{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:6VXTCCQL6R6CMDV325DJDJUXWW","short_pith_number":"pith:6VXTCCQL","schema_version":"1.0","canonical_sha256":"f56f310a0bf47c260ebbd74691a697b5ac5d98a728f9299eeefb8341401fda23","source":{"kind":"arxiv","id":"1212.0021","version":1},"attestation_state":"computed","paper":{"title":"Forced gradings and the Humphreys-Verma conjecture","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Brian Parshall, Leonard Scott","submitted_at":"2012-11-30T21:51:03Z","abstract_excerpt":"Let $G$ be a semisimple, simply connected algebraic group defined and split over a prime field ${\\mathbb F}_p$ of positive characteristic. For a positive integer $r$, let $G_r$ be the $r$th Frobenius kernel of $G$. Let $Q$ be a projective indecomposable (rational) $G_r$-module. The well-known Humprheys-Verma conjecture (cf. \\cite{Ballard}) asserts that the $G_r$-action on $Q$ lifts to an rational action of $G$ on $Q$. For $p\\geq 2h-2$ (where $h$ is the Coxeter number of $G$), this conjecture was proved by Jantzen in 1980, improving on early work of Ballard. However, it remains open for general"},"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":"1212.0021","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2012-11-30T21:51:03Z","cross_cats_sorted":[],"title_canon_sha256":"27220e141e6174fd23c54b01163c691417b312c20cdd01e812fb839bf384b313","abstract_canon_sha256":"e1f806df96f107e498c56e68e5a03defdf7ed15bdd6703dc4a8c407eb0e00472"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:39:27.631422Z","signature_b64":"WzcDDem8M9FoR/hFIYo7zF1fbblrQ3/a4fJ3LLgEfuZfTDZs5sqbtujYpcchEqwQpkD+zmpfsGXrh8AFQf7bAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f56f310a0bf47c260ebbd74691a697b5ac5d98a728f9299eeefb8341401fda23","last_reissued_at":"2026-05-18T03:39:27.630659Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:39:27.630659Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Forced gradings and the Humphreys-Verma conjecture","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Brian Parshall, Leonard Scott","submitted_at":"2012-11-30T21:51:03Z","abstract_excerpt":"Let $G$ be a semisimple, simply connected algebraic group defined and split over a prime field ${\\mathbb F}_p$ of positive characteristic. For a positive integer $r$, let $G_r$ be the $r$th Frobenius kernel of $G$. Let $Q$ be a projective indecomposable (rational) $G_r$-module. The well-known Humprheys-Verma conjecture (cf. \\cite{Ballard}) asserts that the $G_r$-action on $Q$ lifts to an rational action of $G$ on $Q$. For $p\\geq 2h-2$ (where $h$ is the Coxeter number of $G$), this conjecture was proved by Jantzen in 1980, improving on early work of Ballard. However, it remains open for general"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.0021","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":"1212.0021","created_at":"2026-05-18T03:39:27.630771+00:00"},{"alias_kind":"arxiv_version","alias_value":"1212.0021v1","created_at":"2026-05-18T03:39:27.630771+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.0021","created_at":"2026-05-18T03:39:27.630771+00:00"},{"alias_kind":"pith_short_12","alias_value":"6VXTCCQL6R6C","created_at":"2026-05-18T12:26:56.085431+00:00"},{"alias_kind":"pith_short_16","alias_value":"6VXTCCQL6R6CMDV3","created_at":"2026-05-18T12:26:56.085431+00:00"},{"alias_kind":"pith_short_8","alias_value":"6VXTCCQL","created_at":"2026-05-18T12:26:56.085431+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/6VXTCCQL6R6CMDV325DJDJUXWW","json":"https://pith.science/pith/6VXTCCQL6R6CMDV325DJDJUXWW.json","graph_json":"https://pith.science/api/pith-number/6VXTCCQL6R6CMDV325DJDJUXWW/graph.json","events_json":"https://pith.science/api/pith-number/6VXTCCQL6R6CMDV325DJDJUXWW/events.json","paper":"https://pith.science/paper/6VXTCCQL"},"agent_actions":{"view_html":"https://pith.science/pith/6VXTCCQL6R6CMDV325DJDJUXWW","download_json":"https://pith.science/pith/6VXTCCQL6R6CMDV325DJDJUXWW.json","view_paper":"https://pith.science/paper/6VXTCCQL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1212.0021&json=true","fetch_graph":"https://pith.science/api/pith-number/6VXTCCQL6R6CMDV325DJDJUXWW/graph.json","fetch_events":"https://pith.science/api/pith-number/6VXTCCQL6R6CMDV325DJDJUXWW/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6VXTCCQL6R6CMDV325DJDJUXWW/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6VXTCCQL6R6CMDV325DJDJUXWW/action/storage_attestation","attest_author":"https://pith.science/pith/6VXTCCQL6R6CMDV325DJDJUXWW/action/author_attestation","sign_citation":"https://pith.science/pith/6VXTCCQL6R6CMDV325DJDJUXWW/action/citation_signature","submit_replication":"https://pith.science/pith/6VXTCCQL6R6CMDV325DJDJUXWW/action/replication_record"}},"created_at":"2026-05-18T03:39:27.630771+00:00","updated_at":"2026-05-18T03:39:27.630771+00:00"}