{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:XQ7XJWQYY6EKEN4IDEYI3UO3R2","short_pith_number":"pith:XQ7XJWQY","schema_version":"1.0","canonical_sha256":"bc3f74da18c788a2378819308dd1db8eaf517ebe0d356acf608053c3ccde3eed","source":{"kind":"arxiv","id":"1704.02405","version":1},"attestation_state":"computed","paper":{"title":"Polynomially and Infinitesimally Injective Modules","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Haralampos Geranios, Stephen Donkin","submitted_at":"2017-04-08T00:03:36Z","abstract_excerpt":"The injective polynomial modules for a general linear group $G$ of degree $n$ are labelled by the partitions with at most $n$ parts. Working over an algebraically closed field of characteristic $p$, we consider the question of which partitions correspond to polynomially injective modules that are also injective as modules for the restricted enveloping algebra of the Lie algebra of $G$. The question is related to the \"index of divisibility\" of a polynomial module in general, and an explicit answer is given for $n=2$."},"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":"1704.02405","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2017-04-08T00:03:36Z","cross_cats_sorted":[],"title_canon_sha256":"539e59e352517993221d136e73004c7c3e1cd838c53be7e217823637ea25d4d2","abstract_canon_sha256":"95fe666c412d8af40d6ee50e1f93d9f556c4c069f86aa48a45ffa31585327bc7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:46:45.686544Z","signature_b64":"02TnvOm4OLP8ctRoivFUKUeKD4mO7KhFK1O1ROj2dqg8uFudsXrzuljDhn/v+NaGG0DMoPFQYeO7oDXRvjyACQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bc3f74da18c788a2378819308dd1db8eaf517ebe0d356acf608053c3ccde3eed","last_reissued_at":"2026-05-18T00:46:45.685871Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:46:45.685871Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Polynomially and Infinitesimally Injective Modules","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Haralampos Geranios, Stephen Donkin","submitted_at":"2017-04-08T00:03:36Z","abstract_excerpt":"The injective polynomial modules for a general linear group $G$ of degree $n$ are labelled by the partitions with at most $n$ parts. Working over an algebraically closed field of characteristic $p$, we consider the question of which partitions correspond to polynomially injective modules that are also injective as modules for the restricted enveloping algebra of the Lie algebra of $G$. The question is related to the \"index of divisibility\" of a polynomial module in general, and an explicit answer is given for $n=2$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.02405","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":"1704.02405","created_at":"2026-05-18T00:46:45.685968+00:00"},{"alias_kind":"arxiv_version","alias_value":"1704.02405v1","created_at":"2026-05-18T00:46:45.685968+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.02405","created_at":"2026-05-18T00:46:45.685968+00:00"},{"alias_kind":"pith_short_12","alias_value":"XQ7XJWQYY6EK","created_at":"2026-05-18T12:31:56.362134+00:00"},{"alias_kind":"pith_short_16","alias_value":"XQ7XJWQYY6EKEN4I","created_at":"2026-05-18T12:31:56.362134+00:00"},{"alias_kind":"pith_short_8","alias_value":"XQ7XJWQY","created_at":"2026-05-18T12:31:56.362134+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/XQ7XJWQYY6EKEN4IDEYI3UO3R2","json":"https://pith.science/pith/XQ7XJWQYY6EKEN4IDEYI3UO3R2.json","graph_json":"https://pith.science/api/pith-number/XQ7XJWQYY6EKEN4IDEYI3UO3R2/graph.json","events_json":"https://pith.science/api/pith-number/XQ7XJWQYY6EKEN4IDEYI3UO3R2/events.json","paper":"https://pith.science/paper/XQ7XJWQY"},"agent_actions":{"view_html":"https://pith.science/pith/XQ7XJWQYY6EKEN4IDEYI3UO3R2","download_json":"https://pith.science/pith/XQ7XJWQYY6EKEN4IDEYI3UO3R2.json","view_paper":"https://pith.science/paper/XQ7XJWQY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1704.02405&json=true","fetch_graph":"https://pith.science/api/pith-number/XQ7XJWQYY6EKEN4IDEYI3UO3R2/graph.json","fetch_events":"https://pith.science/api/pith-number/XQ7XJWQYY6EKEN4IDEYI3UO3R2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XQ7XJWQYY6EKEN4IDEYI3UO3R2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XQ7XJWQYY6EKEN4IDEYI3UO3R2/action/storage_attestation","attest_author":"https://pith.science/pith/XQ7XJWQYY6EKEN4IDEYI3UO3R2/action/author_attestation","sign_citation":"https://pith.science/pith/XQ7XJWQYY6EKEN4IDEYI3UO3R2/action/citation_signature","submit_replication":"https://pith.science/pith/XQ7XJWQYY6EKEN4IDEYI3UO3R2/action/replication_record"}},"created_at":"2026-05-18T00:46:45.685968+00:00","updated_at":"2026-05-18T00:46:45.685968+00:00"}