{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:O2R3OPEZDCI2MZON4RU6BOUAW5","short_pith_number":"pith:O2R3OPEZ","schema_version":"1.0","canonical_sha256":"76a3b73c991891a665cde469e0ba80b74c9c843c212c3d0903a10e410a333cb5","source":{"kind":"arxiv","id":"2502.18165","version":1},"attestation_state":"computed","paper":{"title":"Connectivity for square percolation and coarse cubical rigidity in random right-angled Coxeter groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.GR","math.GT"],"primary_cat":"math.PR","authors_text":"Jason Behrstock, R. Altar Ciceksiz, Victor Falgas-Ravry","submitted_at":"2025-02-25T12:51:33Z","abstract_excerpt":"We consider random right-angled Coxeter groups, $W_{\\Gamma}$, whose presentation graph $\\Gamma$ is taken to be an Erd\\H{o}s--R\\'enyi random graph, i.e., $\\Gamma\\sim \\mathcal{G}_{n,p}$. We use techniques from probabilistic combinatorics to establish several new results about the geometry of these random groups.\n  We resolve a conjecture of Susse and determine the connectivity threshold for square percolation on the random graph $\\Gamma \\sim \\mathcal{G}_{n,p}$. We use this result to determine a large range of $p$ for which the random right-angled Coxeter group $W_{\\Gamma}$ has a unique cubical c"},"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":"2502.18165","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2025-02-25T12:51:33Z","cross_cats_sorted":["math.CO","math.GR","math.GT"],"title_canon_sha256":"21f3d999590daaec34557f12c0e45d0524b68e5e8ce7295d9ff1df327395756d","abstract_canon_sha256":"0ced86726a9d7ccb938369d842e702fa2df481458f76270caf7c9056b9f87161"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:19:49.890251Z","signature_b64":"GoHaBDy4H4w1eccCSUnJ7E0AAkDrRxjkcvuHMRd79QH2NPnviZkTQMOlTgKOoRan1u0yeGkThsoQ22cQ6HkOBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"76a3b73c991891a665cde469e0ba80b74c9c843c212c3d0903a10e410a333cb5","last_reissued_at":"2026-07-05T10:19:49.889843Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:19:49.889843Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Connectivity for square percolation and coarse cubical rigidity in random right-angled Coxeter groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.GR","math.GT"],"primary_cat":"math.PR","authors_text":"Jason Behrstock, R. Altar Ciceksiz, Victor Falgas-Ravry","submitted_at":"2025-02-25T12:51:33Z","abstract_excerpt":"We consider random right-angled Coxeter groups, $W_{\\Gamma}$, whose presentation graph $\\Gamma$ is taken to be an Erd\\H{o}s--R\\'enyi random graph, i.e., $\\Gamma\\sim \\mathcal{G}_{n,p}$. We use techniques from probabilistic combinatorics to establish several new results about the geometry of these random groups.\n  We resolve a conjecture of Susse and determine the connectivity threshold for square percolation on the random graph $\\Gamma \\sim \\mathcal{G}_{n,p}$. We use this result to determine a large range of $p$ for which the random right-angled Coxeter group $W_{\\Gamma}$ has a unique cubical c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.18165","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/2502.18165/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":"2502.18165","created_at":"2026-07-05T10:19:49.889902+00:00"},{"alias_kind":"arxiv_version","alias_value":"2502.18165v1","created_at":"2026-07-05T10:19:49.889902+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2502.18165","created_at":"2026-07-05T10:19:49.889902+00:00"},{"alias_kind":"pith_short_12","alias_value":"O2R3OPEZDCI2","created_at":"2026-07-05T10:19:49.889902+00:00"},{"alias_kind":"pith_short_16","alias_value":"O2R3OPEZDCI2MZON","created_at":"2026-07-05T10:19:49.889902+00:00"},{"alias_kind":"pith_short_8","alias_value":"O2R3OPEZ","created_at":"2026-07-05T10:19:49.889902+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2506.16789","citing_title":"RAAGedy right-angled Coxeter groups","ref_index":4,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/O2R3OPEZDCI2MZON4RU6BOUAW5","json":"https://pith.science/pith/O2R3OPEZDCI2MZON4RU6BOUAW5.json","graph_json":"https://pith.science/api/pith-number/O2R3OPEZDCI2MZON4RU6BOUAW5/graph.json","events_json":"https://pith.science/api/pith-number/O2R3OPEZDCI2MZON4RU6BOUAW5/events.json","paper":"https://pith.science/paper/O2R3OPEZ"},"agent_actions":{"view_html":"https://pith.science/pith/O2R3OPEZDCI2MZON4RU6BOUAW5","download_json":"https://pith.science/pith/O2R3OPEZDCI2MZON4RU6BOUAW5.json","view_paper":"https://pith.science/paper/O2R3OPEZ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2502.18165&json=true","fetch_graph":"https://pith.science/api/pith-number/O2R3OPEZDCI2MZON4RU6BOUAW5/graph.json","fetch_events":"https://pith.science/api/pith-number/O2R3OPEZDCI2MZON4RU6BOUAW5/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/O2R3OPEZDCI2MZON4RU6BOUAW5/action/timestamp_anchor","attest_storage":"https://pith.science/pith/O2R3OPEZDCI2MZON4RU6BOUAW5/action/storage_attestation","attest_author":"https://pith.science/pith/O2R3OPEZDCI2MZON4RU6BOUAW5/action/author_attestation","sign_citation":"https://pith.science/pith/O2R3OPEZDCI2MZON4RU6BOUAW5/action/citation_signature","submit_replication":"https://pith.science/pith/O2R3OPEZDCI2MZON4RU6BOUAW5/action/replication_record"}},"created_at":"2026-07-05T10:19:49.889902+00:00","updated_at":"2026-07-05T10:19:49.889902+00:00"}