{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:R4RCK2NMOZFQ5O5G4AYWLACTMO","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"bd825bcb34d729b2b463dcaea6e56fd0d60d9b7159b983d97717d70bdbf8d4a9","cross_cats_sorted":["math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2014-07-07T22:56:56Z","title_canon_sha256":"c4204c69dfcea90c876bc1ab55a8ec5ea77cd8c9f4b671d6266fb7b78419e980"},"schema_version":"1.0","source":{"id":"1407.1902","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.1902","created_at":"2026-05-18T00:23:02Z"},{"alias_kind":"arxiv_version","alias_value":"1407.1902v1","created_at":"2026-05-18T00:23:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.1902","created_at":"2026-05-18T00:23:02Z"},{"alias_kind":"pith_short_12","alias_value":"R4RCK2NMOZFQ","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_16","alias_value":"R4RCK2NMOZFQ5O5G","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_8","alias_value":"R4RCK2NM","created_at":"2026-05-18T12:28:46Z"}],"graph_snapshots":[{"event_id":"sha256:8b49c5d5e729cbcaeb9ef81f657de50eb2d238d06a718b8422d5e5aa2f2493d1","target":"graph","created_at":"2026-05-18T00:23:02Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"In this paper we show that the projective cover of the trivial irreducible module of a finite-dimensional solvable restricted Lie algebra is induced from the one-dimensional trivial module of a maximal torus. As a consequence, we obtain that the number of the isomorphism classes of irreducible modules with a fixed p-character for a finite-dimensional solvable restricted Lie algebra L is bounded above by p^MT(L), where MT(L) denotes the largest dimension of a torus in L. Finally, we prove that in characteristic p>3 the projective cover of the trivial irreducible L-module is only induced from th","authors_text":"J\\\"org Feldvoss, Salvatore Siciliano, Thomas Weigel","cross_cats":["math.RA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2014-07-07T22:56:56Z","title":"Restricted Lie algebras with maximal 0-PIM"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.1902","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:ca2cc84362458ec3fb28af1bbde0a68fad3f08226e689ad6fa2132303aed1036","target":"record","created_at":"2026-05-18T00:23:02Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"bd825bcb34d729b2b463dcaea6e56fd0d60d9b7159b983d97717d70bdbf8d4a9","cross_cats_sorted":["math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2014-07-07T22:56:56Z","title_canon_sha256":"c4204c69dfcea90c876bc1ab55a8ec5ea77cd8c9f4b671d6266fb7b78419e980"},"schema_version":"1.0","source":{"id":"1407.1902","kind":"arxiv","version":1}},"canonical_sha256":"8f222569ac764b0ebba6e03165805363834a15a5ab6a814b475c5ead8b7bb907","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8f222569ac764b0ebba6e03165805363834a15a5ab6a814b475c5ead8b7bb907","first_computed_at":"2026-05-18T00:23:02.227272Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:23:02.227272Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bL8R08DaeM/GhHXTuQXgC2mrF3zRdMJB+I1L0BvAGbvtRPd0gXOgoAs4b4++d/ZR8RN/4Jx1mNYPqSFbQLEGCg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:23:02.227752Z","signed_message":"canonical_sha256_bytes"},"source_id":"1407.1902","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ca2cc84362458ec3fb28af1bbde0a68fad3f08226e689ad6fa2132303aed1036","sha256:8b49c5d5e729cbcaeb9ef81f657de50eb2d238d06a718b8422d5e5aa2f2493d1"],"state_sha256":"a52ffdc6a6551c36182396bcf6c4b6d2287f2f00360c40220ce2444813ac5b8a"}