Geometric Rapid Expansion Is Specific to Unstable Self-Consistent Closures: Causal Discrimination of Onset Modes via Generic Zero-Closure Initial States
Abstract
Sequel to Paper 8 of the dimension-generation series. Executes the systematic control that Paper 8 pre-registered: starting the closed N-body relational-wave dynamics from generic zero-closure states instead of the self-consistent eigenmode. Result: a complete dichotomy of onset modes. Only self-consistent closures (coherent condensates) show the latency-then-geometric amplification (log f linear over 18 decades); all 82 non-equilibrium zero-closure states (42 white harmonic sectors + 40 generic states) leave immediately by finite-angle rotation with no amplification epoch. Mechanism verified by three experiments: one-step residual separates equilibria from non-equilibria by 13 orders of magnitude; tangent-map spectra match measured burst rates (exact at N=5) and show the inert parent is a stable relative equilibrium, establishing the equivalence latency-exponential amplification iff unstable self-consistent relative equilibrium across all 86 tested states; perturbation-amplitude sweep confirms the logarithmic latency law and measures the intrinsic seed floor at the parent eigenmode residual, answering Paper 8 open problem (i). Japanese and English full texts (md/tex/pdf).
Fields of Study & Subjects
Functional Brain Connectivity Studies
Molecular spectroscopy and chirality
Chaos control and synchronization
Publication details
- Journal / source
- Zenodo (CERN European Organization for Nuclear Research)
- Publication date
- 5 August 2026
- Language
- EN
- Document type
- Preprint