{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:MTCYGWT5ECXIPSIP34TMAPXSTG","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":"de16df7713d04df2efaecdfac1c9b39da478d802c1a8fc3d4e893e4029c6b74b","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-09-13T17:18:28Z","title_canon_sha256":"59a4427b01269390819a7b8b29883b3d02e81268f03b47cf0e2719dcfbf7d5c8"},"schema_version":"1.0","source":{"id":"1209.2966","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1209.2966","created_at":"2026-05-18T03:04:49Z"},{"alias_kind":"arxiv_version","alias_value":"1209.2966v1","created_at":"2026-05-18T03:04:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.2966","created_at":"2026-05-18T03:04:49Z"},{"alias_kind":"pith_short_12","alias_value":"MTCYGWT5ECXI","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_16","alias_value":"MTCYGWT5ECXIPSIP","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_8","alias_value":"MTCYGWT5","created_at":"2026-05-18T12:27:14Z"}],"graph_snapshots":[{"event_id":"sha256:23c40a1de5a806953f62e055a94e1c7d5f72a973b985fa0783ea0eb6b8226976","target":"graph","created_at":"2026-05-18T03:04:49Z","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 $A$ be a commutative unital $\\mathbb{R}$-algebra and let $\\rho$ be a seminorm on $A$ which satisfies $\\rho(ab)\\leq\\rho(a)\\rho(b)$. We apply T. Jacobi's representation theorem to determine the closure of a $\\sum A^{2d}$-module $S$ of $A$ in the topology induced by $\\rho$, for any integer $d\\ge1$. We show that this closure is exactly the set of all elements $a\\in A$ such that $\\alpha(a)\\ge0$ for every $\\rho$-continuous $\\mathbb{R}$-algebra homomorphism $\\alpha : A \\rightarrow \\mathbb{R}$ with $\\alpha(S)\\subseteq[0,\\infty)$, and that this result continues to hold when $\\rho$ is replaced by an","authors_text":"Mehdi Ghasemi, Murray Marshall, Salma Kuhlmann","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-09-13T17:18:28Z","title":"Application of Jacobi's Representation Theorem to locally multiplicatively convex topological real Algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.2966","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:ca41d6bddb16c29e64f55f5ce86af3c9da2e7bab7649371cf936b892a4032154","target":"record","created_at":"2026-05-18T03:04:49Z","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":"de16df7713d04df2efaecdfac1c9b39da478d802c1a8fc3d4e893e4029c6b74b","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-09-13T17:18:28Z","title_canon_sha256":"59a4427b01269390819a7b8b29883b3d02e81268f03b47cf0e2719dcfbf7d5c8"},"schema_version":"1.0","source":{"id":"1209.2966","kind":"arxiv","version":1}},"canonical_sha256":"64c5835a7d20ae87c90fdf26c03ef29982c4c03bf2c62c1678889eabd6b2540d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"64c5835a7d20ae87c90fdf26c03ef29982c4c03bf2c62c1678889eabd6b2540d","first_computed_at":"2026-05-18T03:04:49.896797Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:04:49.896797Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FQRD6BzDho2e6BMwWv9OCwZTxCo6P+GcWmMsIIGA4Z7cCyl9dDB/JdN0wpDfd6AVAaoElZYWq/9iG+tlWn7HCA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:04:49.897519Z","signed_message":"canonical_sha256_bytes"},"source_id":"1209.2966","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ca41d6bddb16c29e64f55f5ce86af3c9da2e7bab7649371cf936b892a4032154","sha256:23c40a1de5a806953f62e055a94e1c7d5f72a973b985fa0783ea0eb6b8226976"],"state_sha256":"a7347357834c2c20a06201f414902fbec0bb71a84b920f62daaea1a8cb958fdb"}