# Operator algebras > 19 AI-made results in operator algebras, each explained in plain English with its trust label, Lean status and sources. Canonical: https://closedform.nishachay.tech/science/mathematics/operator-algebras/ Last updated: 2026-10-14 19 results in OpenAI Math 2026. 19 AI-made results in operator algebras, from 31 papers in the OpenAI math collection, each explained in plain English. 15 have a formal Lean proof listed; 4 are claimed in a paper and not yet machine-checked. The oldest question here dates back to 1943: [Isomorphism of the free group factors](https://closedform.nishachay.tech/e/openai-math-2026-287/). Results rated Landmark include [Counterexamples to Baum–Connes and Kadison–Kaplansky](https://closedform.nishachay.tech/e/openai-math-2026-285/) and [Kadison's similarity conjecture](https://closedform.nishachay.tech/e/openai-math-2026-288/). ## Results (19) - [Counterexamples to Baum–Connes and Kadison–Kaplansky](https://closedform.nishachay.tech/e/openai-math-2026-285/) - Entry 285 · Claims torsion-free groups that break the Kadison–Kaplansky projection conjecture and reduced Baum–Connes. (Claimed, not checked) - [Rigidity and arithmetic of lattice von Neumann algebras](https://closedform.nishachay.tech/e/openai-math-2026-286/) - Entry 286 · Claims the von Neumann algebra of a property (T) lattice remembers its group, its twist and its scale. (Claimed, not checked) - [Isomorphism of the free group factors](https://closedform.nishachay.tech/e/openai-math-2026-287/) - Entry 287 · Proves, with a Lean check, that the free group factors L(F₂) and L(F₃) are isomorphic, settling a decades-old problem. (Formal proof listed) - [Kadison's similarity conjecture](https://closedform.nishachay.tech/e/openai-math-2026-288/) - Entry 288 · Every bounded map from a C*-algebra to operators can be straightened to respect the mirror operation. (Formal proof listed) - [Strong Kadison–Kastler stability and its spatial boundaries](https://closedform.nishachay.tech/e/openai-math-2026-289/) - Entry 289 · Proves, with a Lean check, that close von Neumann algebras are conjugate by a unitary near the identity, uniformly. (Formal proof listed) - [Relative bicentralizers and modular spectral recovery](https://closedform.nishachay.tech/e/openai-math-2026-290/) - Entry 290 · Claims every expected inclusion of von Neumann algebras holds an amenable piece with the same commutant in the core. (Formal proof listed) - [Cuntz comparison, nuclear dimension, and equivariant Jiang–Su stability](https://closedform.nishachay.tech/e/openai-math-2026-291/) - Entry 291 · Claims amenable actions on Jiang–Su-stable algebras absorb the Jiang–Su algebra, plus three regularity theorems. (Formal proof listed) - [Kirchberg's O₂ norm-ultrapower embedding problem](https://closedform.nishachay.tech/e/openai-math-2026-292/) - Entry 292 · Proves, with a Lean check, an explicit C*-algebra that fits in no nuclear norm ultrapower, answering Kirchberg. (Formal proof listed) - [Invariant projections, hyperinvariant subspaces, and transitive algebras](https://closedform.nishachay.tech/e/openai-math-2026-293/) - Entry 293 · Proves that some operators on Hilbert space have no hyperinvariant subspace, a negative answer to a long-open problem. (Formal proof listed) - [Kaplansky's quasitrace conjecture and failure of tensor-product stable finiteness](https://closedform.nishachay.tech/e/openai-math-2026-294/) - Entry 294 · Proves Kaplansky's quasitrace conjecture false, and that stable finiteness can fail for tensor products. (Formal proof listed) - [The Kadison–Ringrose cohomology conjecture](https://closedform.nishachay.tech/e/openai-math-2026-295/) - Entry 295 · Proves bounded Hochschild cohomology of von Neumann algebras vanishes in degrees two and up, settling Kadison–Ringrose. (Formal proof listed) - [The generator problem for finite factors](https://closedform.nishachay.tech/e/openai-math-2026-296/) - Entry 296 · Every type II₁ factor with separable predual is generated by a single operator. (Formal proof listed) - [A ZFC counterexample to Naimark's problem](https://closedform.nishachay.tech/e/openai-math-2026-297/) - Entry 297 · An algebra with one irreducible representation that is not the compact operators, built without extra axioms. (Formal proof listed) - [Two notions of free entropy differ even when both are finite](https://closedform.nishachay.tech/e/openai-math-2026-298/) - Entry 298 · Proves two standard notions of free entropy can differ by at least 1/2 even when both are finite. (Formal proof listed) - [The Kirchberg–Rørdam character criterion and infinite tensor-power Jiang–Su stability](https://closedform.nishachay.tech/e/openai-math-2026-299/) - Entry 299 · Proves a separable C*-algebra absorbs the Jiang–Su algebra exactly when its central-sequence algebra has no characters. (Formal proof listed) - [Approximation and quadratic strong-operator paving](https://closedform.nishachay.tech/e/openai-math-2026-300/) - Entry 300 · Claims to settle both paving conjectures of Popa and Vaes for every maximal abelian subalgebra of a von Neumann algebra. (Claimed, not checked) - [Trace cones and Razak–Jacelon stabilization](https://closedform.nishachay.tech/e/openai-math-2026-301/) - Entry 301 · Claims the trace cone determines every separable nuclear C*-algebra once stabilized by the Razak–Jacelon algebra. (Formal proof listed) - [Radius of comparison equals half the mean dimension](https://closedform.nishachay.tech/e/openai-math-2026-302/) - Entry 302 · Claims the radius of comparison of a minimal crossed product is half the mean dimension, the Phillips–Toms conjecture. (Claimed, not checked) - [Weak pure infiniteness and Cuntz-algebra absorption](https://closedform.nishachay.tech/e/openai-math-2026-303/) - Entry 303 · Proves pure infiniteness implies strong pure infiniteness in all C*-algebras, part of a Kirchberg–Rørdam question. 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