This paper presents a recursive dimensional stability framework within the Chronos model in which dimensions emerge through stabilized recursive motion rather than through static spatial coordinates alone. Beginning from a dimensionless equilibrium point, the framework develops a hierarchical geometric progression involving spiral trajectories, cone expansion, toroidal circulation, spherical closure, linked sphere chains, compression-expansion dynamics, higher-order toroidal manifolds, stable radius distribution fields, and a final 11D recursive stability envelope. The framework proposes that dimensionality is fundamentally operational and coherence-based, arising through bounded recursive stabilization across scales. Stability is governed through the Chronos balance condition: χeff=CK→χ where stable systems exist only between collapse and blow-up regimes. The paper further explores the interpretation of gravity as an emergent effect of recursive time-field circulation and curvature redistribution, suggesting that movement through space may fundamentally correspond to movement through recursive stability pathways within the time field itself. The framework also introduces a relational interpretation of dimensional structure, where recursive pathways govern connectivity, synchronization, influence propagation, and multiscale coherence across linked systems. Through analytical geometry, recursive shell formation, toroidal closure dynamics, and bounded stability fields, the work proposes a generalized recursive dimensional architecture intended to model how dimensional systems connect, evolve, stabilize, and propagate coherence through time.
Matthew Hall (Fri,) studied this question.