{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:GJ4RVJH2LF2JNW2QIFHW24NB5N","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":"feafbc06c1cb3dc58ded9fef1dfacea5c8637b7561b1af58cdea620211e97f4d","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2009-02-12T14:33:23Z","title_canon_sha256":"ed24474719265be2c88f067a3ef19187abb4635a25cfaac2c20cc38863ca56fc"},"schema_version":"1.0","source":{"id":"0902.2119","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0902.2119","created_at":"2026-05-17T23:44:05Z"},{"alias_kind":"arxiv_version","alias_value":"0902.2119v2","created_at":"2026-05-17T23:44:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0902.2119","created_at":"2026-05-17T23:44:05Z"},{"alias_kind":"pith_short_12","alias_value":"GJ4RVJH2LF2J","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_16","alias_value":"GJ4RVJH2LF2JNW2Q","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_8","alias_value":"GJ4RVJH2","created_at":"2026-05-18T12:25:59Z"}],"graph_snapshots":[{"event_id":"sha256:d49d2a994eb6e832c44c36bb8c3b3c056d85b62c7d16478c773a8bef95ebe33b","target":"graph","created_at":"2026-05-17T23:44:05Z","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":"We show that there is no algorithm deciding whether the maximal residually free quotient of a given finitely presented group is finitely presentable or not.\n  Given a finitely generated subgroup G of a finite product of limit groups, we discuss the possibility of finding an explicit set of defining equations (i.e. of expressing G as the maximal residually free quotient of an explicit finitely presented group).","authors_text":"Gilbert Levitt, Vincent Guirardel","cross_cats":["math.GT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2009-02-12T14:33:23Z","title":"Computing equations for residually free groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0902.2119","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:dea0375b56321dfcaa53df8be728c24ecde63af08aa1c2973cc010eb87a24481","target":"record","created_at":"2026-05-17T23:44:05Z","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":"feafbc06c1cb3dc58ded9fef1dfacea5c8637b7561b1af58cdea620211e97f4d","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2009-02-12T14:33:23Z","title_canon_sha256":"ed24474719265be2c88f067a3ef19187abb4635a25cfaac2c20cc38863ca56fc"},"schema_version":"1.0","source":{"id":"0902.2119","kind":"arxiv","version":2}},"canonical_sha256":"32791aa4fa597496db50414f6d71a1eb65dae1157699ce691093616243372705","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"32791aa4fa597496db50414f6d71a1eb65dae1157699ce691093616243372705","first_computed_at":"2026-05-17T23:44:05.069258Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:44:05.069258Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2204nqmix1G1qCstOz6/jp1ITH4fIzpliQR5DJvh6AhJsAsGcofVimlWQgx1lvmCf0cHf3sob1unDgPEIHOCDQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:44:05.069658Z","signed_message":"canonical_sha256_bytes"},"source_id":"0902.2119","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dea0375b56321dfcaa53df8be728c24ecde63af08aa1c2973cc010eb87a24481","sha256:d49d2a994eb6e832c44c36bb8c3b3c056d85b62c7d16478c773a8bef95ebe33b"],"state_sha256":"2c29bb0869426a3acb442d98a9f71bc8db184c8668ebd68fba79208f0dd3b33b"}