{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:7O72YLKEQHAHO7XVZBOO5LGVZL","short_pith_number":"pith:7O72YLKE","schema_version":"1.0","canonical_sha256":"fbbfac2d4481c0777ef5c85ceeacd5cafa7eb1d902bdac181461e5b7ca38741e","source":{"kind":"arxiv","id":"2508.14505","version":1},"attestation_state":"computed","paper":{"title":"On the classification and irreducibility of $2$-local representations of the twin group $T_n$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Mohamad N. Nasser, Taher I. Mayassi","submitted_at":"2025-08-20T07:53:59Z","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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2508.14505","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2025-08-20T07:53:59Z","cross_cats_sorted":[],"title_canon_sha256":"1cf39d9664e980d323d7c2d11472dec64288e1e7f6bee5c1a9e7da70e1342bb9","abstract_canon_sha256":"daa211f8e52054a8da9ca8023084308ea71cc9cded7577d743f1b400c822839c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:56:33.217775Z","signature_b64":"Km7ChhmNSeKdLJW4MUNaTjTlss+6LcDNOqwq14wLXbDlm2TqgFFrIZdAQxnajjBipTJrI81dnJP7MNTXarVLAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fbbfac2d4481c0777ef5c85ceeacd5cafa7eb1d902bdac181461e5b7ca38741e","last_reissued_at":"2026-07-05T11:56:33.217361Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:56:33.217361Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the classification and irreducibility of $2$-local representations of the twin group $T_n$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Mohamad N. Nasser, Taher I. Mayassi","submitted_at":"2025-08-20T07:53:59Z","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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2508.14505","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2508.14505/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"2508.14505","created_at":"2026-07-05T11:56:33.217419+00:00"},{"alias_kind":"arxiv_version","alias_value":"2508.14505v1","created_at":"2026-07-05T11:56:33.217419+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2508.14505","created_at":"2026-07-05T11:56:33.217419+00:00"},{"alias_kind":"pith_short_12","alias_value":"7O72YLKEQHAH","created_at":"2026-07-05T11:56:33.217419+00:00"},{"alias_kind":"pith_short_16","alias_value":"7O72YLKEQHAHO7XV","created_at":"2026-07-05T11:56:33.217419+00:00"},{"alias_kind":"pith_short_8","alias_value":"7O72YLKE","created_at":"2026-07-05T11:56:33.217419+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":2,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2605.13090","citing_title":"Presentations and Representations of the Multi-Virtual Twin Group and Associated Subgroups","ref_index":9,"is_internal_anchor":false},{"citing_arxiv_id":"2604.19307","citing_title":"On Universal Virtual and Welded Braid Groups and Their Linear Representations","ref_index":10,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/7O72YLKEQHAHO7XVZBOO5LGVZL","json":"https://pith.science/pith/7O72YLKEQHAHO7XVZBOO5LGVZL.json","graph_json":"https://pith.science/api/pith-number/7O72YLKEQHAHO7XVZBOO5LGVZL/graph.json","events_json":"https://pith.science/api/pith-number/7O72YLKEQHAHO7XVZBOO5LGVZL/events.json","paper":"https://pith.science/paper/7O72YLKE"},"agent_actions":{"view_html":"https://pith.science/pith/7O72YLKEQHAHO7XVZBOO5LGVZL","download_json":"https://pith.science/pith/7O72YLKEQHAHO7XVZBOO5LGVZL.json","view_paper":"https://pith.science/paper/7O72YLKE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2508.14505&json=true","fetch_graph":"https://pith.science/api/pith-number/7O72YLKEQHAHO7XVZBOO5LGVZL/graph.json","fetch_events":"https://pith.science/api/pith-number/7O72YLKEQHAHO7XVZBOO5LGVZL/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7O72YLKEQHAHO7XVZBOO5LGVZL/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7O72YLKEQHAHO7XVZBOO5LGVZL/action/storage_attestation","attest_author":"https://pith.science/pith/7O72YLKEQHAHO7XVZBOO5LGVZL/action/author_attestation","sign_citation":"https://pith.science/pith/7O72YLKEQHAHO7XVZBOO5LGVZL/action/citation_signature","submit_replication":"https://pith.science/pith/7O72YLKEQHAHO7XVZBOO5LGVZL/action/replication_record"}},"created_at":"2026-07-05T11:56:33.217419+00:00","updated_at":"2026-07-05T11:56:33.217419+00:00"}