Current status
The published article claims that a many-to-one observable map is sufficient to prevent every Bell-factorisable completion. Its proof restricts the hidden variable to a function of observable data. Bell locality permits the complete underlying configuration itself as the conditioning variable, so that restriction does not address the claimed theorem.
Decisive countermodel
Let $\Omega=\{-1,+1\}^4\times\{0,1\}$ with the uniform measure and $\Pi_{xy}(A_0,A_1,B_0,B_1,r)=(A_x,B_y)$. Every $\Pi_{xy}$ has fibres of size eight. Nevertheless, $\lambda=\omega$ gives deterministic local responses, a measure independent of the settings, and CHSH $=0$.
More generally, an independent erased label makes any Bell-local model non-injective without changing any observable statistic.
PR-box defect
The proposed global assignment requires $a_0b_0=a_0b_1=a_1b_0=+1$ and $a_1b_1=-1$. Multiplying the four constraints gives $+1=-1$. The support is empty, so no normalised measure reproduces the claimed PR-box distribution.
Entropy and surviving statement
The quantity called projection entropy is the Shannon entropy of the output distribution, not a measure of non-injectivity. A constant, maximally non-injective map gives zero output entropy, while an injective map can give maximal output entropy. The proposed entropy–CHSH interpolation therefore has no derived endpoints.
The standard Bell statement remains valid: a Bell violation excludes a common Bell-local factorisation under the usual assumptions. What is missing from Cosmochrony is a derived obstruction to a setting-independent global coupling across measurement contexts. Non-injectivity alone does not provide that obstruction.
Bibliographic record
Beau, J. Breakdown of Bell Factorization from Non-Injective Effective Descriptions. Quantum Reports 2026, 8, 44. DOI 10.3390/quantum8020044. This page records the scientific status of that publication; it is not a silent replacement of the version of record.