The Coercivity Law of Enaction within Fisher-Generative Informational Realism

In 1991, Varela, Thompson and Rosch introduced enaction as the process by which living systems bring forth a world through structural coupling, so that what is experienced is not passively received but actively constituted by the system’s own organisational dynamics. The concept of enaction was articulated for living systems, which in the Fisher‑Generative Informational Realism (FGIR) framework are a special class of Complex Adaptive Autopoietic Systems (CAAS). Complex Adaptive Systems (CAS) are systems that exhibit adaptive behaviour, learning, and self‑organisation in response to environmental changes; a CAAS is a CAS that additionally possesses autopoiesis, the self‑sustaining closure that distinguishes living from non‑living systems. One may find CAASs that have full-closure autopoiesis, or proto‑autopoiesis which lacks full-closure, and we explore their distinctions. The enactive programme, however, lacked a formal measure of the cost of this bringing‑forth: the compulsion by which a merely potential, dispositional state is forced into stable, enacted existence. This paper supplies that measure. That compulsion is coercivity, and its quantitative expression is the coercivity law  , the foundational structural identity of the FGIR programme. Although this equation appears throughout the FGIR Trilogy, no self‑contained derivation has previously been published. This paper establishes  as a rigorously conditional result: given the Saturation Assumption and the Yolles ontological embedding as working postulates, the coercivity law follows by rigorous derivation from the SRP and Fisher–Rao geometry. The paper’s contribution is to precisely characterise what those postulates require, to show that the derivation is valid conditional on them. The derivation proceeds in three stages. First, the Saturation–Rigidity Principle (SRP) is stated as a meta‑law imposing three simultaneous conditions on any structure that persists: capacity saturation, defect rigidity, and rapid locking. The SRP follows three operational axioms: admissibility, defect rigidity, and coercivity. Second, these axioms are applied to a general information manifold. Under saturation conditions, the admissibility energy necessarily factorises as  , where  is the total information mass and  the global coercivity constant. This factorisation emerges from the geometry of the manifold, not from an assumption. Third, the general law is specialised to probability manifolds equipped with the Fisher–Rao metric, the unique Riemannian structure invariant under all statistically legitimate transformations. The ontological embedding  identifies the abstract information potential with the Fisher information density on the operative field, yielding the FGIR coercivity law  . A freezing projection  then maps the incorporeal law onto corporeal fields via two structurally distinct pathways. The first is a direct freezing projection: under three postulates (dimensional reduction F1, constitutional identification F2, energy preservation F3),  projects onto each corporeal context, yielding a domain‑specific persistence law. Einstein’s  is one such direct projection, the most familiar, but conditional on the discharge of bridge conditions. The second pathway is the Constitutional Persistence Cycle (CPC): following Łojasiewicz rigidity lock, Berezin–Pfaffian entity collapse, and Picard–Lefschetz monodromy reset, the CPC generates a persistent random walk governed by the telegrapher’s equation, from which the Schrödinger equation (quantum), the diffusion equation (classical), and the Dirac equation (relativistic quantum) emerge as limiting cases. The Schrödinger equation is therefore more structurally significant than the Einstein projection: it is dynamic rather than static, and domain‑transcendent through the telegrapher’s equation.