{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:5NGZOSE5WBV7PK5HNEKB6E2LCP","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":"1d40218ae4d20d624d3e33307b082d90b1dfd0910a463989bc36884a5326841f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2012-04-19T08:17:43Z","title_canon_sha256":"6274283bef75411eaa2ace73615a81f2d197c12d5618c6a926b4ebf4396e7af2"},"schema_version":"1.0","source":{"id":"1204.4279","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1204.4279","created_at":"2026-05-18T03:57:27Z"},{"alias_kind":"arxiv_version","alias_value":"1204.4279v1","created_at":"2026-05-18T03:57:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.4279","created_at":"2026-05-18T03:57:27Z"},{"alias_kind":"pith_short_12","alias_value":"5NGZOSE5WBV7","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_16","alias_value":"5NGZOSE5WBV7PK5H","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_8","alias_value":"5NGZOSE5","created_at":"2026-05-18T12:26:56Z"}],"graph_snapshots":[{"event_id":"sha256:f199d9c9df6599fe0b2ca2131c49726f3e1800eca10dccf16cdf671cc0c6f87a","target":"graph","created_at":"2026-05-18T03:57:27Z","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":"Self-similar groups provide a rich source of groups with interesting properties; e.g., infinite torsion groups (Burnside groups) and groups with an intermediate word growth. Various self-similar groups can be described by a recursive (possibly infinite) presentation, a so-called finite $L$-presentation. Finite $L$-presentations allow numerous algorithms for finitely presented groups to be generalized to this special class of recursive presentations. We give an overview of the algorithms for finitely $L$-presented groups. As applications, we demonstrate how their implementation in a computer al","authors_text":"Ren\\'e Hartung","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2012-04-19T08:17:43Z","title":"Investigating self-similar groups using their finite $L$-presentation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.4279","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":"sha256:12cf73102d292cbd4c726dddede12e53eb8b67113e6b236828c1a45930839123","target":"record","created_at":"2026-05-18T03:57:27Z","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":"1d40218ae4d20d624d3e33307b082d90b1dfd0910a463989bc36884a5326841f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2012-04-19T08:17:43Z","title_canon_sha256":"6274283bef75411eaa2ace73615a81f2d197c12d5618c6a926b4ebf4396e7af2"},"schema_version":"1.0","source":{"id":"1204.4279","kind":"arxiv","version":1}},"canonical_sha256":"eb4d97489db06bf7aba769141f134b13c443bc3e810916b2a7916daf6406034f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"eb4d97489db06bf7aba769141f134b13c443bc3e810916b2a7916daf6406034f","first_computed_at":"2026-05-18T03:57:27.970019Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:57:27.970019Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zfU1LkDJzWarMzJhq+XtVdQLqk70Hb1VO9tPiEE15dcNvB+kR1r0p2ZJxNWoqyhmLjck6CBLnlaPHneGyng5AA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:57:27.970575Z","signed_message":"canonical_sha256_bytes"},"source_id":"1204.4279","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:12cf73102d292cbd4c726dddede12e53eb8b67113e6b236828c1a45930839123","sha256:f199d9c9df6599fe0b2ca2131c49726f3e1800eca10dccf16cdf671cc0c6f87a"],"state_sha256":"bed2f0871c0519c399447ab90058eb18d4bbb2e0754c024ca03d8f5bafad886b"}