":[],"title_canon_sha256":"a839417f353446421c49d0e91f94e7585164e50deb82b4440748ba089702272b","abstract_canon_sha256":"359189a565068f88c34b8b0f257086075e64d37514aa16bcfe7c6bc11a3bb6d8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:28:06.576212Z","signature_b64":"taa0iVMfkg2G9wJn45BDGgr4C2oQGAujnIs3d4DTWZPVnwTqcHe7ab6c9z73NkvSTJ8LzHZ1jVONJesbZwhyBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"77e963930ce388ca4ad4591c5cf5d41fcb9ab3156f6c660f5f186466ca6ae07d","last_reissued_at":"2026-05-18T03:28:06.575578Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:28:06.575578Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Harmonic analysis on Heisenberg--Clifford Lie supergroups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Alexander Alldridge, Joachim Hilgert, Martin Laubinger","submitted_at":"2011-02-22T11:53:48Z","abstract_excerpt":"We define a Fourier transform and a convolution product for functions and distributions on Heisenberg--Clifford Lie supergroups. The Fourier transform exchanges the convolution and a pointwise product, and is an intertwining operator for the left regular representation. We generalize various classical theorems, including the Paley--Wiener--Schwartz theorem, and define a convolution Banach algebra."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.4475","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":"1102.4475","created_at":"2026-05-18T03:28:06.575666+00:00"},{"alias_kind":"arxiv_version","alias_value":"1102.4475v1","created_at":"2026-05-18T03:28:06.575666+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1102.4475","created_at":"2026-05-18T03:28:06.575666+00:00"},{"alias_kind":"pith_short_12","alias_value":"O7UWHEYM4OEM","created_at":"2026-05-18T12:26:37.096874+00:00"},{"alias_kind":"pith_short_16","alias_value":"O7UWHEYM4OEMUSWU","created_at":"2026-05-18T12:26:37.096874+00:00"},{"alias_kind":"pith_short_8","alias_value":"O7UWHEYM","created_at":"2026-05-18T12:26:37.096874+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/O7UWHEYM4OEMUSWULEOFZ5OUD7","json":"https://pith.science/pith/O7UWHEYM4OEMUSWULEOFZ5OUD7.json","graph_json":"https://pith.science/api/pith-number/O7UWHEYM4OEMUSWULEOFZ5OUD7/graph.json","events_json":"https://pith.science/api/pith-number/O7UWHEYM4OEMUSWULEOFZ5OUD7/events.json","paper":"https://pith.science/paper/O7UWHEYM"},"agent_actions":{"view_html":"https://pith.science/pith/O7UWHEYM4OEMUSWULEOFZ5OUD7","download_json":"https://pith.science/pith/O7UWHEYM4OEMUSWULEOFZ5OUD7.json","view_paper":"https://pith.science/paper/O7UWHEYM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1102.4475&json=true","fetch_graph":"https://pith.science/api/pith-number/O7UWHEYM4OEMUSWULEOFZ5OUD7/graph.json","fetch_events":"https://pith.science/api/pith-number/O7UWHEYM4OEMUSWULEOFZ5OUD7/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/O7UWHEYM4OEMUSWULEOFZ5OUD7/action/timestamp_anchor","attest_storage":"https://pith.science/pith/O7UWHEYM4OEMUSWULEOFZ5OUD7/action/storage_attestation","attest_author":"https://pith.science/pith/O7UWHEYM4OEMUSWULEOFZ5OUD7/action/author_attestation","sign_citation":"https://pith.science/pith/O7UWHEYM4OEMUSWULEOFZ5OUD7/action/citation_signature","submit_replication":"https://pith.science/pith/O7UWHEYM4OEMUSWULEOFZ5OUD7/action/replication_record"}},"created_at":"2026-05-18T03:28:06.575666+00:00","updated_at":"2026-05-18T03:28:06.575666+00:00"}