{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:RJ4H2QRUU4VIZQQCIER7KB5MP6","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":"1daf8176d008fb8a906142198c4a6b9e271929267e050d18bdf8fd2b1aed505d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2019-01-15T10:12:23Z","title_canon_sha256":"c716347db6c5f3758bafde8eb1f1e7aa0838fcb6617626a657ced5f4161fe25b"},"schema_version":"1.0","source":{"id":"1901.04743","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1901.04743","created_at":"2026-05-17T23:56:09Z"},{"alias_kind":"arxiv_version","alias_value":"1901.04743v2","created_at":"2026-05-17T23:56:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1901.04743","created_at":"2026-05-17T23:56:09Z"},{"alias_kind":"pith_short_12","alias_value":"RJ4H2QRUU4VI","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_16","alias_value":"RJ4H2QRUU4VIZQQC","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_8","alias_value":"RJ4H2QRU","created_at":"2026-05-18T12:33:27Z"}],"graph_snapshots":[{"event_id":"sha256:1aae4ee722a04b59434d4332ddb0c95ebddbbf87aa9c90f1d38955ea684cd6e6","target":"graph","created_at":"2026-05-17T23:56:09Z","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":"This paper introduces and studies a notion of \\emph{algorithmic randomness} for subgroups of rationals. Given a randomly generated additive subgroup $(G,+)$ of rationals, two main questions are addressed: first, what are the model-theoretic and recursion-theoretic properties of $(G,+)$; second, what learnability properties can one extract from $G$ and its subclass of finitely generated subgroups?\n  For the first question, it is shown that the theory of $(G,+)$ coincides with that of the additive group of integers and is therefore decidable; furthermore, while the word problem for $G$ with resp","authors_text":"Alexander Melnikov, Bakhadyr Khoussainov, Frank Stephan, Karen Seidel, Sanjay Jain, Wei Li, Ziyuan Gao","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2019-01-15T10:12:23Z","title":"Random Subgroups of Rationals"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.04743","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":"sha256:951e742c331eb653bc99b669562f1d0f9701e35a55ce4fe4ad5016619cdd104a","target":"record","created_at":"2026-05-17T23:56:09Z","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":"1daf8176d008fb8a906142198c4a6b9e271929267e050d18bdf8fd2b1aed505d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2019-01-15T10:12:23Z","title_canon_sha256":"c716347db6c5f3758bafde8eb1f1e7aa0838fcb6617626a657ced5f4161fe25b"},"schema_version":"1.0","source":{"id":"1901.04743","kind":"arxiv","version":2}},"canonical_sha256":"8a787d4234a72a8cc2024123f507ac7fa6f0e2041d522fb8e41fb4825e244d51","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8a787d4234a72a8cc2024123f507ac7fa6f0e2041d522fb8e41fb4825e244d51","first_computed_at":"2026-05-17T23:56:09.159305Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:56:09.159305Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xZd2BbLe5WT/tZ1ZqDMtcsiOtHFnqTpNBMJgGQ58CwfASETI7u1YqP0dikXzKv6tSODqHciHt8zCbGQYIOjmBQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:56:09.159934Z","signed_message":"canonical_sha256_bytes"},"source_id":"1901.04743","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:951e742c331eb653bc99b669562f1d0f9701e35a55ce4fe4ad5016619cdd104a","sha256:1aae4ee722a04b59434d4332ddb0c95ebddbbf87aa9c90f1d38955ea684cd6e6"],"state_sha256":"89354cd155bb87611a50cae51aed749254acd3bdad2c8c5b42c83770bf597e4a"}