{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:EHEO6ER3CYNU2OODAYOLW3L4XN","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":"4299dd4e7cf225a974a50f77ac9eacc8971dbcfb0728657c5b666924e19a4379","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2024-11-22T20:37:21Z","title_canon_sha256":"3e1f9260896aefad68736dc26da84af1e000b2206e840ab1f41d332716829cac"},"schema_version":"1.0","source":{"id":"2411.15337","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2411.15337","created_at":"2026-07-05T11:03:18Z"},{"alias_kind":"arxiv_version","alias_value":"2411.15337v3","created_at":"2026-07-05T11:03:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.15337","created_at":"2026-07-05T11:03:18Z"},{"alias_kind":"pith_short_12","alias_value":"EHEO6ER3CYNU","created_at":"2026-07-05T11:03:18Z"},{"alias_kind":"pith_short_16","alias_value":"EHEO6ER3CYNU2OOD","created_at":"2026-07-05T11:03:18Z"},{"alias_kind":"pith_short_8","alias_value":"EHEO6ER3","created_at":"2026-07-05T11:03:18Z"}],"graph_snapshots":[{"event_id":"sha256:e85378ecf76a4606916e35813c88358b9762f9a38266ac16114b43b00a37328d","target":"graph","created_at":"2026-07-05T11:03:18Z","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/2411.15337/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"By analogy with the Cayley graph of a group with respect to a finite generating set or the Cayley--Abels graph of a totally disconnected, locally compact group, we detail countable connected graphs associated to Polish groups that we term Cayley--Abels--Rosendal graphs. A group admitting a Cayley--Abels--Rosendal graph acts on it continuously, coarsely metrically properly and cocompactly by isometries of the path metric. By an expansion of the Milnor--Schwarz lemma, it follows that the group is generated by a coarsely bounded set and the group equipped with a word metric with respect to a coar","authors_text":"Beth Branman, George Domat, Hannah Hoganson, Robert Alonzo Lyman","cross_cats":["math.GT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2024-11-22T20:37:21Z","title":"Graphical models for topological groups: A case study on countable Stone spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.15337","kind":"arxiv","version":3},"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:faf9ad6c063e190ac6683152c1c206dabb21a01b8cc9713e330c9a82ca9783f1","target":"record","created_at":"2026-07-05T11:03:18Z","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":"4299dd4e7cf225a974a50f77ac9eacc8971dbcfb0728657c5b666924e19a4379","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2024-11-22T20:37:21Z","title_canon_sha256":"3e1f9260896aefad68736dc26da84af1e000b2206e840ab1f41d332716829cac"},"schema_version":"1.0","source":{"id":"2411.15337","kind":"arxiv","version":3}},"canonical_sha256":"21c8ef123b161b4d39c3061cbb6d7cbb6ed3ae0f1ac4cb17c0f9d58075cfd641","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"21c8ef123b161b4d39c3061cbb6d7cbb6ed3ae0f1ac4cb17c0f9d58075cfd641","first_computed_at":"2026-07-05T11:03:18.656521Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:03:18.656521Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ylQ5+ZHuns0CH39/UV8PolXZ96rXa42rL53GkiWOhu8UBq+RzgfgP5fIEv3i5cpRE/fR7ak6nua3+HtI7Sp1BA==","signature_status":"signed_v1","signed_at":"2026-07-05T11:03:18.656942Z","signed_message":"canonical_sha256_bytes"},"source_id":"2411.15337","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:faf9ad6c063e190ac6683152c1c206dabb21a01b8cc9713e330c9a82ca9783f1","sha256:e85378ecf76a4606916e35813c88358b9762f9a38266ac16114b43b00a37328d"],"state_sha256":"8c0b9c43af899b5a00ea710a2372d7862d733a2951435388bea6d1d68bef4eef"}