{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:Z4HWASKPQGLRHTPV4MHT5V66LM","short_pith_number":"pith:Z4HWASKP","schema_version":"1.0","canonical_sha256":"cf0f60494f819713cdf5e30f3ed7de5b39f0df47a927694b4fc194119c6a4829","source":{"kind":"arxiv","id":"1907.06755","version":1},"attestation_state":"computed","paper":{"title":"Finite Singular Orbit Modules for Algebraic Groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Aluna Rizzoli","submitted_at":"2019-07-15T21:06:43Z","abstract_excerpt":"Building on the classification of modules for algebraic groups with finitely many orbits on subspaces, we determine all faithful irreducible modules for simple and maximal-semisimple connected algebraic groups that are orthogonal and have finitely many orbits on singular $1$-spaces. This question is naturally connected with the problem of finding for which pairs of subgroups $H,K$ of an algebraic group $G$ there are finitely many $(H,K)$-double cosets. This paper provides a solution to the question when $K$ is a maximal parabolic subgroup $P_1$ of a classical group $SO_n$. We find an interesti"},"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":"1907.06755","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2019-07-15T21:06:43Z","cross_cats_sorted":[],"title_canon_sha256":"82a4cc224a003a6d6e0c5b5126e6c0608095469421a985b17eb4fcbe7f600452","abstract_canon_sha256":"7bee7bc8351b51c19daad5ce085ea4fd81eef4c498dead8af489fc0da0176d5e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:40:29.277441Z","signature_b64":"9ovDJp36WItjlJxHw2wAcP8V3b/BkabHIGr2UkVSSLAOyVDsyGqF/6emkf6VrPQ4F9W9aNuP/rPI7h9AY7iuBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cf0f60494f819713cdf5e30f3ed7de5b39f0df47a927694b4fc194119c6a4829","last_reissued_at":"2026-05-17T23:40:29.276885Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:40:29.276885Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Finite Singular Orbit Modules for Algebraic Groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Aluna Rizzoli","submitted_at":"2019-07-15T21:06:43Z","abstract_excerpt":"Building on the classification of modules for algebraic groups with finitely many orbits on subspaces, we determine all faithful irreducible modules for simple and maximal-semisimple connected algebraic groups that are orthogonal and have finitely many orbits on singular $1$-spaces. This question is naturally connected with the problem of finding for which pairs of subgroups $H,K$ of an algebraic group $G$ there are finitely many $(H,K)$-double cosets. This paper provides a solution to the question when $K$ is a maximal parabolic subgroup $P_1$ of a classical group $SO_n$. We find an interesti"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.06755","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":"1907.06755","created_at":"2026-05-17T23:40:29.276956+00:00"},{"alias_kind":"arxiv_version","alias_value":"1907.06755v1","created_at":"2026-05-17T23:40:29.276956+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.06755","created_at":"2026-05-17T23:40:29.276956+00:00"},{"alias_kind":"pith_short_12","alias_value":"Z4HWASKPQGLR","created_at":"2026-05-18T12:33:33.725879+00:00"},{"alias_kind":"pith_short_16","alias_value":"Z4HWASKPQGLRHTPV","created_at":"2026-05-18T12:33:33.725879+00:00"},{"alias_kind":"pith_short_8","alias_value":"Z4HWASKP","created_at":"2026-05-18T12:33:33.725879+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/Z4HWASKPQGLRHTPV4MHT5V66LM","json":"https://pith.science/pith/Z4HWASKPQGLRHTPV4MHT5V66LM.json","graph_json":"https://pith.science/api/pith-number/Z4HWASKPQGLRHTPV4MHT5V66LM/graph.json","events_json":"https://pith.science/api/pith-number/Z4HWASKPQGLRHTPV4MHT5V66LM/events.json","paper":"https://pith.science/paper/Z4HWASKP"},"agent_actions":{"view_html":"https://pith.science/pith/Z4HWASKPQGLRHTPV4MHT5V66LM","download_json":"https://pith.science/pith/Z4HWASKPQGLRHTPV4MHT5V66LM.json","view_paper":"https://pith.science/paper/Z4HWASKP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1907.06755&json=true","fetch_graph":"https://pith.science/api/pith-number/Z4HWASKPQGLRHTPV4MHT5V66LM/graph.json","fetch_events":"https://pith.science/api/pith-number/Z4HWASKPQGLRHTPV4MHT5V66LM/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/Z4HWASKPQGLRHTPV4MHT5V66LM/action/timestamp_anchor","attest_storage":"https://pith.science/pith/Z4HWASKPQGLRHTPV4MHT5V66LM/action/storage_attestation","attest_author":"https://pith.science/pith/Z4HWASKPQGLRHTPV4MHT5V66LM/action/author_attestation","sign_citation":"https://pith.science/pith/Z4HWASKPQGLRHTPV4MHT5V66LM/action/citation_signature","submit_replication":"https://pith.science/pith/Z4HWASKPQGLRHTPV4MHT5V66LM/action/replication_record"}},"created_at":"2026-05-17T23:40:29.276956+00:00","updated_at":"2026-05-17T23:40:29.276956+00:00"}