{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:VLV2M3MLW5KPSDDQ65QX47JYVZ","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":"ebcee0aa8d0cfb956059ada4a8b349b77756d95054ec0760121712ee16b9c74b","cross_cats_sorted":["math.CO","math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2016-11-01T03:03:39Z","title_canon_sha256":"b6d7cbf22dc6db55ff1cedff4a9a0469f8da7430e0025a0eca74fb74f851b657"},"schema_version":"1.0","source":{"id":"1611.00114","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.00114","created_at":"2026-05-18T00:29:31Z"},{"alias_kind":"arxiv_version","alias_value":"1611.00114v3","created_at":"2026-05-18T00:29:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.00114","created_at":"2026-05-18T00:29:31Z"},{"alias_kind":"pith_short_12","alias_value":"VLV2M3MLW5KP","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_16","alias_value":"VLV2M3MLW5KPSDDQ","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_8","alias_value":"VLV2M3ML","created_at":"2026-05-18T12:30:48Z"}],"graph_snapshots":[{"event_id":"sha256:b55baa0530b371713ec77d0b9249ffba1fcbf4eea8ca73eb59ab539a9072c89c","target":"graph","created_at":"2026-05-18T00:29:31Z","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":"Let $V$ be a highest weight module over a Kac-Moody algebra $\\mathfrak{g}$, and let conv $V$ denote the convex hull of its weights. We determine the combinatorial isomorphism type of conv $V$, i.e. we completely classify the faces and their inclusions. In the special case where $\\mathfrak{g}$ is semisimple, this brings closure to a question studied by Cellini-Marietti [IMRN 2015] for the adjoint representation, and by Khare [J. Algebra 2016; Trans. Amer. Math. Soc. 2017] for most modules. The determination of faces of finite-dimensional modules up to the Weyl group action and some of their inc","authors_text":"Apoorva Khare, Gurbir Dhillon","cross_cats":["math.CO","math.MG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2016-11-01T03:03:39Z","title":"Faces of highest weight modules and the universal Weyl polyhedron"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.00114","kind":"arxiv","version":3},"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":"sha256:33940ec6de58200165722ce9f60d2f7c47dbe9b6966e5e79a1e06be19883d351","target":"record","created_at":"2026-05-18T00:29:31Z","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":"ebcee0aa8d0cfb956059ada4a8b349b77756d95054ec0760121712ee16b9c74b","cross_cats_sorted":["math.CO","math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2016-11-01T03:03:39Z","title_canon_sha256":"b6d7cbf22dc6db55ff1cedff4a9a0469f8da7430e0025a0eca74fb74f851b657"},"schema_version":"1.0","source":{"id":"1611.00114","kind":"arxiv","version":3}},"canonical_sha256":"aaeba66d8bb754f90c70f7617e7d38ae5cf79e31cec75acd06626b6a8172b4a0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"aaeba66d8bb754f90c70f7617e7d38ae5cf79e31cec75acd06626b6a8172b4a0","first_computed_at":"2026-05-18T00:29:31.264258Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:29:31.264258Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gffRDlVSnZkKgcqaI7Wm7+NyYa3qdLhSD4i8yrVl/Dx4lVUCfZsfUNJWmLYKGNSWvN7v/9ZMVIBhxO0gPcjzAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:29:31.264931Z","signed_message":"canonical_sha256_bytes"},"source_id":"1611.00114","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:33940ec6de58200165722ce9f60d2f7c47dbe9b6966e5e79a1e06be19883d351","sha256:b55baa0530b371713ec77d0b9249ffba1fcbf4eea8ca73eb59ab539a9072c89c"],"state_sha256":"cec1472e08d4bedf97783620167f58e6c7aece2636e4dda93cb3eb36255073c1"}