Can Fundamental Constants Be Derived as Irreducible Residues of Structural Self-Consistency?

A long-standing question in the foundations of physics concerns the status of fundamental constants: are quantities such as the speed of light c, Planck's constant ℏ, the gravitational constant G, and dimensionless couplings like the fine-structure constant α ≈ 1/137 contingent parameters that happen to take the values they do, or do they arise from some deeper principle? This paper develops a framework in which the question receives a precise answer. Five axioms characterising any system capable of sustaining persistent structure — persistence, self-reference, closure, non-degeneracy, and distinguishability — are formulated, and it is proved that any model satisfying these axioms necessarily contains free parameters that are simultaneously irreducible (not derivable from the axioms alone) and non-contingent (constrained to measure-zero subsets of parameter space by the requirement of self-consistency). These parameters are termed irreducible residues of structural self-consistency. Two classes of residues are distinguished: scale residues (dimensional constants such as c, ℏ, G that fix the units of measurement) and coupling residues (dimensionless constants such as α that fix the ratios and strengths of interactions). The central existence theorem is proved by two independent methods — a Brouwer fixed-point argument and a topological degree argument — and is illustrated by five computational toy models with numerical simulations. The framework connects to three active research programmes in theoretical physics: asymptotic safety in quantum gravity, the conformal bootstrap, and the swampland programme, identifying each as a concrete instantiation of the self-consistency mechanism. A cross-programme prediction is stated: any programme constraining parameters through self-consistency must produce discrete constraints decomposable into scale and coupling types. The anthropic principle is shown to be a special case of a more general persistence filter: the requirement is not that constants permit observers but that they permit persistent structure of any kind. Nine objections are addressed, six falsifiable predictions are identified (with explicit testability classification), and the scope and limitations of the framework are delineated. The paper includes a complete peer review and revision history documenting two rounds of review with detailed author responses. Keywords: fundamental constants, structural self-consistency, persistence, irreducible parameters, fine-structure constant, fixed-point theory, topological degree, dimensional analysis, anthropic principle, persistence filter, asymptotic safety, conformal bootstrap, swampland programme License: CC BY 4.0 Author: Boris Kriger — ORCID: 0009-0001-0034-2903 Affiliations: Information Physics Institute, Gosport, Hampshire, United Kingdom; Institute of Integrative and Interdisciplinary Research, Toronto, Canada