A representation of a system resolves some perturbations of its states and leaves others undetected, and the orbit-stabiliser relation turns that division into an exact two-term conservation law for information. Between the perturbations that move nothing and those that move the output without any law lies a third class, the perturbations that move the output by a single fixed symmetry of the value space. We prove that, once a groupAof admissible value symmetries is fixed, this class is governed by one canonical object. The covariant perturbations form a group, the twisted stabiliser, and the quotientBthey realise over the invisible subgroup is the maximal quotient of perturbations carried by a state-independent value-space law, and it is universal, in that every admissible state-independent law-symbol assignment factors through it uniquely. The quotient induces an exact tripartite refinement of the conservation law, log|G|= log|Orb G (φA) |+ log|B|+ log|Stab|, an exact noiseless channel of capacitylog|B|, and the entropy splitH (X|M) =H ∂+Hᵢnvin the uniform finite setting. A converse limits the refinement, since the identity determines the sizes of the three sectors but not the boundary homomorphism itself, for which inequivalent orientations share identical identities. The sector classification extends beyond finite counting, to Haar measure, Lie dimension, and Hausdorff dimension for tail-set residuals, and the operational reading separates the algebraic existence of the boundary from the injectivity of the access map that reads its symbol.
Csaba Balogh (Fri,) studied this question.