{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:CLH7M72ZVXRTOABLRBS5XGAEZI","short_pith_number":"pith:CLH7M72Z","schema_version":"1.0","canonical_sha256":"12cff67f59ade337002b8865db9804ca3abc45e360f3d7d73e1dfa9f16dba931","source":{"kind":"arxiv","id":"1707.07720","version":1},"attestation_state":"computed","paper":{"title":"Modality of representations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.GR"],"primary_cat":"math.RT","authors_text":"Vladimir L. Popov","submitted_at":"2017-07-24T19:39:26Z","abstract_excerpt":"We first establish several general properties of modality of algebraic group actions. In particular, we introduce the notion of a modality-regular action and prove that every visible action is modality-regular. Then, using these results, we classify irreducible linear representations of connected simple algebraic groups of every fixed modality $\\leqslant 2$. Next, exploring a finer geometric structure of linear actions, we generalize to the case of any cyclically graded semisimple Lie algebra the notion of a packet (or a Jordan/decomposition class) and establish the properties of packets."},"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":"1707.07720","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2017-07-24T19:39:26Z","cross_cats_sorted":["math.AG","math.GR"],"title_canon_sha256":"f50b9fe987aa5f495a3ebc4b7349ebc96dc9ca7f0e20906e99263daa16e5c43a","abstract_canon_sha256":"b9e043e1719fc2af5b03fe08ac04e05a374cf3e31b16cca0b73822da5dc1a507"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:39:30.616534Z","signature_b64":"m/U9BGKzxsmYv3duoSFx2wxdthCmwp9gC86Nkcps3y7eH4ZPvuKqs81weoWrVp8tDkEp23ydX7VwQz6a7bwNDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"12cff67f59ade337002b8865db9804ca3abc45e360f3d7d73e1dfa9f16dba931","last_reissued_at":"2026-05-18T00:39:30.616001Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:39:30.616001Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Modality of representations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.GR"],"primary_cat":"math.RT","authors_text":"Vladimir L. Popov","submitted_at":"2017-07-24T19:39:26Z","abstract_excerpt":"We first establish several general properties of modality of algebraic group actions. In particular, we introduce the notion of a modality-regular action and prove that every visible action is modality-regular. Then, using these results, we classify irreducible linear representations of connected simple algebraic groups of every fixed modality $\\leqslant 2$. Next, exploring a finer geometric structure of linear actions, we generalize to the case of any cyclically graded semisimple Lie algebra the notion of a packet (or a Jordan/decomposition class) and establish the properties of packets."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.07720","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":"1707.07720","created_at":"2026-05-18T00:39:30.616091+00:00"},{"alias_kind":"arxiv_version","alias_value":"1707.07720v1","created_at":"2026-05-18T00:39:30.616091+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.07720","created_at":"2026-05-18T00:39:30.616091+00:00"},{"alias_kind":"pith_short_12","alias_value":"CLH7M72ZVXRT","created_at":"2026-05-18T12:31:10.602751+00:00"},{"alias_kind":"pith_short_16","alias_value":"CLH7M72ZVXRTOABL","created_at":"2026-05-18T12:31:10.602751+00:00"},{"alias_kind":"pith_short_8","alias_value":"CLH7M72Z","created_at":"2026-05-18T12:31:10.602751+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/CLH7M72ZVXRTOABLRBS5XGAEZI","json":"https://pith.science/pith/CLH7M72ZVXRTOABLRBS5XGAEZI.json","graph_json":"https://pith.science/api/pith-number/CLH7M72ZVXRTOABLRBS5XGAEZI/graph.json","events_json":"https://pith.science/api/pith-number/CLH7M72ZVXRTOABLRBS5XGAEZI/events.json","paper":"https://pith.science/paper/CLH7M72Z"},"agent_actions":{"view_html":"https://pith.science/pith/CLH7M72ZVXRTOABLRBS5XGAEZI","download_json":"https://pith.science/pith/CLH7M72ZVXRTOABLRBS5XGAEZI.json","view_paper":"https://pith.science/paper/CLH7M72Z","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1707.07720&json=true","fetch_graph":"https://pith.science/api/pith-number/CLH7M72ZVXRTOABLRBS5XGAEZI/graph.json","fetch_events":"https://pith.science/api/pith-number/CLH7M72ZVXRTOABLRBS5XGAEZI/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CLH7M72ZVXRTOABLRBS5XGAEZI/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CLH7M72ZVXRTOABLRBS5XGAEZI/action/storage_attestation","attest_author":"https://pith.science/pith/CLH7M72ZVXRTOABLRBS5XGAEZI/action/author_attestation","sign_citation":"https://pith.science/pith/CLH7M72ZVXRTOABLRBS5XGAEZI/action/citation_signature","submit_replication":"https://pith.science/pith/CLH7M72ZVXRTOABLRBS5XGAEZI/action/replication_record"}},"created_at":"2026-05-18T00:39:30.616091+00:00","updated_at":"2026-05-18T00:39:30.616091+00:00"}