{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:V4DCTHEXLMN3FOYAQZPTPXR2ME","short_pith_number":"pith:V4DCTHEX","schema_version":"1.0","canonical_sha256":"af06299c975b1bb2bb00865f37de3a612f35268474c4de5967c99552570d6764","source":{"kind":"arxiv","id":"2501.13404","version":1},"attestation_state":"computed","paper":{"title":"Classification of Homogeneous Local Representations of the Singular Braid Monoid","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":"2025-01-23T06:06:47Z","abstract_excerpt":"For a natural number $n$, denote by $B_n$ the braid group on $n$ strings and by $SM_n$ the singular braid monoid on $n$ strings. $SM_n$ is one of the most important extensions of $B_n$. In [13], Y. Mikhalchishina classified all homogeneous $2$-local representations of $B_n$ for all $n \\geq 3$. In this article, we extend the result of Mikhalchishina in two ways. First, we classify all homogeneous $3$-local representations of $B_n$ for all $n \\geq 4$. Second, we classify all homogeneous $2$-local representations of $SM_n$ for all $n\\geq 2$ and all homogeneous $3$-local representations of $SM_n$ "},"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":"2501.13404","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2025-01-23T06:06:47Z","cross_cats_sorted":[],"title_canon_sha256":"f38949547d5c0f286f096f71dbba016727c1fe25bb8510911bf6f2efbb1b96c8","abstract_canon_sha256":"5116817555390ca09b47a9922b5b38d026f1a056a162e4155c345865fb80c9f6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:04:28.051459Z","signature_b64":"iaXj9wIoB5naT16oD4ReZ0lqAWTZ1RCjqcGZEVdJ5LIZTtfGvD+Rdshl+EgJMWBeG9dcHVZ5bbqeUUo5PBBSDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"af06299c975b1bb2bb00865f37de3a612f35268474c4de5967c99552570d6764","last_reissued_at":"2026-07-05T10:04:28.050994Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:04:28.050994Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Classification of Homogeneous Local Representations of the Singular Braid Monoid","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":"2025-01-23T06:06:47Z","abstract_excerpt":"For a natural number $n$, denote by $B_n$ the braid group on $n$ strings and by $SM_n$ the singular braid monoid on $n$ strings. $SM_n$ is one of the most important extensions of $B_n$. In [13], Y. Mikhalchishina classified all homogeneous $2$-local representations of $B_n$ for all $n \\geq 3$. In this article, we extend the result of Mikhalchishina in two ways. First, we classify all homogeneous $3$-local representations of $B_n$ for all $n \\geq 4$. Second, we classify all homogeneous $2$-local representations of $SM_n$ for all $n\\geq 2$ and all homogeneous $3$-local representations of $SM_n$ "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.13404","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/2501.13404/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":"2501.13404","created_at":"2026-07-05T10:04:28.051045+00:00"},{"alias_kind":"arxiv_version","alias_value":"2501.13404v1","created_at":"2026-07-05T10:04:28.051045+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2501.13404","created_at":"2026-07-05T10:04:28.051045+00:00"},{"alias_kind":"pith_short_12","alias_value":"V4DCTHEXLMN3","created_at":"2026-07-05T10:04:28.051045+00:00"},{"alias_kind":"pith_short_16","alias_value":"V4DCTHEXLMN3FOYA","created_at":"2026-07-05T10:04:28.051045+00:00"},{"alias_kind":"pith_short_8","alias_value":"V4DCTHEX","created_at":"2026-07-05T10:04:28.051045+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2507.15005","citing_title":"Twin groups representations","ref_index":6,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/V4DCTHEXLMN3FOYAQZPTPXR2ME","json":"https://pith.science/pith/V4DCTHEXLMN3FOYAQZPTPXR2ME.json","graph_json":"https://pith.science/api/pith-number/V4DCTHEXLMN3FOYAQZPTPXR2ME/graph.json","events_json":"https://pith.science/api/pith-number/V4DCTHEXLMN3FOYAQZPTPXR2ME/events.json","paper":"https://pith.science/paper/V4DCTHEX"},"agent_actions":{"view_html":"https://pith.science/pith/V4DCTHEXLMN3FOYAQZPTPXR2ME","download_json":"https://pith.science/pith/V4DCTHEXLMN3FOYAQZPTPXR2ME.json","view_paper":"https://pith.science/paper/V4DCTHEX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2501.13404&json=true","fetch_graph":"https://pith.science/api/pith-number/V4DCTHEXLMN3FOYAQZPTPXR2ME/graph.json","fetch_events":"https://pith.science/api/pith-number/V4DCTHEXLMN3FOYAQZPTPXR2ME/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/V4DCTHEXLMN3FOYAQZPTPXR2ME/action/timestamp_anchor","attest_storage":"https://pith.science/pith/V4DCTHEXLMN3FOYAQZPTPXR2ME/action/storage_attestation","attest_author":"https://pith.science/pith/V4DCTHEXLMN3FOYAQZPTPXR2ME/action/author_attestation","sign_citation":"https://pith.science/pith/V4DCTHEXLMN3FOYAQZPTPXR2ME/action/citation_signature","submit_replication":"https://pith.science/pith/V4DCTHEXLMN3FOYAQZPTPXR2ME/action/replication_record"}},"created_at":"2026-07-05T10:04:28.051045+00:00","updated_at":"2026-07-05T10:04:28.051045+00:00"}