The Missing Lock: Why Relational Time Requires a Coherence Threshold (λ(c)) A Constructive Critique of Carlo Rovelli’s Relationalism

Contemporary relationalism, most notably the program developed by Carlo Rovelli, posits that time is not a fundamental dimension but an emergent effect of correlations between physical systems. However, this framework faces a significant ontological gap: the insufficient specification of the conditions under which temporal order arises. By treating relations as generative of time, relationalism does not clearly distinguish between incoherent relational noise and robust, directed temporal order. This paper introduces a mediating ontological condition: the Coherence Threshold (λ (c) ​ ). Drawing on the Superrhythm framework, I argue that operational time is not a passive byproduct of relations but an achieved state arising only when a system exceeds a critical level of phase coherence. Temporal endurance, in turn, depends on an active info-structural process in which the rate of coherence reconstruction matches or exceeds the rate of dissipation (T rek ​ ≤T dys ​ ). Empirical phenomena such as the abrupt bioelectrical synchronization observed in the embryonic zebrafish heart (Zhang et al., Nature, 2023) can be interpreted as indicative of such threshold dynamics. On this view, the emergence of operational time is not gradual but phase-like, involving a discrete transition into global coordination. The proposed framework does not reject relationalism, but supplements it by specifying the conditions under which relations become temporally operative. CONCEPTUAL SUMMARY — SEVEN CORE THESES OF SUPERRHYTHM (Condensed statement of the theory’s ontological commitments): 1. Time is not an a priori background; it is an achieved operational state. 2. Relations are necessary but insufficient for the emergence of temporal order. 3. Operational time arises only upon crossing a discrete coherence threshold, lambda(c). 4. A system endures if and only if its rate of phase reconstruction matches or exceeds dissipation: Trek≤ Tdys. 5. The Superrhythm can be understood as a global phase structure stabilizing nested fractal cascades across scales. 6. To be is to actively maintain phase, not merely to occupy a coordinate. 7. The transition from relational noise to operational being takes the form of a phase-like ontological switch.