On Bayesian Mechanics: A Physics of and by Beliefs

The paper correctly asserts the Gibbs form p(x) ∝ e^{-λ J(x)} and the parallel-transport differential relation dp = −λ p dJ (equivalently ∂x log p = −λ ∂x J), and sketches a gauge-theoretic interpretation of constrained maximum entropy (see eqs. (6–9) and (10), and the claims “p(x)=e^{−λJ(x)}” and “maximum of entropy is parallel transport” ). However, the derivation omits the normalization constraint multiplier α and subsequently makes the imprecise claim that the “−1” term can be absorbed into λ (footnote 17), which mixes a constant with the multiplier of J(x) and obscures the necessary normalizing constant Z(λ) ( ). The candidate solution provides the standard, complete variational treatment with both constraints, the partition function, and the conditions for existence/uniqueness of λ, and derives the same dp = −λ p dJ relation rigorously. Hence, the model’s solution is correct and technically complete, while the paper’s argument is sound in essence but technically incomplete.