Beyond the Free-Energy Principle: Embedding and Expressive Limits in the Möbius Reflective Geometry
Year: 2026
Type: preprint
Abstract: This preprint gives a non-adversarial state-space analysis of the relation between the Free-Energy Principle and the MOBIUS reflective framework. It does not claim that the Free-Energy Principle is wrong, useless, or refuted. Instead, it locates FEP as a special case of a larger reflective geometry. The paper states and proves an Embedding Theorem showing that FEP-style gradient dynamics can be reproduced exactly on an invariant submanifold where reflective coordinates are frozen. It then states an Expressive Limitation Theorem: once reflective coordinates such as question geometry, subject mode, ethical tensor, and reflective gain are allowed to vary, there exist behaviorally distinct cases that no policy on the original FEP state manifold can distinguish. Finally, it states a Reflective No-Go Principle for non-integrable reflective fields, where no single global scalar potential can organize the full dynamics. The paper introduces no new physics and makes no claims about open problems in mathematics or physical theory.
Author: Toeda, Taiko
Language: English
Subfield: Cognitive Neuroscience
Field: Neuroscience
Domain: Life Sciences
Open Access status: green
OpenAlex ID: W7165006882