{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:DSS3EI4ZJ4QXHCEVU6LAA4H2SQ","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":"89152011f5fae80955c587d786e8b320b364338556e55345b56b31ea20cce996","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2016-01-27T22:17:58Z","title_canon_sha256":"1f3133811644cb17436ee68e4822c5a6b99575cdd3e9eb2f3176c0f0e027f7ee"},"schema_version":"1.0","source":{"id":"1601.07587","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.07587","created_at":"2026-05-18T00:01:47Z"},{"alias_kind":"arxiv_version","alias_value":"1601.07587v1","created_at":"2026-05-18T00:01:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.07587","created_at":"2026-05-18T00:01:47Z"},{"alias_kind":"pith_short_12","alias_value":"DSS3EI4ZJ4QX","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_16","alias_value":"DSS3EI4ZJ4QXHCEV","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_8","alias_value":"DSS3EI4Z","created_at":"2026-05-18T12:30:12Z"}],"graph_snapshots":[{"event_id":"sha256:6d2176bda067f6ea86be4cabe82f4bf483549e8dd72871f34fc0b29b998b6332","target":"graph","created_at":"2026-05-18T00:01:47Z","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"},"paper":{"abstract_excerpt":"Every self-similar group acts on the space $X^\\omega$ of infinite words over some alphabet $X$. We study the Schreier graphs $\\Gamma_w$ for $w\\in X^\\omega$ of the action of self-similar groups generated by bounded automata on the space $X^\\omega$. Using sofic subshifts we determine the number of ends for every Schreier graph $\\Gamma_w$. Almost all Schreier graphs $\\Gamma_w$ with respect to the uniform measure on $X^\\omega$ have one or two ends, and we characterize bounded automata whose Schreier graphs have two ends almost surely. The connection with (local) cut-points of limit spaces of self-","authors_text":"Daniele D'Angeli, Ievgen Bondarenko, Tatiana Nagnibeda","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2016-01-27T22:17:58Z","title":"Ends of Schreier graphs and cut-points of limit spaces of self-similar groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.07587","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":"sha256:3109e3f9a2345065e8ff3e23ce203ac1e2841540cc4c89eae5a4026353d32adf","target":"record","created_at":"2026-05-18T00:01:47Z","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":"89152011f5fae80955c587d786e8b320b364338556e55345b56b31ea20cce996","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2016-01-27T22:17:58Z","title_canon_sha256":"1f3133811644cb17436ee68e4822c5a6b99575cdd3e9eb2f3176c0f0e027f7ee"},"schema_version":"1.0","source":{"id":"1601.07587","kind":"arxiv","version":1}},"canonical_sha256":"1ca5b223994f21738895a7960070fa9436a5c28ec4bfbb66d43501a67cb3fbae","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1ca5b223994f21738895a7960070fa9436a5c28ec4bfbb66d43501a67cb3fbae","first_computed_at":"2026-05-18T00:01:47.571610Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:01:47.571610Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"B7ZZ7ywGEQvqXb58m6HMBr1DT+jD/8Xw0G4RgDyQPlQRSTc05dPH6F6DDfLpMC/FW/L7WztkG8ly6+xvqHYiAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:01:47.572353Z","signed_message":"canonical_sha256_bytes"},"source_id":"1601.07587","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3109e3f9a2345065e8ff3e23ce203ac1e2841540cc4c89eae5a4026353d32adf","sha256:6d2176bda067f6ea86be4cabe82f4bf483549e8dd72871f34fc0b29b998b6332"],"state_sha256":"0462cce45d33ba011e9607b5a097961b150f95160531b6a93ef2033d364f9f9d"}