Causal Separation of the Time Structure of Three-Direction Formation in Closed N-Body Relational Wave Systems via Two-Stage Seed Removal

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.

Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-07-27
DOI
https://doi.org/10.5281/zenodo.21614403
Primary Topic
Nonlinear Dynamics and Pattern Formation
Type
preprint
Controls
|||
ALL TIME
JAN
FEB
MAR
APR
MAY
JUN
JUL
AUG
SEP
OCT
preprint

Causal Separation of the Time Structure of Three-Direction Formation in Closed N-Body Relational Wave Systems via Two-Stage Seed Removal

Noriaki Kihara
Zenodo (CERN European Organization for Nuclear Research)
Nonlinear Dynamics and Pattern Formation
preprint

Causal Separation of the Time Structure of Three-Direction Formation in Closed N-Body Relational Wave Systems via Two-Stage Seed Removal

Noriaki Kihara
preprint en

Abstract

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.

Zenodo (CERN European Organization for Nuclear Research)
Life in Land
Nonlinear Dynamics and Pattern Formation
AI Navigator

Ask Laika to Summarize, Analyze, and Connect papers live on the map.

Summarize Papers & Methodologies

Extract key findings, datasets, and comparative methods across publications.

Benchmark Rankings & Visual Analytics

Rank top research institutions, authors, funders, topics, and journals by Field-Weighted Citation Impact (FWCI) and paper volume with instant charts.

Connect Distant Disciplines

Bridge topological clusters on the map to find hidden collaborative intersections.

Causal Separation of the Time Structure of Three-Direction Formation in Closed N-Body Relational Wave Systems via Two-Stage Seed Removal — Noriaki Kihara · Zenodo (CERN European Organization for Nuclear Research) (2026) | TGRS Research Map | TGRS