OpenAI · 286-02 · 2026-09-23 · Operator algebras
The arithmetic category and stable recovery of lattice factors
preprints/The-arithmetic-category-and-stable-recovery-of-lattice-factors-September-23-2026
Family 286. Arithmetic rigidity of lattice von Neumann algebras.
The authors are OpenAI. This companion does not verify the proof and does not adopt it as a theorem of Ngo Cheung’s series. It is not a premise. O.1 stays NOT_CLOSED. Anti-de Sitter results are not a de Sitter state, not Em02-E’s relational lapse, not XVI-P’s QdS scheme, and not XVI-Q’s sigma-image record. No quantum coefficient is admitted. No compilation is asserted.
Read against the standing problems
Standing problems. No standing problem is named in this text. It was still read against the nine problems and does not close any of them. The authors are OpenAI. The companion does not verify the proof. This is not a premise of a manuscript by Ngo Cheung. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted. XVI-P · XVI-N
Classifies finite-index bimodules between scalar-twisted group factors of ICC groups commensurable with property- lattices over characteristic-zero local fields and arbitrary ICC group factors. Every such bimodule is a summand of finite sums of models arising from finite-index subgroup isomorphisms and finite-dimensional projective representations. The classification also recovers the group, scalar cocycle and amplification scale up to the stated stable equivalence.
We prove stable canonical recovery for scalar-twisted group factors of ICC groups commensurable with property- lattices over characteristic-zero local fields. Every specified stable isomorphism to a scalar-twisted factor of any countably infinite ICC group recovers the group, the cocycle up to a normalized cochain, and equal amplification scales, with an implementing partial isometry in the given matrix corners. We compute the arithmetic correspondence subcategory for arbitrary countable ICC groups, including all bounded maps, summands, conjugates, and Connes fusion, and combine it with the companion's arithmetic exhaustion theorem. Multiplication also recovers arbitrary finite-index factor neighbors, with the exact projective condition on the matched cocycle ratio.
Preprint source and Lean scope
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