A Unified Structural Theory of Time: PQR Coherence, the Spiral Coherence Clock, and the Emergent Arrow of Time

This paper presents a structural theory of time grounded in the universal triad of Pattern (P), Process (Q), and Rhythm (R). The Spiral Coherence Clock (SCC) is defined as the generative engine of temporal existence: top = SCC(t) = P(t)Q(t)R(t). In this framework, time is not a background dimension but the emergent rhythm of coherent systems. The macroscopic arrow of time emerges from monotonic, non-oscillatory drift in at least one factor. Three results are established. First, across an adversarial cross-scale test spanning atomic, mechanical, stellar, single-particle, and massless photon systems, a system keeps intrinsic time if and only if all three factors are present. Second, the multiplicative form of the clock is selected quantitatively by the measured composition of independent time dilations in the Global Positioning System (+38.5 us/day). Third, when coherent form is fed back as the next Pattern via the recursion Pn+1 = Fn, the persistence threshold SC >= 1 is derived as the fixed-point boundary of the feedback rather than assumed. Time remains one of the most conceptually unresolved constructs in science. General relativity treats it as a geometric coordinate; thermodynamics ties its direction to entropy; quantum mechanics treats it as an external parameter. No single account spans the scales at which time is actually read, from hyperfine atomic transitions to biological aging. This paper proposes a structural solution: time is the emergent rhythm of coherent systems, dynamically generated by an irreducible triad of Pattern, Process, and Rhythm. The construction is dimensionless and cross-scale, and yields the operational clock, the arrow, and the persistence threshold from a single product.