{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:QPFHXXFZOQNFCWIIV3QG44ZNJU","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":"65bd1707bd433fae5e7f1b58df3e02c184a58172c939f5a8e8584d6f4ba71220","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2025-05-20T20:15:53Z","title_canon_sha256":"81f9476b7d238042bb35fd0551db2d92675384a43c42fd92257b5e2bca0b9f71"},"schema_version":"1.0","source":{"id":"2505.14885","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2505.14885","created_at":"2026-06-24T01:14:20Z"},{"alias_kind":"arxiv_version","alias_value":"2505.14885v2","created_at":"2026-06-24T01:14:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.14885","created_at":"2026-06-24T01:14:20Z"},{"alias_kind":"pith_short_12","alias_value":"QPFHXXFZOQNF","created_at":"2026-06-24T01:14:20Z"},{"alias_kind":"pith_short_16","alias_value":"QPFHXXFZOQNFCWII","created_at":"2026-06-24T01:14:20Z"},{"alias_kind":"pith_short_8","alias_value":"QPFHXXFZ","created_at":"2026-06-24T01:14:20Z"}],"graph_snapshots":[{"event_id":"sha256:468d2e7225f80af5c8470984b7fc9fcaf9db1f59cf7dddca88a744165754aa65","target":"graph","created_at":"2026-06-24T01:14:20Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2505.14885/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"For finite groups $G$, we show that bosonic-fermionic coinvariant rings have a natural $U(\\mathfrak{gl}(k|j)) \\otimes \\mathbb{C}[G]$-module structure. In particular, we show that their character series are sums of super Schur functions $s_\\lambda(\\mathbf{q}/\\mathbf{u})$ times irreducible characters of $G$ with universal coefficients, which do not depend on $k,j$. In the case where $G$ is the symmetric group with diagonal action, this proves the \"Diagonal Supersymmetry\" conjecture of F. Bergeron (2020).","authors_text":"John Lentfer","cross_cats":["math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2025-05-20T20:15:53Z","title":"Diagonal supersymmetry for coinvariant rings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.14885","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":"sha256:7bfe5546fc70e289e041574bae583a418af66818ac8e639c552102d72f62933f","target":"record","created_at":"2026-06-24T01:14:20Z","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":"65bd1707bd433fae5e7f1b58df3e02c184a58172c939f5a8e8584d6f4ba71220","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2025-05-20T20:15:53Z","title_canon_sha256":"81f9476b7d238042bb35fd0551db2d92675384a43c42fd92257b5e2bca0b9f71"},"schema_version":"1.0","source":{"id":"2505.14885","kind":"arxiv","version":2}},"canonical_sha256":"83ca7bdcb9741a515908aee06e732d4d218903ec1be272e66aef3c581e631e91","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"83ca7bdcb9741a515908aee06e732d4d218903ec1be272e66aef3c581e631e91","first_computed_at":"2026-06-24T01:14:20.387112Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-24T01:14:20.387112Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DPABKekJB8gPub6i6ieJ9XIRWxRgui82lR5HNH2wDSfNYsTPf1tI1C0to/ApRjkwmBT993WgbJ4ag37CGueSAw==","signature_status":"signed_v1","signed_at":"2026-06-24T01:14:20.387609Z","signed_message":"canonical_sha256_bytes"},"source_id":"2505.14885","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7bfe5546fc70e289e041574bae583a418af66818ac8e639c552102d72f62933f","sha256:468d2e7225f80af5c8470984b7fc9fcaf9db1f59cf7dddca88a744165754aa65"],"state_sha256":"5d5f70f26f31a398f7e3254a3a29345bf81c408a4b455590c377aa02daeae309"}