RAYOBETH Atlas Preregistration, Version 1.1: Amendment on the Blind Coding of Reflexivity, Outcome Classes and Fixed Core Years

Preregistered protocol, deposited before any analysis of the RAYOBETH Atlas data. The attached protocol and preregistration form fix the hypotheses, sampling frame, coding rules, estimators and falsification thresholds in advance. Description RAYOBETH Theory models any stock N that is generated and removed as dN/dt = sigma + c N^beta − (k0 + k N^phi), where beta is the generative elasticity (how generation scales with the stock), phi is the control elasticity (how removal scales with it), sigma is reseeding and k0 is a fixed core of removal capacity. Its core consists of three laws, stated and proved in the attached protocol (Ndambiri, 2026, “The RAYOBETH Core”). The regime law classifies stocks as contracting, bounded, exponential or explosive. The duality law shows that a stock can be driven to zero from some level if and only if it can grow without bound from another, which happens exactly when beta exceeds phi; when phi exceeds beta the stock has a stable positive floor, and zero is reachable only with a fixed core of capacity. The reflexive closure law shows that under constant returns explosion is impossible, and that it requires the system to reproduce its own inputs, at least one of which is nonrival. These motivate the reflexivity conjecture: natural and social systems are bounded unless they are reflexive. The RAYOBETH Atlas will estimate beta, phi, the gap Delta = phi − beta and the endgame elasticity for 60 systems in six domains (life and ecology; health and disease; environment and energy; economy and finance; technology and knowledge; society, governance and security), using public time series and one estimation protocol fixed in advance. Reflexivity will be coded blind, before estimation. The study tests five hypotheses with stated falsifiers and compares the forecasting performance of the theory with standard growth models. The full protocol, sampling frame and decision rules are in the accompanying protocol, which forms part of this preregistration. Hypotheses H1 (Bounded world). Non reflexive systems lie in the bounded regime: their generative elasticity beta is below one. Falsified if more than 5% of non reflexive systems have a 95% interval for beta lying wholly above one, or at least three such systems if fewer than 60 systems are coded non reflexive. H2 (Reflexivity conjecture). Reflexive systems have higher generative elasticities than non reflexive systems, and account for most estimates above one. Directional prediction: pooled mean beta is higher for reflexive systems by at least 0.2, and the odds that beta exceeds one are higher for reflexive systems. Falsified if the difference in pooled means is below 0.2 or the 95% interval of the odds ratio includes one. H3 (Duality law). Systems that reached zero or near zero were threshold systems (Delta < 0) in their final removal phase, and systems that settled on a floor were attractor systems (Delta > 0). Falsified if Delta is significantly positive in a majority of eliminated systems, or significantly negative in a majority of floor systems. H4 (Two instrument principle). Eliminations follow the introduction of a fixed core of removal capacity (control whose strength does not fall with the stock), dated before estimation. Prediction: the rate of decline accelerates after the dated introduction. Falsified if there is no acceleration in a majority of eliminated systems. H5 (Predictive value). Out of sample, forecasts from the RAYOBETH phase model are at least as accurate as those of exponential, logistic, Gompertz and Richards models. Falsified if the RAYOBETH model has a larger root mean squared error in logs than the logistic or the Richards model in a majority of systems.