{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:DLTGLCPAMXAGKBCLVVIQVCEIH5","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":"411e872bb9d196a47f8fa52455ff9704a59860d7143d57ed006b9e8c3094dcb4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2011-05-23T05:19:17Z","title_canon_sha256":"9a23bfbec84a9ebf2a61568d2934d62717648d95aafff1a699a81574691b67ec"},"schema_version":"1.0","source":{"id":"1105.4405","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1105.4405","created_at":"2026-05-18T04:21:22Z"},{"alias_kind":"arxiv_version","alias_value":"1105.4405v2","created_at":"2026-05-18T04:21:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.4405","created_at":"2026-05-18T04:21:22Z"},{"alias_kind":"pith_short_12","alias_value":"DLTGLCPAMXAG","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_16","alias_value":"DLTGLCPAMXAGKBCL","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_8","alias_value":"DLTGLCPA","created_at":"2026-05-18T12:26:26Z"}],"graph_snapshots":[{"event_id":"sha256:201c072fb21d4c135ba57ce54c36dabde542c4ef8c11ef61deb8eb4c454e19cf","target":"graph","created_at":"2026-05-18T04:21:22Z","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 obtain a closed formula for the $v$-decomposition numbers $d_{\\lambda\\mu}(v)$ arising from the canonical basis of the Fock space representation of $U_v(\\hat{\\mathfrak{sl}}_e)$, where the partition $\\lambda$ is obtained from $\\mu$ by moving some nodes in its Young diagram, all of which having the same $e$-residue. We also show that when these $v$-decomposition numbers are evaluated at $v=1$, we obtain the corresponding decomposition numbers for the Schur algebras and symmetric groups.","authors_text":"Kai Meng Tan, Wei Hao Teo","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2011-05-23T05:19:17Z","title":"Sign sequences and decomposition numbers"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.4405","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:accd71e8fa97fdcda8d24b6eb91f281ec58606f5041621d7ce5435398df2d879","target":"record","created_at":"2026-05-18T04:21:22Z","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":"411e872bb9d196a47f8fa52455ff9704a59860d7143d57ed006b9e8c3094dcb4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2011-05-23T05:19:17Z","title_canon_sha256":"9a23bfbec84a9ebf2a61568d2934d62717648d95aafff1a699a81574691b67ec"},"schema_version":"1.0","source":{"id":"1105.4405","kind":"arxiv","version":2}},"canonical_sha256":"1ae66589e065c065044bad510a88883f70e3c728aa9ba5a0fd01d9453204b1cb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1ae66589e065c065044bad510a88883f70e3c728aa9ba5a0fd01d9453204b1cb","first_computed_at":"2026-05-18T04:21:22.053166Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:21:22.053166Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mns7Z5FWOtxbztv6Uu9tl6ShJHKK1EBj9nlYHa1AOojcSnJn0dPeaAyOwbiHq7MxQrg5S5eu5KbojRsjBcQnAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:21:22.053617Z","signed_message":"canonical_sha256_bytes"},"source_id":"1105.4405","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:accd71e8fa97fdcda8d24b6eb91f281ec58606f5041621d7ce5435398df2d879","sha256:201c072fb21d4c135ba57ce54c36dabde542c4ef8c11ef61deb8eb4c454e19cf"],"state_sha256":"68d44092d874cebb85837ddb6996dac867e89bc6e119ab3c75bff066399c2359"}