The Gradient-Balance Principle (GBP) identifies a recurring formal pattern—a five component tuple (S, ∂Ω, ω,H, h)—across quantum decoherence, semantic processing in neural language models, connectome development, and protein folding. Whether these instantiations are related by structure-preserving maps or merely by superficial analogy is the central open question. We address this question by embedding both quantum decoherence and transformerbased semantic dynamics in the framework of Generalised Probabilistic Theories with Memory (GPTMem), a category whose objects are ordered vector spaces equipped with discretememory kernels and whose morphisms are positive, normalisation-preserving maps that intertwinethese kernels. The holding function h of the GBP framework is identified with the operator-norm tail mass of the memory kernel; the attention mechanism of transformer architectures is identified as a discrete, state-dependent instantiation of this kernel—a formalisation of the observation by Parr, Pezzulo (2) the algebraic criterion—the chiasmus operator χ provides atest distinguishing genuine holding from thermostat behaviour; (3) the metabolic pathology— a mechanistic taxonomy of Traitor Head types (Petrifier, Leaky, Hallucinator) grounded in the fluid–solid gradient transition, with a complete Pathology Triangle; (4) the alignment reframing—alignment requires holding capacity, not merely value representation, bounded below by a semantic uncertainty relation Δτdwell · Δλ ≳ ℏsem, and the alignment conditions are constitutively incompletable.
Jonas Jakob Gebendorfer (Sat,) studied this question.