{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:ULTJMJUOJSSXCCDM5A2FM7CCCX","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":"278a74e2c1bdb1758a9c228fa8de3d45ca6114c0ca8611286e660b3f1a78fb7b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2025-10-03T18:48:39Z","title_canon_sha256":"9171bdc0062fee4a044e776ca7292fae6285c7ed6c3ec72e817fb0440e2ee7c6"},"schema_version":"1.0","source":{"id":"2510.03430","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2510.03430","created_at":"2026-07-23T00:23:36Z"},{"alias_kind":"arxiv_version","alias_value":"2510.03430v2","created_at":"2026-07-23T00:23:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2510.03430","created_at":"2026-07-23T00:23:36Z"},{"alias_kind":"pith_short_12","alias_value":"ULTJMJUOJSSX","created_at":"2026-07-23T00:23:36Z"},{"alias_kind":"pith_short_16","alias_value":"ULTJMJUOJSSXCCDM","created_at":"2026-07-23T00:23:36Z"},{"alias_kind":"pith_short_8","alias_value":"ULTJMJUO","created_at":"2026-07-23T00:23:36Z"}],"graph_snapshots":[{"event_id":"sha256:2bb0ffcc825bde282653bc3701d907667730aa1bd2ba26a5bcd3998c6bdad08c","target":"graph","created_at":"2026-07-23T00:23:36Z","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/2510.03430/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We introduce a graph-theoretic condition, called $(n,m)$--branching, that ensures a combinatorial round tree with controlled branching parameters can be quasi-isometrically embedded in the Davis complex of the right-angled Coxeter group defined by the graph. This construction yields a lower bound on the conformal dimension of the boundary of such a hyperbolic group. We exhibit numerous families of graphs with this property, including many 1-dimensional spherical buildings.\n  We prove an embedding result, showing that under mild hypotheses a flag-no-square graph embeds as an induced subgraph in","authors_text":"Christopher H. Cashen, Emily Stark, Kevin Schreve, Pallavi Dani","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2025-10-03T18:48:39Z","title":"Conformal dimension bounds, Pontryagin sphere boundaries, and algebraic fibering of right-angled Coxeter groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2510.03430","kind":"arxiv","version":2},"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":"sha256:6308354845c2a8776a8318dbf89633e271a2f0baed1768d16dd831e63ce0df66","target":"record","created_at":"2026-07-23T00:23:36Z","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":"278a74e2c1bdb1758a9c228fa8de3d45ca6114c0ca8611286e660b3f1a78fb7b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2025-10-03T18:48:39Z","title_canon_sha256":"9171bdc0062fee4a044e776ca7292fae6285c7ed6c3ec72e817fb0440e2ee7c6"},"schema_version":"1.0","source":{"id":"2510.03430","kind":"arxiv","version":2}},"canonical_sha256":"a2e696268e4ca571086ce834567c4215ecd33bd687fcc4078d1d2745a1c03578","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a2e696268e4ca571086ce834567c4215ecd33bd687fcc4078d1d2745a1c03578","first_computed_at":"2026-07-23T00:23:36.217794Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-23T00:23:36.217794Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"pGnvQfIhhLqxfZYlyU8yoKNRdnAeGnKF0K1C4NaGZJo68Yge4Xrr5oI+9trMgKUerq+irMkTROEYFBBRJloMDw==","signature_status":"signed_v1","signed_at":"2026-07-23T00:23:36.218697Z","signed_message":"canonical_sha256_bytes"},"source_id":"2510.03430","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6308354845c2a8776a8318dbf89633e271a2f0baed1768d16dd831e63ce0df66","sha256:2bb0ffcc825bde282653bc3701d907667730aa1bd2ba26a5bcd3998c6bdad08c"],"state_sha256":"fb3ede5ef3cbc66995183f529fb6d44cde9cf185338a8f4ff1c9cd00afb30ff6"}