{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:F7GITONWQJ5AIQ3OMQHLZ7DCUZ","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":"3295751e29e2901502f0107e6538e2007193155107ed5a7309c9674dd1f311fc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2011-05-25T09:10:34Z","title_canon_sha256":"675448ec43b07a63e46a56a1a5945deaa489c07ed80b3027095b74d9395cca08"},"schema_version":"1.0","source":{"id":"1105.4969","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1105.4969","created_at":"2026-05-18T02:43:59Z"},{"alias_kind":"arxiv_version","alias_value":"1105.4969v2","created_at":"2026-05-18T02:43:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.4969","created_at":"2026-05-18T02:43:59Z"},{"alias_kind":"pith_short_12","alias_value":"F7GITONWQJ5A","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_16","alias_value":"F7GITONWQJ5AIQ3O","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_8","alias_value":"F7GITONW","created_at":"2026-05-18T12:26:28Z"}],"graph_snapshots":[{"event_id":"sha256:5417d230ee68ddbd24f71aa821bb7bfd0c92ceb5edbd03deeb9ffb906aedf415","target":"graph","created_at":"2026-05-18T02:43:59Z","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":"Let $G$ be a finitely generated torsion-free nilpotent group and $\\phi:H\\rightarrow G$ be a surjective homomorphism from a subgroup $H<G$ of finite index with trivial $\\phi$-core. For every choice of coset representatives of $H$ in $G$ there is a faithful self-similar action of the group $G$ associated with $(G,\\phi)$. We are interested in what cases all these actions are finite-state and in what cases there exists a finite-state self-similar action for $(G,\\phi)$. These two properties are characterized in terms of the Jordan normal form of the corresponding automorphism $\\widehat{\\phi}$ of th","authors_text":"Ievgen Bondarenko, Rostyslav Kravchenko","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2011-05-25T09:10:34Z","title":"Finite-state self-similar actions of nilpotent groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.4969","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:a122156c30076c5e18556872dd0e8bcd7a8bf6ba59ea76ee119fb2e2759a2f58","target":"record","created_at":"2026-05-18T02:43:59Z","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":"3295751e29e2901502f0107e6538e2007193155107ed5a7309c9674dd1f311fc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2011-05-25T09:10:34Z","title_canon_sha256":"675448ec43b07a63e46a56a1a5945deaa489c07ed80b3027095b74d9395cca08"},"schema_version":"1.0","source":{"id":"1105.4969","kind":"arxiv","version":2}},"canonical_sha256":"2fcc89b9b6827a04436e640ebcfc62a674b914ac019d9e5bf890269a31a0d536","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2fcc89b9b6827a04436e640ebcfc62a674b914ac019d9e5bf890269a31a0d536","first_computed_at":"2026-05-18T02:43:59.509935Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:43:59.509935Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CPaxN72RuPRGYo3x9AbB8W2N4fFCKGtv00iG3XRtzzvbYUifod/97xBkNIlnKlzEXIPdatiNc1M2UVX6JPFdAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:43:59.510364Z","signed_message":"canonical_sha256_bytes"},"source_id":"1105.4969","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a122156c30076c5e18556872dd0e8bcd7a8bf6ba59ea76ee119fb2e2759a2f58","sha256:5417d230ee68ddbd24f71aa821bb7bfd0c92ceb5edbd03deeb9ffb906aedf415"],"state_sha256":"ff1258e52140a1336bc4796759fbe51f2180e05c32ff4cd855ab8a4cb5b8823e"}