{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:Y7RNPLFXIPGYGNFZVTUJBC74T3","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":"494ca4fdf1736d1558bc15beb03dc6a2eb8a69b91e5dde3bd60ab30615e4ac82","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2023-11-27T17:36:53Z","title_canon_sha256":"cfc6888b107b25ec00b45aee2c5410ef8bd4e680198552f7a0c551d4a559216a"},"schema_version":"1.0","source":{"id":"2311.16022","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2311.16022","created_at":"2026-07-05T08:15:42Z"},{"alias_kind":"arxiv_version","alias_value":"2311.16022v2","created_at":"2026-07-05T08:15:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2311.16022","created_at":"2026-07-05T08:15:42Z"},{"alias_kind":"pith_short_12","alias_value":"Y7RNPLFXIPGY","created_at":"2026-07-05T08:15:42Z"},{"alias_kind":"pith_short_16","alias_value":"Y7RNPLFXIPGYGNFZ","created_at":"2026-07-05T08:15:42Z"},{"alias_kind":"pith_short_8","alias_value":"Y7RNPLFX","created_at":"2026-07-05T08:15:42Z"}],"graph_snapshots":[{"event_id":"sha256:9a9e13d913d8767400331832d163d6693f6916950c9b0c5d67c42b578f15c02d","target":"graph","created_at":"2026-07-05T08:15:42Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2311.16022/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"For any root system of rank $r$, we study the \"dominant weight polytope\" $P^\\lambda$ associated with a strongly dominant weight $\\lambda$. We prove that $P^\\lambda$ is combinatorially equivalent to the $r$-dimensional cube. As an application, we give a new proof of the known formulas for Betti numbers of Peterson varieties in classical Lie types.","authors_text":"Gaston Burrull, Hongsheng Hu, Tao Gui","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2023-11-27T17:36:53Z","title":"Strongly dominant weight polytopes are cubes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2311.16022","kind":"arxiv","version":2},"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:c0f2f389b2786ebf8c3beb6b9a000fae2b2b5a0ec390a452844416d3a8665665","target":"record","created_at":"2026-07-05T08:15:42Z","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":"494ca4fdf1736d1558bc15beb03dc6a2eb8a69b91e5dde3bd60ab30615e4ac82","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2023-11-27T17:36:53Z","title_canon_sha256":"cfc6888b107b25ec00b45aee2c5410ef8bd4e680198552f7a0c551d4a559216a"},"schema_version":"1.0","source":{"id":"2311.16022","kind":"arxiv","version":2}},"canonical_sha256":"c7e2d7acb743cd8334b9ace8908bfc9efcc226ce16d2f99873c47bd6820a6be9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c7e2d7acb743cd8334b9ace8908bfc9efcc226ce16d2f99873c47bd6820a6be9","first_computed_at":"2026-07-05T08:15:42.350591Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:15:42.350591Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"e5HYZPnUwR1ZV7zawC/AArK0dvkCDLjBLBHWIOh/f8cHvmmjzb5cyzvfpQBO+Y/RVnuD2PK9l2qns34wYoOZCg==","signature_status":"signed_v1","signed_at":"2026-07-05T08:15:42.351069Z","signed_message":"canonical_sha256_bytes"},"source_id":"2311.16022","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c0f2f389b2786ebf8c3beb6b9a000fae2b2b5a0ec390a452844416d3a8665665","sha256:9a9e13d913d8767400331832d163d6693f6916950c9b0c5d67c42b578f15c02d"],"state_sha256":"6f42043c1b52f3640cc8d4780e9e6f5da87bf87959c21043571fadaee60f6893"}