{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:PO4RRE5FFM5VO3QAUFSUI4DO5V","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":"e92822b8a3c0251fd8480c17c1532d2d0ba027db551c1db11ee373c64e407d9f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2018-06-27T23:16:38Z","title_canon_sha256":"fe2446c066d3fcffe86d1d70f24920f615a53680ea12d90321a19d1edd7b7e80"},"schema_version":"1.0","source":{"id":"1806.10711","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.10711","created_at":"2026-05-18T00:12:08Z"},{"alias_kind":"arxiv_version","alias_value":"1806.10711v1","created_at":"2026-05-18T00:12:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.10711","created_at":"2026-05-18T00:12:08Z"},{"alias_kind":"pith_short_12","alias_value":"PO4RRE5FFM5V","created_at":"2026-05-18T12:32:46Z"},{"alias_kind":"pith_short_16","alias_value":"PO4RRE5FFM5VO3QA","created_at":"2026-05-18T12:32:46Z"},{"alias_kind":"pith_short_8","alias_value":"PO4RRE5F","created_at":"2026-05-18T12:32:46Z"}],"graph_snapshots":[{"event_id":"sha256:185aa43b27180e3988eb5e90556ddf583d0eab6cff76015fc04b4bf1625c710a","target":"graph","created_at":"2026-05-18T00:12:08Z","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 $R$ be an algebra over a commutative ring $k$. Suppose that $R$ is endowed with a descending filtration indexed on an ordered group $(G,<)$ such that the restriction to $k$ is positive. We show that the existence of free algebras on a certain set of generators in the induced graded ring $grad(R)$ implies the existence of free group algebras in $R$. Our best results are obtained for division rings endowed with a valuation.","authors_text":"Javier S\\'anchez","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2018-06-27T23:16:38Z","title":"Free group algebras in division rings with valuation I"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.10711","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":"sha256:8d9669038eb73a8e769d44a4eb8fc95a01cd0199c9f6f207c46dfd4cae1e2a2e","target":"record","created_at":"2026-05-18T00:12:08Z","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":"e92822b8a3c0251fd8480c17c1532d2d0ba027db551c1db11ee373c64e407d9f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2018-06-27T23:16:38Z","title_canon_sha256":"fe2446c066d3fcffe86d1d70f24920f615a53680ea12d90321a19d1edd7b7e80"},"schema_version":"1.0","source":{"id":"1806.10711","kind":"arxiv","version":1}},"canonical_sha256":"7bb91893a52b3b576e00a16544706eed77311460bdf05fbe97adb0f9e4424b2c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7bb91893a52b3b576e00a16544706eed77311460bdf05fbe97adb0f9e4424b2c","first_computed_at":"2026-05-18T00:12:08.203858Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:12:08.203858Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"C9z5QZX7Y7xSGGQvrUsZjYd3jylvYM+T9HG0Kre53nmH8PaTGrGP4wml81cn2mgDmXvnMDe3ptm3Da20SxogAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:12:08.204420Z","signed_message":"canonical_sha256_bytes"},"source_id":"1806.10711","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8d9669038eb73a8e769d44a4eb8fc95a01cd0199c9f6f207c46dfd4cae1e2a2e","sha256:185aa43b27180e3988eb5e90556ddf583d0eab6cff76015fc04b4bf1625c710a"],"state_sha256":"855e59eab2b259e599936a1a49cf89e5da994e4873725be02788a1dfd357754a"}