{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2007:SPEARHNM573BMDHY6TVR572H6W","short_pith_number":"pith:SPEARHNM","schema_version":"1.0","canonical_sha256":"93c8089daceff6160cf8f4eb1eff47f5b6508062f0199c2c87b6dd4c3aca7395","source":{"kind":"arxiv","id":"0712.1769","version":2},"attestation_state":"computed","paper":{"title":"The Schrodinger model for the minimal representation of the indefinite orthogonal group O(p, q)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.AP","math.MP"],"primary_cat":"math.RT","authors_text":"Gen Mano, Toshiyuki Kobayashi","submitted_at":"2007-12-11T18:22:13Z","abstract_excerpt":"We introduce the `Fourier transform' F_C on the isotropic cone C associated to an indefinite quadratic form of signature (n_1,n_2) on R^n (n=n_1+n_2: even). This transform is in some sense the unique and natural unitary operator on L^2(C), as is the case with the Euclidean Fourier transform.\n  Inspired by recent developments of algebraic representation theory of reductive groups, we shed new light on classical analysis on the one hand, and give the global formulas for the L^2-model of the minimal representation of the simple Lie group G=O(n_1+1,n_2+1) on the other hand.\n  The transform F_C exp"},"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":"0712.1769","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2007-12-11T18:22:13Z","cross_cats_sorted":["math-ph","math.AP","math.MP"],"title_canon_sha256":"2b851ac260bc4914e3d2d0b047fcccc1b5c9978e9f198d2dc70469b3ec5f3e46","abstract_canon_sha256":"fad879e9bb6f198922084e69f8a9b4cb5cb14f2d8bea36f1cee4aebf75b940b9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:19:33.677867Z","signature_b64":"Dk1E8IJzaG+VQV+HMUmeCjhwB9XmCZ46MFjzna8iZVN51tnV+v/cL+DeuMoa0/hwbxh88LmxzcQ+SCwcX9MSDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"93c8089daceff6160cf8f4eb1eff47f5b6508062f0199c2c87b6dd4c3aca7395","last_reissued_at":"2026-05-18T04:19:33.677361Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:19:33.677361Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Schrodinger model for the minimal representation of the indefinite orthogonal group O(p, q)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.AP","math.MP"],"primary_cat":"math.RT","authors_text":"Gen Mano, Toshiyuki Kobayashi","submitted_at":"2007-12-11T18:22:13Z","abstract_excerpt":"We introduce the `Fourier transform' F_C on the isotropic cone C associated to an indefinite quadratic form of signature (n_1,n_2) on R^n (n=n_1+n_2: even). This transform is in some sense the unique and natural unitary operator on L^2(C), as is the case with the Euclidean Fourier transform.\n  Inspired by recent developments of algebraic representation theory of reductive groups, we shed new light on classical analysis on the one hand, and give the global formulas for the L^2-model of the minimal representation of the simple Lie group G=O(n_1+1,n_2+1) on the other hand.\n  The transform F_C exp"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0712.1769","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":"0712.1769","created_at":"2026-05-18T04:19:33.677427+00:00"},{"alias_kind":"arxiv_version","alias_value":"0712.1769v2","created_at":"2026-05-18T04:19:33.677427+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0712.1769","created_at":"2026-05-18T04:19:33.677427+00:00"},{"alias_kind":"pith_short_12","alias_value":"SPEARHNM573B","created_at":"2026-05-18T12:25:56.245647+00:00"},{"alias_kind":"pith_short_16","alias_value":"SPEARHNM573BMDHY","created_at":"2026-05-18T12:25:56.245647+00:00"},{"alias_kind":"pith_short_8","alias_value":"SPEARHNM","created_at":"2026-05-18T12:25:56.245647+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/SPEARHNM573BMDHY6TVR572H6W","json":"https://pith.science/pith/SPEARHNM573BMDHY6TVR572H6W.json","graph_json":"https://pith.science/api/pith-number/SPEARHNM573BMDHY6TVR572H6W/graph.json","events_json":"https://pith.science/api/pith-number/SPEARHNM573BMDHY6TVR572H6W/events.json","paper":"https://pith.science/paper/SPEARHNM"},"agent_actions":{"view_html":"https://pith.science/pith/SPEARHNM573BMDHY6TVR572H6W","download_json":"https://pith.science/pith/SPEARHNM573BMDHY6TVR572H6W.json","view_paper":"https://pith.science/paper/SPEARHNM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0712.1769&json=true","fetch_graph":"https://pith.science/api/pith-number/SPEARHNM573BMDHY6TVR572H6W/graph.json","fetch_events":"https://pith.science/api/pith-number/SPEARHNM573BMDHY6TVR572H6W/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/SPEARHNM573BMDHY6TVR572H6W/action/timestamp_anchor","attest_storage":"https://pith.science/pith/SPEARHNM573BMDHY6TVR572H6W/action/storage_attestation","attest_author":"https://pith.science/pith/SPEARHNM573BMDHY6TVR572H6W/action/author_attestation","sign_citation":"https://pith.science/pith/SPEARHNM573BMDHY6TVR572H6W/action/citation_signature","submit_replication":"https://pith.science/pith/SPEARHNM573BMDHY6TVR572H6W/action/replication_record"}},"created_at":"2026-05-18T04:19:33.677427+00:00","updated_at":"2026-05-18T04:19:33.677427+00:00"}