Beyond Zhou and Astra 2026: Conservative Reconstruction, Cabin 1/2, and Real-World Decision Risk

This record gathers the main article and technical supplements of Thierry Origas’s 13 August 2026 reassessment of contemporary mathematical results associated with Shuoxing Zhou and the Astra/OpenAI-assisted mathematics corpus. The mathematical core studies a general reconstruction problem. Given a representation P:X→Y, formal correctness inside Y does not by itself imply that P preserves every source variable required for reconstruction or for a subsequent decision. If P(x1)=P(x2) while a relevant source quantity J(x1)=J(x2), no function of P alone can universally reconstruct J. Zhou’s 2026 counterexample concerning ICC property-(T) groups and group von Neumann algebras provides a concrete mathematical witness of this distinction between formal validity and reconstructive sufficiency. The record develops this observation using information theory, Bayesian decision theory, Blackwell comparison of experiments, provenance, history variables, conservative lifting, and falsification protocols. The proposed Cabin 1/2 framework is represented abstractly by an enriched observationP̃(x) = (P(x), K(x), T(x)) where K denotes separating or provenance information and T records ordering/history information that may be absent from the projected representation. The record also examines ten contemporary AI-assisted mathematical developments as a transversal audit of the distinction between proof certification, source reconstruction, transportability and decision sufficiency. Physical interpretations involving +t, −t, a global variable T, EPR structure, or a non-local “World B” are explicitly separated from the exact mathematical results and remain hypotheses requiring independent experimental falsification. Files in this record Main Article — Zhou, Astra and Cabin 1/2. Supplement A — Detailed mathematical audit: Zhou vs Origas. Supplement B — Astra 2026 and ten related mathematical advances. Supplement C, if included — Real-world legal and information-conservation case study.