{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:7O72YLKEQHAHO7XVZBOO5LGVZL","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":"daa211f8e52054a8da9ca8023084308ea71cc9cded7577d743f1b400c822839c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2025-08-20T07:53:59Z","title_canon_sha256":"1cf39d9664e980d323d7c2d11472dec64288e1e7f6bee5c1a9e7da70e1342bb9"},"schema_version":"1.0","source":{"id":"2508.14505","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2508.14505","created_at":"2026-07-05T11:56:33Z"},{"alias_kind":"arxiv_version","alias_value":"2508.14505v1","created_at":"2026-07-05T11:56:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2508.14505","created_at":"2026-07-05T11:56:33Z"},{"alias_kind":"pith_short_12","alias_value":"7O72YLKEQHAH","created_at":"2026-07-05T11:56:33Z"},{"alias_kind":"pith_short_16","alias_value":"7O72YLKEQHAHO7XV","created_at":"2026-07-05T11:56:33Z"},{"alias_kind":"pith_short_8","alias_value":"7O72YLKE","created_at":"2026-07-05T11:56:33Z"}],"graph_snapshots":[{"event_id":"sha256:9edb3ceb7c4aecac8743632255dd98de859fe838add02d53ad60649dcc93bb7a","target":"graph","created_at":"2026-07-05T11:56:33Z","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/2508.14505/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We investigate the homogeneous $2$-local representations of the twin group $T_n$ for all integers $n\\geqslant 2$. A complete classification is obtained, yielding three distinct families of representations. We show that each of these families is reducible by explicitly constructing one-dimensional invariant subspaces, with particular emphasis on the first family, namely $\\xi_1: T_n \\rightarrow \\text{GL}_n(\\mathbb{C})$. Passing to the corresponding quotients, we construct a reduced representation of $\\xi_1$, namely $\\tilde{\\xi}_1: T_n \\rightarrow \\text{GL}_{n-1}(\\mathbb{C})$. The core of the pap","authors_text":"Mohamad N. Nasser, Taher I. Mayassi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2025-08-20T07:53:59Z","title":"On the classification and irreducibility of $2$-local representations of the twin group $T_n$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2508.14505","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:c8d62e8670326713a38dfac32ba3a8c7d6a8135d4c88edb44ad4871e7f25b7f2","target":"record","created_at":"2026-07-05T11:56:33Z","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":"daa211f8e52054a8da9ca8023084308ea71cc9cded7577d743f1b400c822839c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2025-08-20T07:53:59Z","title_canon_sha256":"1cf39d9664e980d323d7c2d11472dec64288e1e7f6bee5c1a9e7da70e1342bb9"},"schema_version":"1.0","source":{"id":"2508.14505","kind":"arxiv","version":1}},"canonical_sha256":"fbbfac2d4481c0777ef5c85ceeacd5cafa7eb1d902bdac181461e5b7ca38741e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fbbfac2d4481c0777ef5c85ceeacd5cafa7eb1d902bdac181461e5b7ca38741e","first_computed_at":"2026-07-05T11:56:33.217361Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:56:33.217361Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Km7ChhmNSeKdLJW4MUNaTjTlss+6LcDNOqwq14wLXbDlm2TqgFFrIZdAQxnajjBipTJrI81dnJP7MNTXarVLAQ==","signature_status":"signed_v1","signed_at":"2026-07-05T11:56:33.217775Z","signed_message":"canonical_sha256_bytes"},"source_id":"2508.14505","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c8d62e8670326713a38dfac32ba3a8c7d6a8135d4c88edb44ad4871e7f25b7f2","sha256:9edb3ceb7c4aecac8743632255dd98de859fe838add02d53ad60649dcc93bb7a"],"state_sha256":"a081415060edb9603e36f4cc261f9a43e0ee19400a5f4b4a104320badb7ab74f"}