{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:5T7HMN57J2FU2BMOGFFGA6LYXU","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":"83f9e77fcc77fa9338565ece0e7b75cbb6091b33f388651cc408ee4f78995bf8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2011-10-13T18:00:43Z","title_canon_sha256":"79e57620476f758ca9e14c83c7a35b643d8f5c2613f5d21650cda02e17dfa7b1"},"schema_version":"1.0","source":{"id":"1110.3016","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.3016","created_at":"2026-05-18T03:39:51Z"},{"alias_kind":"arxiv_version","alias_value":"1110.3016v3","created_at":"2026-05-18T03:39:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.3016","created_at":"2026-05-18T03:39:51Z"},{"alias_kind":"pith_short_12","alias_value":"5T7HMN57J2FU","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_16","alias_value":"5T7HMN57J2FU2BMO","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_8","alias_value":"5T7HMN57","created_at":"2026-05-18T12:26:20Z"}],"graph_snapshots":[{"event_id":"sha256:d05e1ecd1afd6b5e50c557e30961386a1c5ffc1c7d7372d256418eb312b40792","target":"graph","created_at":"2026-05-18T03:39:51Z","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 a unitary commutative real algebra and $K\\subseteq Hom(R,\\mathbb{R})$, closed with respect to the product topology. We consider $R$ endowed with the topology $\\mathcal{T}_K$, induced by the family of seminorms $\\rho_{\\alpha}(a):=|\\alpha(a)|$, for $\\alpha\\in K$ and $a\\in R$. In case $K$ is compact, we also consider the topology induced by $\\|a\\|_K:=\\sup_{\\alpha\\in K}|\\alpha(a)|$ for $a\\in R$. If $K$ is Zariski dense, then those topologies are Hausdorff. In this paper we prove that the closure of the cone of sums of 2d-powers, $\\sum R^{2d}$, with respect to those two topologies is equ","authors_text":"Mehdi Ghasemi, Salma Kuhlmann","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2011-10-13T18:00:43Z","title":"Closure of the cone of sums of 2d-powers in real topological algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.3016","kind":"arxiv","version":3},"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":"sha256:2f22d7df20e2bf330895b3348c7d1f3f33b444cf7fb55083be60370afffe9d29","target":"record","created_at":"2026-05-18T03:39:51Z","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":"83f9e77fcc77fa9338565ece0e7b75cbb6091b33f388651cc408ee4f78995bf8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2011-10-13T18:00:43Z","title_canon_sha256":"79e57620476f758ca9e14c83c7a35b643d8f5c2613f5d21650cda02e17dfa7b1"},"schema_version":"1.0","source":{"id":"1110.3016","kind":"arxiv","version":3}},"canonical_sha256":"ecfe7637bf4e8b4d058e314a607978bd203f8fa8fc87f352374d9ac2088fcb88","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ecfe7637bf4e8b4d058e314a607978bd203f8fa8fc87f352374d9ac2088fcb88","first_computed_at":"2026-05-18T03:39:51.140953Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:39:51.140953Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"befPhtM+QeQJ9+M2t3comGhGyh+Lbh1zvM9gkVQehnjrP0wR1vMLFJ571Ut0QjGjJYCrq0uSRvKYZp2Frkn0Bw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:39:51.141477Z","signed_message":"canonical_sha256_bytes"},"source_id":"1110.3016","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2f22d7df20e2bf330895b3348c7d1f3f33b444cf7fb55083be60370afffe9d29","sha256:d05e1ecd1afd6b5e50c557e30961386a1c5ffc1c7d7372d256418eb312b40792"],"state_sha256":"6934be5d124561d2ae412c6beb38f3f37e661c5bab17e032d4aeb33c8c3b163a"}