This preprint develops a dynamic extension of the “Theory of Relativity of Theories” (TRoT) and its no-meta variant, formulated entirely in law space over persistence-first holographic systems (PFHS) and fibered Bures–Hellinger–Kantorovich (FBHK) entropy–transport geometry. Instead of a single global theory catalogue, each location or agent in a PFHS/Post-FBHK universe carries a local catalogue of effective theories and a probability distribution over them. The resulting TRoT field lives in a finite product of Hellinger–Kantorovich spaces and is equipped with a product-type HK metric. Under standard geodesic-convexity assumptions, we prove existence, uniqueness, and exponential contraction of EVI gradient flows for value-anchored functionals on this field. The framework internalises evaluators, meta-evaluators, and governance mechanisms as natural-law objects in the same universe. A design-time closure axiom for Lipschitz monotone aggregators yields a finite-network collapse result: any admissible evaluator network can be represented by a single evaluation theory without introducing an external meta-agent. This “no-meta” property is interpreted as a fixed-point representation of mutual evaluation inside a closed evaluator network, while keeping meta-level choices explicit at design time. The TRoT field is then coupled to law dynamics, design parameters, defect-based self-purification, and a global theory distribution within an extended joint-contraction and input-to-state stability (ISS) framework. Functional-level Lipschitz assumptions lead to a positive linear comparison system with a Metzler matrix; spectral conditions on this matrix yield incremental exponential stability for the full architecture. Finally, we show how holographic observation quotients (HOQ) and related scalar complexity measures can be embedded into the field-level value functional so that EVI flows automatically favour theories that are both persistence-aligned and compute-efficient. The result is a law-space design discipline for superintelligent architectures, AI alignment, and AI governance, where environment models, theories, evaluators, and governance rules are treated as internal natural-law fields over a common persistence-first background.
Takahashi, K (Thu,) studied this question.