{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:AGENIDDLWEB2Y2OJWJ6Q4JPCNN","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":"0d0280f07d3fce7d3747bd7c559fea0cd0fdcebb001353adc683a35e3395d009","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2013-10-28T11:24:08Z","title_canon_sha256":"c976cd336bda7d9dd0defecb072ca5fbfb369bb5a97bb9851f293feb147e6104"},"schema_version":"1.0","source":{"id":"1310.7379","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.7379","created_at":"2026-05-18T01:53:09Z"},{"alias_kind":"arxiv_version","alias_value":"1310.7379v2","created_at":"2026-05-18T01:53:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.7379","created_at":"2026-05-18T01:53:09Z"},{"alias_kind":"pith_short_12","alias_value":"AGENIDDLWEB2","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_16","alias_value":"AGENIDDLWEB2Y2OJ","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_8","alias_value":"AGENIDDL","created_at":"2026-05-18T12:27:38Z"}],"graph_snapshots":[{"event_id":"sha256:9eda5f00aa026f24813705227690001243828d9e74468fa34b631aa6b47e7b97","target":"graph","created_at":"2026-05-18T01:53:09Z","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":"We study the decomposition matrices for the unipotent $\\ell$-blocks of finite special unitary groups SU$_n(q)$ for unitary primes $\\ell$ larger than $n$. Up to very few unknown entries, we give a complete solution for $n=2,\\ldots,10$. We also prove a general result for two-column partitions when $\\ell$ divides $q+1$. This is achieved using projective modules coming from the $\\ell$-adic cohomology of Deligne--Lusztig varieties.","authors_text":"Gunter Malle, Olivier Dudas","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2013-10-28T11:24:08Z","title":"Decomposition matrices for low rank unitary groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.7379","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":"sha256:7c162ce9abf629ab038185eb7bb62c01e3cdb1f7d30aa01b95fbf10e508e1ed0","target":"record","created_at":"2026-05-18T01:53:09Z","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":"0d0280f07d3fce7d3747bd7c559fea0cd0fdcebb001353adc683a35e3395d009","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2013-10-28T11:24:08Z","title_canon_sha256":"c976cd336bda7d9dd0defecb072ca5fbfb369bb5a97bb9851f293feb147e6104"},"schema_version":"1.0","source":{"id":"1310.7379","kind":"arxiv","version":2}},"canonical_sha256":"0188d40c6bb103ac69c9b27d0e25e26b68fa0308bb0ea62248b305e0d3313641","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0188d40c6bb103ac69c9b27d0e25e26b68fa0308bb0ea62248b305e0d3313641","first_computed_at":"2026-05-18T01:53:09.649753Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:53:09.649753Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MYdWVJQMCR/+vQuM4ivZ7qCeklgBfLECOe8zAzrVpxqE9dje+EnNNWtz7CHy10aGxGBtAmXeHCncp8x3c9nXCA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:53:09.650203Z","signed_message":"canonical_sha256_bytes"},"source_id":"1310.7379","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7c162ce9abf629ab038185eb7bb62c01e3cdb1f7d30aa01b95fbf10e508e1ed0","sha256:9eda5f00aa026f24813705227690001243828d9e74468fa34b631aa6b47e7b97"],"state_sha256":"a52a03efc6572b96730923f4770ec653d63c9db97650709aaf21a976ffb3ed90"}