Constants, Coherence, and Ontological Invariance SeriesFeigenbaum’s δ is interpreted as the transition constant of coherence bifurcation, the invariant contraction ratio by which a system that can no longer remain singular preserves coherence through recursive branching. Feigenbaum’s constant δ is usually introduced as the universal scaling ratio governing period-doubling routes to chaos. Its significance lies not merely in its numerical value, but in the fact that the same ratio appears across many systems whose local equations differ. This paper proposes a coherence-based interpretation of Feigenbaum scaling. Rather than treating bifurcation as a merely technical event in nonlinear maps, we interpret it as a universal mode of coherence redistribution under increasing phase tension. The paper introduces a minimal formal spine: a coherence scalar field over direction-sensitive phaspace, a phase-tension threshold condition, a bifurcation operator, and the standard Feigenbaum interval-scaling law. In this framework, a stable attractor functions as a coherence carrier. When local phase tension exceeds the carrying capacity of a singular attractor, the system bifurcates into nested resonance branches. Feigenbaum’s δ is then interpreted as the invariant contraction ratio governing successive phase-tension gaps under recursive bifurcation. The paper does not claim to replace the standard renormalization-based theory of Feigenbaum universality. Rather, it proposes an ontological reinterpretation: Feigenbaum scaling may be the mathematical trace of a deeper coherence-bifurcation principle. Chaos is therefore not understood as the simple absence of order, but as coherence distributed through recursive branching beyond singular attractor stability. The appendices present a derivation pathway based on phase-tension conservation, branch inheritance, and recursive contraction, while explicitly distinguishing this pathway from a completed conventional proof. The broader implication is that bifurcation may be intrinsic to phaspace. Logical opposition, biological differentiation, vascular and neural branching, and hyperfractal morphology may be interpreted as higher-order analogues of coherence-preserving bifurcation. These extensions are offered as structural research directions rather than as direct numerical claims. The central thesis is that Feigenbaum’s δ functions as a transition constant: when coherence can no longer remain singular, it branches; when branching remains coherent, complexity emerges. Keywords Feigenbaum constant; period doubling; bifurcation; chaos theory; universality; coherence; phase tension; nonlinear dynamics; hyperfractal phaspace; morphogenesis; logical bifurcation; complexity; emergence
Philip Lilien (Thu,) studied this question.