{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:65ZQOXOGTO6MWNQWFEEUWUU5BV","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":"e97d141907674185d93b06600ec8ef1b81d88da56ceced7849cb42c63ff27b1f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2011-12-14T06:09:53Z","title_canon_sha256":"bf8454f1aa58bc845d2c47e087859271c4455afacea288f3949f10e848ff4b45"},"schema_version":"1.0","source":{"id":"1112.3127","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1112.3127","created_at":"2026-05-18T04:06:20Z"},{"alias_kind":"arxiv_version","alias_value":"1112.3127v1","created_at":"2026-05-18T04:06:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.3127","created_at":"2026-05-18T04:06:20Z"},{"alias_kind":"pith_short_12","alias_value":"65ZQOXOGTO6M","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_16","alias_value":"65ZQOXOGTO6MWNQW","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_8","alias_value":"65ZQOXOG","created_at":"2026-05-18T12:26:22Z"}],"graph_snapshots":[{"event_id":"sha256:4b508a12621f9e4c0a5eebfd04e1d8c722621ef82eb4fe14bf2ac5604907466a","target":"graph","created_at":"2026-05-18T04:06:20Z","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 prove that the representation ring of the symmetric group on $n$ letters is generated by the exterior powers of its natural $(n-1)$-dimensional representation. The proof we give illustrates a strikingly simple formula due to Y. Dvir. We provide an application and investigate a possible generalization of this result to some other reflection groups.","authors_text":"Ivan Marin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2011-12-14T06:09:53Z","title":"Hooks generate the representation ring of the symmetric group"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.3127","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":"sha256:8286f5e2a977e07bab8ee758c8957d8c78f92b6767cc84e221450df6960ab3b8","target":"record","created_at":"2026-05-18T04:06:20Z","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":"e97d141907674185d93b06600ec8ef1b81d88da56ceced7849cb42c63ff27b1f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2011-12-14T06:09:53Z","title_canon_sha256":"bf8454f1aa58bc845d2c47e087859271c4455afacea288f3949f10e848ff4b45"},"schema_version":"1.0","source":{"id":"1112.3127","kind":"arxiv","version":1}},"canonical_sha256":"f773075dc69bbccb361629094b529d0d790685af7cdf54ebc096a9d8f846f524","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f773075dc69bbccb361629094b529d0d790685af7cdf54ebc096a9d8f846f524","first_computed_at":"2026-05-18T04:06:20.106191Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:06:20.106191Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fbtTbyYRpAT6lkCEECHVTEp3/mmvKYBv+2cov2ZA6lBr9ASQ7+jyHzmV6lAXM78LzuxEl3WmWJUanDBHTKnXDw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:06:20.106851Z","signed_message":"canonical_sha256_bytes"},"source_id":"1112.3127","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8286f5e2a977e07bab8ee758c8957d8c78f92b6767cc84e221450df6960ab3b8","sha256:4b508a12621f9e4c0a5eebfd04e1d8c722621ef82eb4fe14bf2ac5604907466a"],"state_sha256":"177f3fa3ea62231cd3d1e073941b157971560e2ae4ae429d095dd654968a92d4"}