Complexity as a Gauge Artefact: A Counter-Article on Weakness, Abstraction, and Admissibility Curvature

Abstract This paper argues that recent claims that “complexity is an illusion” are not empirical discoveries but gauge artefacts produced by granting an inadmissibly rich descriptive vocabulary. In maximal-vocabulary regimes (e.g., allowing all set-theoretic predicates over the environment), description length collapses to singleton naming and thereby trivializes any complexity proxy by construction. We show that this collapse is not “no abstraction” but an extreme abstraction that presupposes an exterior catalogue of distinctions, unavailable to any operational learner. To restore operational meaning, we replace static language games with an immanent admissibility geometry induced by an interface (membrane) M: Φ → Y. Admissible continuations form a metric–measure space (D, g, μ) whose transport structure (connection) and intrinsic invariants (scalar curvature) quantify brittleness under deformation. We introduce availability volume V and admissibility curvature κ as membrane-compatible observables and define a deformation-stability functional G that remains non-trivial under bounded-distortion (bi-Lipschitz) gauge changes. Recursio Intensitatis (RI) is modelled as a curvature-transport flow with drift and scaling; δ* acts as a controlled regime reconfiguration of geometry and measure. A numerical audit appendix reports a reference RI run with explicit non-collapse and bounded-distortion diagnostics, illustrating that the proposed invariants are computable and resistant to representational quotienting. The result is a shift from “complexity versus weakness” to a geometry of admissibility: what matters is not how short a description can be made under an unlimited vocabulary, but how availability and curvature behave under membrane-constrained deformations. Keywords admissibility geometry; gauge artefact; complexity measures; generalization; weakness; abstraction; metric–measure space; scalar curvature; Christoffel symbols; Ricci flow; deformation invariants; bounded distortion; bi-Lipschitz; interface constraint; Recursio Intensitatis; delta* operator; robustness under shift; operational semantics