Randomized trial investigates time structure in relational wave systems, suggesting implications for metastable state formation.
Paper 8 of the dimensional generation series. Paper 7 found that a closed N-body relational wave system, governed by the two axioms of nontrivial zero-square-sum closure and finite recurrence, exhibits a long low-change region followed by geometric amplification and the spontaneous formation of a metastable three-direction structure. This paper causally separates that time structure by independently removing the two explicit seeds of the Paper 7 protocol. With both seeds removed, the full sequence reproduces at N=5, 40, 300. Every-step inspection of the seedless N=5 orbit (1129 forward differences, zero negative) rejects a hidden second bottom inside the latent region; the seeds select neither the timing (first-passage differences at most 1 step) nor the initial direction subspace (same-step overlap median 0.999999987). The direction subspace reorganizes during amplification (early-late overlap 0.14), rank_q=4 appears at the numerical floor and does not mark direction establishment, and the metastable state shows no second geometric expansion up to t=110000. The initial two-direction state itself is a consequence of the closure axiom: all M relation waves are nonzero yet collapse to real rank 2. Open problems are narrowed to the origin of the latency, the selection of three directions during reorganization, and the stabilization mechanism of the formed state. Japanese and English full texts with a reproduction package.
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Noriaki Kihara (2026) studied this question.
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