{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:SUMZ7UD655EEQT4RY6ZG6DFQBH","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":"7a2da3e84bebfc4258f6d53035140b3c57057d943fcaed03ce54df8da9f0c09f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2017-09-02T09:22:52Z","title_canon_sha256":"57756226925cac7d068064a323079f144a0001b9c9b297d6dfe30777a0d2f08b"},"schema_version":"1.0","source":{"id":"1709.00547","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.00547","created_at":"2026-05-18T00:36:07Z"},{"alias_kind":"arxiv_version","alias_value":"1709.00547v1","created_at":"2026-05-18T00:36:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.00547","created_at":"2026-05-18T00:36:07Z"},{"alias_kind":"pith_short_12","alias_value":"SUMZ7UD655EE","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_16","alias_value":"SUMZ7UD655EEQT4R","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_8","alias_value":"SUMZ7UD6","created_at":"2026-05-18T12:31:43Z"}],"graph_snapshots":[{"event_id":"sha256:6375ed6519f299f9690a90a7f32901ce2ba5b714aba3ad03ed56c2ac8a040475","target":"graph","created_at":"2026-05-18T00:36:07Z","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 problem of indecomposability of translations of simple modules in the principal block of BGG category $\\mathcal{O}$ for $\\mathfrak{sl}_n$, as conjectured in \\cite{KiM}. We describe some general techniques and prove a few general results which may be applied to study various special cases of this problem. We apply our results to verify indecomposability for $n\\leq 6$. We also study the problem of indecomposability of shufflings and twistings of simple modules and obtain some partial results.","authors_text":"Kevin Coulembier, Volodymyr Mazorchuk, Xiaoting Zhang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2017-09-02T09:22:52Z","title":"Indecomposable manipulations with simple modules in category O"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.00547","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:d4b39186ac51a76efd339496eb27400b3ccde27136b42770590d279e381ef050","target":"record","created_at":"2026-05-18T00:36:07Z","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":"7a2da3e84bebfc4258f6d53035140b3c57057d943fcaed03ce54df8da9f0c09f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2017-09-02T09:22:52Z","title_canon_sha256":"57756226925cac7d068064a323079f144a0001b9c9b297d6dfe30777a0d2f08b"},"schema_version":"1.0","source":{"id":"1709.00547","kind":"arxiv","version":1}},"canonical_sha256":"95199fd07eef48484f91c7b26f0cb009e9b6511c1c9a960d39d8e40184789efc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"95199fd07eef48484f91c7b26f0cb009e9b6511c1c9a960d39d8e40184789efc","first_computed_at":"2026-05-18T00:36:07.719675Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:36:07.719675Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"D43wbTroLD5GapNXgjsgYyUACiLkwsPhL7RuEQXc+DWe36VQ8NL59lmhGIdTSOQXruS3Y3fj805ar7bmrYTUAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:36:07.720391Z","signed_message":"canonical_sha256_bytes"},"source_id":"1709.00547","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d4b39186ac51a76efd339496eb27400b3ccde27136b42770590d279e381ef050","sha256:6375ed6519f299f9690a90a7f32901ce2ba5b714aba3ad03ed56c2ac8a040475"],"state_sha256":"b2904907af983e99bc5ba5fef931446ca912dcb33e383934e505e2414f0078b2"}