The Diophantine Vacuum
收藏DataCite Commons2026-03-30 更新2026-05-04 收录
下载链接：
https://data.mendeley.com/datasets/ypkp4p5nxs/1
下载链接
链接失效反馈官方服务：
资源简介：
Arithmetic Lattice Strain and the Dimensional Origin of Cosmic Acceleration
with Direct Multi-Dimensional Verification (d = 2, 3, 4, 5)
Tony Newton | tony.newton79@gmail.com | March 2026
Abstract
We present the Diophantine Vacuum framework with the first direct multi-dimensional verification of the
Dimensional Equation of State Ladder. By computing exact lattice-point errors Ed(R) and
boundary-normalized strains Sigmad(R) in dimensions d = 2, 3, 4, and 5, we measure the strain decay
exponent alphad and the corresponding equation of state wd = -1 - alphad/3 in each dimension directly.
Results: d=2 gives w = -0.706 (domain-wall regime), d=3 gives w = -0.479, d=4 gives w = -0.437, d=5
gives w = -0.263. All values increase monotonically with dimension, confirming the dimensional
ordering. The measured wd values sit between two candidate ladder formulae: Ladder A (w = -1 +
(d-1)/3) and Ladder B (w = -1 + (d-2)/3), with A fitting better at low d and B at high d. We also confirm: (i)
the yield-memory reservoir model drives w -> -1 at saturation, (ii) Sigma2 ~ 10-123 at Planck-lattice
cosmic scale (conditional on the Gauss Circle Conjecture), (iii) the Pythagorean defect hierarchy has
Berends-Giele recursion structure with 6% coupling, and (iv) Boltzmann growth tests show 3-5%
f*sigma8 suppression.
提供机构：
Mendeley Data
创建时间：
2026-03-30
