Chronoscalar Dynamics of Multi-Planet Systems: Machian Distortion of Stellar Rotation in the Exoplanet Archive

Abstract

Chronoscalar Field Theory (CFT) postulates a scalar time field T(x) whose gradient and Hessian govern both the geometry of large-scale structure and the resonant architecture of planetary orbits. In this framework planetary systems are not arbitrary outcomes of stochastic disk evolution but projections of a chronoscalar resonance lattice. A key prediction is that planets in a given system occupy discrete period ratios which collapse onto a single effective chronoscalar period Peff when divided by appropriate integers, whereas the observed stellar rotation period P⋆ is generally a Machian–distorted quantity that need not coincide with Peff . Using the NASA Exoplanet Archive composite table, I analyze all host stars with at least three confirmed planets for which both the planetary orbital periods Porb and stellar rotation period P⋆ are reported. For each system I infer Peff by searching for the integer assignments ki that minimize the dispersion of Porb,i/ki across all planets. The ratio Peff/P⋆ then quantifies the Machian distortion of the stellar envelope relative to the underlying chronoscalar clock. Across 46 multi-planet hosts the inferred ratios satisfy median(Peff/P⋆) ≃ 9 × 10−3 and mean(Peff/P⋆) ≃ 5 × 10−2, with three quarters of systems having Peff/P⋆ < 0.02. Case studies such as TRAPPIST-1, GJ 3293 and Kepler-51 reveal extremely tight internal chronoscalar ladders—with several planets sharing a common Peff to better than one per cent—while their host stars rotate an order of magnitude or more slowly. These results are difficult to reconcile with a view in which the stellar spin and planetary periods are governed by unrelated processes, but they are natural in CFT, where planetary systems remember the primordial T-field while the stellar photosphere is gradually torqued by Machian and Hessian perturbations. This first chronoscalar census of the exoplanet archive demonstrates that multi-planet systems encode an effective time scalar distinct from the observed stellar rotation, and that the ratio of these clocks provides a direct observational handle on local Machian distortion. I outline how combining these chronoscalar periods with environmental information (voids, filaments, and galactocentric

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