Feigenbaum Scaling as a Coherence Invariant A Structural Reconstruction of Period-Doubling Universality within the Unified Coherence Closure Framework

Feigenbaum scaling is not chaos; it is the coherence-structured precondition that makesthe route to chaos possible.Feigenbaum’s constant is one of the central universal quantities in nonlinear dynamics, governing the geometric scaling of period-doubling bifurcations on the route to chaos. It is commonly associated with chaotic systems, yet the scaling relation itself appears before fully developed chaotic motion. This paper proposes a structural reconstruction of Feigenbaum scaling within the Unified Coherence Closure Framework, with UCTE understood as its physical and cosmological expression. Bifurcation is interpreted as a coherence-preserving response to accumulated phase tension, and universal scaling is understood as the signature of constrained redistribution under minimal phase-gradient conditions. Rather than treating Feigenbaum’s constant as a map specific numerical artifact or merely as a formal renormalization-group eigenvalue, the paper interprets it as a coherence invariant: a universal ratio governing structural reorganization before chaos. Renormalization-group theory is preserved as the established mathematical description of how the scaling repeats, while the coherence framework supplies an ontological account of why such scaling appears across diverse systems. Feigenbaum scaling is therefore not chaos itself; it is the coherence-structured precondition that makes the route to chaos possible. Keywords Feigenbaum constant; coherence invariant; bifurcation scaling; period-doubling; chaos theory; phase tension;renormalization group; universality; Finslerian phaspace; Unified Coherence Closure Framework; UCTE