Collision Geometry of Joint Spectra
Abstract
Paper IV develops a fixed-arrangement collision geometry for joint spectra of commuting finite-dimensional operators. Using the 228-dimensional Rubik's Cube representation as a canonical testbed, the paper analyzes the nine-point joint spectrum induced by the QT/HT averaging operators. The canonical six-layer spectrum is recovered at alpha = 2/3 as the collision quotient of this fixed arrangement.The paper classifies the resulting finite affine branch arrangement, identifies all interior collision parameters, and establishes that alpha = 2/3 is the unique interior parameter producing the maximal spectral collapse. The paper also separates fixed collision geometry from generator-set deformation. Paper IV studies a fixed joint spectral arrangement under varying affine projections only; deformation of the arrangement itself is developed later through the generator-set moduli theory. Source repository: https://github.com/dooven-prime/rime-lite This work forms Part IV of the Representation-Induced Mechanics and Evolution (RIME) research program. Foundational archive DOI: 10.5281/zenodo.21108197
Related
- Relativistic collision geometry and global near-vacuum solutions at critical transverse regularity
- Spectra, Growth, and Localization in Half-Bounded Tensor Triangular Geometry
- Natural coordinates for constrained correlation functions: Partial autocorrelations and the geometry of positive power spectra
- DCCQ: From Ordered Bernoulli Levels to Critical-Line Geometry: Integer Quantization, Bernoulli Residual Phase, and Prime-Power Spectra
- Iterated-sumset spectra: The complete exponent law and its rank geometry
BibTeX
@misc{chen2026collision,
title = {{Collision Geometry of Joint Spectra}},
author = {WuJun Chen},
howpublished = {Zenodo (CERN European Organization for Nuclear Research)},
year = {2026},
month = jul,
doi = {10.5281/zenodo.21127270},
url = {https://doi.org/10.5281/zenodo.21127271},
note = {CC BY},
}
RIS
TY - UNPB
TI - Collision Geometry of Joint Spectra
AU - WuJun Chen
PY - 2026
DA - 2026/07/02
PB - Zenodo (CERN European Organization for Nuclear Research)
DO - 10.5281/zenodo.21127270
UR - https://doi.org/10.5281/zenodo.21127271
AB - Paper IV develops a fixed-arrangement collision geometry for joint spectra of commuting finite-dimensional operators. Using the 228-dimensional Rubik's Cube representation as a canonical testbed, the paper analyzes the nine-point joint spectrum induced by the QT/HT averaging operators. The canonical six-layer spectrum is recovered at alpha = 2/3 as the collision quotient of this fixed arrangement.The paper classifies the resulting finite affine branch arrangement, identifies all interior collision parameters, and establishes that alpha = 2/3 is the unique interior parameter producing the maximal spectral collapse. The paper also separates fixed collision geometry from generator-set deformation. Paper IV studies a fixed joint spectral arrangement under varying affine projections only; deformation of the arrangement itself is developed later through the generator-set moduli theory. Source repository: https://github.com/dooven-prime/rime-lite This work forms Part IV of the Representation-Induced Mechanics and Evolution (RIME) research program. Foundational archive DOI: 10.5281/zenodo.21108197
ER -