{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:73YR75OM5YWLSLRVY6OMIFKQCM","short_pith_number":"pith:73YR75OM","schema_version":"1.0","canonical_sha256":"fef11ff5ccee2cb92e35c79cc4155013375edcc55a731ae870042b36f440b0e3","source":{"kind":"arxiv","id":"2407.09275","version":3},"attestation_state":"computed","paper":{"title":"Coarse obstructions to cocompact cubulation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MG"],"primary_cat":"math.GR","authors_text":"Harry Petyt, Zachary Munro","submitted_at":"2024-07-12T14:03:18Z","abstract_excerpt":"We provide geometric methods to give bounds on the large-scale dimension of CAT(0) cube complexes quasiisometric to a given group $G$. In situations where these bounds conflict we obtain obstructions to $G$ being cocompactly cubulated. More strongly, the obstructions prevent $G$ from being a coarse median space.\n  As applications, we show that many free-by-cyclic groups cannot be cocompactly cubulated, even virtually, and prove that any tubular group with a coarse median is virtually compact special. We also exhibit a group that is CAT(0), $C(6)$, and virtually special, yet is not quasiisometr"},"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":"2407.09275","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2024-07-12T14:03:18Z","cross_cats_sorted":["math.MG"],"title_canon_sha256":"71eeab2e9546a2dfc2227bf40b1d22e7876496b5954ec8ca38891240fad34d1c","abstract_canon_sha256":"342a1f8743025639ab9da8836803aa41d562550b5e7b010eb1bbb49e943c0537"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:19:49.074531Z","signature_b64":"z4ijsY/YsNrXQ46x9FGVQWC7RfqTeOkfCbPEUyV3eWOmI0YBklS9JketYB8G8KFLJTNbGY/pQKL8/bzwbyvKAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fef11ff5ccee2cb92e35c79cc4155013375edcc55a731ae870042b36f440b0e3","last_reissued_at":"2026-07-05T11:19:49.074088Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:19:49.074088Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Coarse obstructions to cocompact cubulation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MG"],"primary_cat":"math.GR","authors_text":"Harry Petyt, Zachary Munro","submitted_at":"2024-07-12T14:03:18Z","abstract_excerpt":"We provide geometric methods to give bounds on the large-scale dimension of CAT(0) cube complexes quasiisometric to a given group $G$. In situations where these bounds conflict we obtain obstructions to $G$ being cocompactly cubulated. More strongly, the obstructions prevent $G$ from being a coarse median space.\n  As applications, we show that many free-by-cyclic groups cannot be cocompactly cubulated, even virtually, and prove that any tubular group with a coarse median is virtually compact special. We also exhibit a group that is CAT(0), $C(6)$, and virtually special, yet is not quasiisometr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2407.09275","kind":"arxiv","version":3},"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/2407.09275/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":"2407.09275","created_at":"2026-07-05T11:19:49.074146+00:00"},{"alias_kind":"arxiv_version","alias_value":"2407.09275v3","created_at":"2026-07-05T11:19:49.074146+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2407.09275","created_at":"2026-07-05T11:19:49.074146+00:00"},{"alias_kind":"pith_short_12","alias_value":"73YR75OM5YWL","created_at":"2026-07-05T11:19:49.074146+00:00"},{"alias_kind":"pith_short_16","alias_value":"73YR75OM5YWLSLRV","created_at":"2026-07-05T11:19:49.074146+00:00"},{"alias_kind":"pith_short_8","alias_value":"73YR75OM","created_at":"2026-07-05T11:19:49.074146+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":2,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2607.08356","citing_title":"Coarse embeddings of products of trees as quasi-isometry invariants","ref_index":21,"is_internal_anchor":true},{"citing_arxiv_id":"2508.15738","citing_title":"Characterizing hierarchically hyperbolic free by cyclic groups","ref_index":10,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/73YR75OM5YWLSLRVY6OMIFKQCM","json":"https://pith.science/pith/73YR75OM5YWLSLRVY6OMIFKQCM.json","graph_json":"https://pith.science/api/pith-number/73YR75OM5YWLSLRVY6OMIFKQCM/graph.json","events_json":"https://pith.science/api/pith-number/73YR75OM5YWLSLRVY6OMIFKQCM/events.json","paper":"https://pith.science/paper/73YR75OM"},"agent_actions":{"view_html":"https://pith.science/pith/73YR75OM5YWLSLRVY6OMIFKQCM","download_json":"https://pith.science/pith/73YR75OM5YWLSLRVY6OMIFKQCM.json","view_paper":"https://pith.science/paper/73YR75OM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2407.09275&json=true","fetch_graph":"https://pith.science/api/pith-number/73YR75OM5YWLSLRVY6OMIFKQCM/graph.json","fetch_events":"https://pith.science/api/pith-number/73YR75OM5YWLSLRVY6OMIFKQCM/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/73YR75OM5YWLSLRVY6OMIFKQCM/action/timestamp_anchor","attest_storage":"https://pith.science/pith/73YR75OM5YWLSLRVY6OMIFKQCM/action/storage_attestation","attest_author":"https://pith.science/pith/73YR75OM5YWLSLRVY6OMIFKQCM/action/author_attestation","sign_citation":"https://pith.science/pith/73YR75OM5YWLSLRVY6OMIFKQCM/action/citation_signature","submit_replication":"https://pith.science/pith/73YR75OM5YWLSLRVY6OMIFKQCM/action/replication_record"}},"created_at":"2026-07-05T11:19:49.074146+00:00","updated_at":"2026-07-05T11:19:49.074146+00:00"}