{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:O2R3OPEZDCI2MZON4RU6BOUAW5","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"0ced86726a9d7ccb938369d842e702fa2df481458f76270caf7c9056b9f87161","cross_cats_sorted":["math.CO","math.GR","math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2025-02-25T12:51:33Z","title_canon_sha256":"21f3d999590daaec34557f12c0e45d0524b68e5e8ce7295d9ff1df327395756d"},"schema_version":"1.0","source":{"id":"2502.18165","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2502.18165","created_at":"2026-07-05T10:19:49Z"},{"alias_kind":"arxiv_version","alias_value":"2502.18165v1","created_at":"2026-07-05T10:19:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2502.18165","created_at":"2026-07-05T10:19:49Z"},{"alias_kind":"pith_short_12","alias_value":"O2R3OPEZDCI2","created_at":"2026-07-05T10:19:49Z"},{"alias_kind":"pith_short_16","alias_value":"O2R3OPEZDCI2MZON","created_at":"2026-07-05T10:19:49Z"},{"alias_kind":"pith_short_8","alias_value":"O2R3OPEZ","created_at":"2026-07-05T10:19:49Z"}],"graph_snapshots":[{"event_id":"sha256:0dbdec4ae4e8eb7fc0c9dddc7756693aa0f5dc8c57b1487e537eca4b7e0abcf1","target":"graph","created_at":"2026-07-05T10:19:49Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2502.18165/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"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","authors_text":"Jason Behrstock, R. Altar Ciceksiz, Victor Falgas-Ravry","cross_cats":["math.CO","math.GR","math.GT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2025-02-25T12:51:33Z","title":"Connectivity for square percolation and coarse cubical rigidity in random right-angled Coxeter groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.18165","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:e5395e9e56d0fb18d81a2b9c08ef6de867a05e17446e9c88752c2f40520d95a1","target":"record","created_at":"2026-07-05T10:19:49Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"0ced86726a9d7ccb938369d842e702fa2df481458f76270caf7c9056b9f87161","cross_cats_sorted":["math.CO","math.GR","math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2025-02-25T12:51:33Z","title_canon_sha256":"21f3d999590daaec34557f12c0e45d0524b68e5e8ce7295d9ff1df327395756d"},"schema_version":"1.0","source":{"id":"2502.18165","kind":"arxiv","version":1}},"canonical_sha256":"76a3b73c991891a665cde469e0ba80b74c9c843c212c3d0903a10e410a333cb5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"76a3b73c991891a665cde469e0ba80b74c9c843c212c3d0903a10e410a333cb5","first_computed_at":"2026-07-05T10:19:49.889843Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:19:49.889843Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GoHaBDy4H4w1eccCSUnJ7E0AAkDrRxjkcvuHMRd79QH2NPnviZkTQMOlTgKOoRan1u0yeGkThsoQ22cQ6HkOBQ==","signature_status":"signed_v1","signed_at":"2026-07-05T10:19:49.890251Z","signed_message":"canonical_sha256_bytes"},"source_id":"2502.18165","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e5395e9e56d0fb18d81a2b9c08ef6de867a05e17446e9c88752c2f40520d95a1","sha256:0dbdec4ae4e8eb7fc0c9dddc7756693aa0f5dc8c57b1487e537eca4b7e0abcf1"],"state_sha256":"3a1d7b5948a7beb5212cf85ba3f4da422422a42741376c1df3903d0d1c03edf8"}