{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:KSITAELR4J2TYVZ4H4573MMZBL","short_pith_number":"pith:KSITAELR","schema_version":"1.0","canonical_sha256":"5491301171e2753c573c3f3bfdb1990ad9bc2b0f1d2e62362da82a3f418ea88e","source":{"kind":"arxiv","id":"2404.15652","version":1},"attestation_state":"computed","paper":{"title":"Rotation groups virtually embed into right-angled rotation groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MG"],"primary_cat":"math.GR","authors_text":"Anthony Genevois","submitted_at":"2024-04-24T05:12:18Z","abstract_excerpt":"It is a theorem due to F. Haglund and D. Wise that reflection groups (aka Coxeter groups) virtually embed into right-angled reflection groups (aka right-angled Coxeter groups). In this article, we generalise this observation to rotation groups, which can be thought of as a common generalisation of Coxeter groups and graph products of groups. More precisely, we prove that rotation groups (aka periagroups) virtually embed into right-angled rotation groups (aka graph products of groups)."},"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":"2404.15652","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2024-04-24T05:12:18Z","cross_cats_sorted":["math.MG"],"title_canon_sha256":"2723b0d3103ba91dbd72d7e07db382f754d418c183d84e713545a452afb3bf5e","abstract_canon_sha256":"b717860b31d07303e934a89b0b4fa4c5acee287f577c0552bc32cb6e26f13bc0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:23:06.717564Z","signature_b64":"/arunBdsqh95f5buJRpMQ9r2uTJMk3WpWhxwdnAp3PVQVABsVkT6N/2ZK05ZWS6d1uxWrf33+fqYULcY0HazCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5491301171e2753c573c3f3bfdb1990ad9bc2b0f1d2e62362da82a3f418ea88e","last_reissued_at":"2026-07-05T11:23:06.717055Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:23:06.717055Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Rotation groups virtually embed into right-angled rotation groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MG"],"primary_cat":"math.GR","authors_text":"Anthony Genevois","submitted_at":"2024-04-24T05:12:18Z","abstract_excerpt":"It is a theorem due to F. Haglund and D. Wise that reflection groups (aka Coxeter groups) virtually embed into right-angled reflection groups (aka right-angled Coxeter groups). In this article, we generalise this observation to rotation groups, which can be thought of as a common generalisation of Coxeter groups and graph products of groups. More precisely, we prove that rotation groups (aka periagroups) virtually embed into right-angled rotation groups (aka graph products of groups)."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2404.15652","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/2404.15652/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":"2404.15652","created_at":"2026-07-05T11:23:06.717119+00:00"},{"alias_kind":"arxiv_version","alias_value":"2404.15652v1","created_at":"2026-07-05T11:23:06.717119+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2404.15652","created_at":"2026-07-05T11:23:06.717119+00:00"},{"alias_kind":"pith_short_12","alias_value":"KSITAELR4J2T","created_at":"2026-07-05T11:23:06.717119+00:00"},{"alias_kind":"pith_short_16","alias_value":"KSITAELR4J2TYVZ4","created_at":"2026-07-05T11:23:06.717119+00:00"},{"alias_kind":"pith_short_8","alias_value":"KSITAELR","created_at":"2026-07-05T11:23:06.717119+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2505.23293","citing_title":"Cell structure of mediangle graphs","ref_index":19,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/KSITAELR4J2TYVZ4H4573MMZBL","json":"https://pith.science/pith/KSITAELR4J2TYVZ4H4573MMZBL.json","graph_json":"https://pith.science/api/pith-number/KSITAELR4J2TYVZ4H4573MMZBL/graph.json","events_json":"https://pith.science/api/pith-number/KSITAELR4J2TYVZ4H4573MMZBL/events.json","paper":"https://pith.science/paper/KSITAELR"},"agent_actions":{"view_html":"https://pith.science/pith/KSITAELR4J2TYVZ4H4573MMZBL","download_json":"https://pith.science/pith/KSITAELR4J2TYVZ4H4573MMZBL.json","view_paper":"https://pith.science/paper/KSITAELR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2404.15652&json=true","fetch_graph":"https://pith.science/api/pith-number/KSITAELR4J2TYVZ4H4573MMZBL/graph.json","fetch_events":"https://pith.science/api/pith-number/KSITAELR4J2TYVZ4H4573MMZBL/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KSITAELR4J2TYVZ4H4573MMZBL/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KSITAELR4J2TYVZ4H4573MMZBL/action/storage_attestation","attest_author":"https://pith.science/pith/KSITAELR4J2TYVZ4H4573MMZBL/action/author_attestation","sign_citation":"https://pith.science/pith/KSITAELR4J2TYVZ4H4573MMZBL/action/citation_signature","submit_replication":"https://pith.science/pith/KSITAELR4J2TYVZ4H4573MMZBL/action/replication_record"}},"created_at":"2026-07-05T11:23:06.717119+00:00","updated_at":"2026-07-05T11:23:06.717119+00:00"}