{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:MXRSEBYTNUHGE7JXKL3KITPZBW","short_pith_number":"pith:MXRSEBYT","schema_version":"1.0","canonical_sha256":"65e32207136d0e627d3752f6a44df90d8fb4f443346f29dacf9e300318ae8fca","source":{"kind":"arxiv","id":"1609.02441","version":2},"attestation_state":"computed","paper":{"title":"Presentations for singular wreath products","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.GR","authors_text":"Asawer Al-Aadhami, Igor Dolinka, James East, Victoria Gould, Ying-Ying Feng","submitted_at":"2016-09-08T14:14:47Z","abstract_excerpt":"For a monoid $M$ and a subsemigroup $S$ of the full transformation semigroup $T_n$, the wreath product $M\\wr S$ is defined to be the semidirect product $M^n\\rtimes S$, with the coordinatewise action of $S$ on $M^n$. The full wreath product $M\\wr T_n$ is isomorphic to the endomorphism monoid of the free $M$-act on $n$ generators. Here, we are particularly interested in the case that $S=Sing_n$ is the singular part of $T_n$, consisting of all non-invertible transformations. Our main results are presentations for $M\\wr Sing_n$ in terms of certain natural generating sets, and we prove these via ge"},"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":"1609.02441","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2016-09-08T14:14:47Z","cross_cats_sorted":["math.RA"],"title_canon_sha256":"ae139789373267f7db8e7c524135f25d42d56aad77c18ef2641695366f0c2d2c","abstract_canon_sha256":"d7d55a78d3d05e35e621b1e63c2d5a653e4a140edd04538b3476c8fbd5e8a02c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:16:09.589449Z","signature_b64":"HjmQdURF20xWxT8A/kOIuBZI5IQu6x82DSMez4ENXVTGI1sAkM0Wy9BXJXqJ/br0jRrmY17o5a4IuOoaFYgDAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"65e32207136d0e627d3752f6a44df90d8fb4f443346f29dacf9e300318ae8fca","last_reissued_at":"2026-05-18T00:16:09.588877Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:16:09.588877Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Presentations for singular wreath products","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.GR","authors_text":"Asawer Al-Aadhami, Igor Dolinka, James East, Victoria Gould, Ying-Ying Feng","submitted_at":"2016-09-08T14:14:47Z","abstract_excerpt":"For a monoid $M$ and a subsemigroup $S$ of the full transformation semigroup $T_n$, the wreath product $M\\wr S$ is defined to be the semidirect product $M^n\\rtimes S$, with the coordinatewise action of $S$ on $M^n$. The full wreath product $M\\wr T_n$ is isomorphic to the endomorphism monoid of the free $M$-act on $n$ generators. Here, we are particularly interested in the case that $S=Sing_n$ is the singular part of $T_n$, consisting of all non-invertible transformations. Our main results are presentations for $M\\wr Sing_n$ in terms of certain natural generating sets, and we prove these via ge"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.02441","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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":"1609.02441","created_at":"2026-05-18T00:16:09.588976+00:00"},{"alias_kind":"arxiv_version","alias_value":"1609.02441v2","created_at":"2026-05-18T00:16:09.588976+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.02441","created_at":"2026-05-18T00:16:09.588976+00:00"},{"alias_kind":"pith_short_12","alias_value":"MXRSEBYTNUHG","created_at":"2026-05-18T12:30:32.724797+00:00"},{"alias_kind":"pith_short_16","alias_value":"MXRSEBYTNUHGE7JX","created_at":"2026-05-18T12:30:32.724797+00:00"},{"alias_kind":"pith_short_8","alias_value":"MXRSEBYT","created_at":"2026-05-18T12:30:32.724797+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/MXRSEBYTNUHGE7JXKL3KITPZBW","json":"https://pith.science/pith/MXRSEBYTNUHGE7JXKL3KITPZBW.json","graph_json":"https://pith.science/api/pith-number/MXRSEBYTNUHGE7JXKL3KITPZBW/graph.json","events_json":"https://pith.science/api/pith-number/MXRSEBYTNUHGE7JXKL3KITPZBW/events.json","paper":"https://pith.science/paper/MXRSEBYT"},"agent_actions":{"view_html":"https://pith.science/pith/MXRSEBYTNUHGE7JXKL3KITPZBW","download_json":"https://pith.science/pith/MXRSEBYTNUHGE7JXKL3KITPZBW.json","view_paper":"https://pith.science/paper/MXRSEBYT","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1609.02441&json=true","fetch_graph":"https://pith.science/api/pith-number/MXRSEBYTNUHGE7JXKL3KITPZBW/graph.json","fetch_events":"https://pith.science/api/pith-number/MXRSEBYTNUHGE7JXKL3KITPZBW/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MXRSEBYTNUHGE7JXKL3KITPZBW/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MXRSEBYTNUHGE7JXKL3KITPZBW/action/storage_attestation","attest_author":"https://pith.science/pith/MXRSEBYTNUHGE7JXKL3KITPZBW/action/author_attestation","sign_citation":"https://pith.science/pith/MXRSEBYTNUHGE7JXKL3KITPZBW/action/citation_signature","submit_replication":"https://pith.science/pith/MXRSEBYTNUHGE7JXKL3KITPZBW/action/replication_record"}},"created_at":"2026-05-18T00:16:09.588976+00:00","updated_at":"2026-05-18T00:16:09.588976+00:00"}