{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:5HP6OCLWJSMNPAYCHL4TXHIXLD","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":"3d6cbdb033f12456a9dfe864c2461dac866c917f52c4f38e21fb98338171d6c7","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-02-24T13:05:42Z","title_canon_sha256":"bd3942f13972bf149393b263c9bfc5727658d8936d650cea3d9c069f75bd5293"},"schema_version":"1.0","source":{"id":"1102.4979","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1102.4979","created_at":"2026-05-18T01:32:11Z"},{"alias_kind":"arxiv_version","alias_value":"1102.4979v1","created_at":"2026-05-18T01:32:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1102.4979","created_at":"2026-05-18T01:32:11Z"},{"alias_kind":"pith_short_12","alias_value":"5HP6OCLWJSMN","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_16","alias_value":"5HP6OCLWJSMNPAYC","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_8","alias_value":"5HP6OCLW","created_at":"2026-05-18T12:26:20Z"}],"graph_snapshots":[{"event_id":"sha256:e69a4a915d9bbfc0d2e070954f9139e116f639026cce075769b629d69000e393","target":"graph","created_at":"2026-05-18T01:32:11Z","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":"Mother groups are the basic building blocks for polynomial automaton groups. We show that, in contrast with mother groups of degree 0 or 1, any bounded, symmetric, generating random walk on the mother groups of degree at least 3 has positive speed. The proof is based on an analysis of resistance in fractal mother graphs. We give upper bounds on resistances in these graphs, and show that infinite versions are tran- sient.","authors_text":"Balint Virag, Gideon Amir","cross_cats":["math.GR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-02-24T13:05:42Z","title":"Positive speed for high-degree automaton groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.4979","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:d68cf028d4f2a655deaba09d4294eff481b946342e7d48b73fab1e1a38f68ee4","target":"record","created_at":"2026-05-18T01:32:11Z","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":"3d6cbdb033f12456a9dfe864c2461dac866c917f52c4f38e21fb98338171d6c7","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-02-24T13:05:42Z","title_canon_sha256":"bd3942f13972bf149393b263c9bfc5727658d8936d650cea3d9c069f75bd5293"},"schema_version":"1.0","source":{"id":"1102.4979","kind":"arxiv","version":1}},"canonical_sha256":"e9dfe709764c98d783023af93b9d1758ee84317a7fc8fdd6181df6084aa406c0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e9dfe709764c98d783023af93b9d1758ee84317a7fc8fdd6181df6084aa406c0","first_computed_at":"2026-05-18T01:32:11.167562Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:32:11.167562Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"AsfOCLmUeNHtLgSd+ws2eq9bEjvri7vnQcHS8CRW0oTpATObwo6Dax+I66YxsX6BNqKzSwZRNBpeB3uOmOjsCg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:32:11.168238Z","signed_message":"canonical_sha256_bytes"},"source_id":"1102.4979","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d68cf028d4f2a655deaba09d4294eff481b946342e7d48b73fab1e1a38f68ee4","sha256:e69a4a915d9bbfc0d2e070954f9139e116f639026cce075769b629d69000e393"],"state_sha256":"8c787f2683ef8c41d20b497765996f376e899f97ca8b9ad5d49cc0443d908a8e"}