Articles

This is a geometrical model, it uses 2 dimensionless constants (alpha and Omega). The articles are referenced, they have also been transcribed onto wiki pages as this is a familiar format.

• Overview
  
• Mass, space and time as geometrical objects
  
• 1. Relativity as the mathematics of perspective
  
• 2. The cosmic microwave in a Planck scaffolding
  
• 3. Gravitational orbitals
  
• 4. Atomic orbitals
  

Overview of the model

Cite: "Planck scale Simulation Hypothesis via a mathematical electron model (overview)".
download: doi:10.13140/RG.2.2.18574.00326/3

Mass, length, time, ampere (MLTA) as geometrical objects

Cite:"Programming Planck units from a virtual electron; a Simulation Hypothesis"
Eur. Phys. J. Plus (2018) 133: 278. https://doi.org/10.1140/epjp/i2018-12094-x

Links 

• The geometries of the natural units; Mass, Length, Time, Ampere
  wiki: Planck units (geometrical)
  
• Do the physical constants embed evidence we are in a simulation?
  wiki: Physical constants (anomalies)
  
• The electron as a mathematical particle
  wiki: electron (mathematical)
  
• The square root of Planck momentum
  wiki: sqrt planck momentum
  
• Mathematical electron (JP)
  wiki: 数理電子
  

1) Programming relativity as mathematics of perspective

In hypersphere coordinates all particles travel at, and only at, the velocity of expansion c. Photons are the mechanism of information exchange, as they lack a mass state they can only travel laterally (in hypersphere co-ordinate terms) between particles and so this hypersphere expansion cannot be observed via the electro-magnetic spectrum, relativity then becomes the mathematics of perspective translating between the absolute (hypersphere) and relative motion (3D surface space) co-ordinate systems.

Cite: "Programming relativity for use in Planck scale Simulation Hypothesis modeling".
download: doi:10.13140/RG.2.2.18574.00326/3

• Relativity as the mathematics of perspective
  wiki: Relativity_(Planck)
  

2) Programming cosmic microwave background parameters

Described is a method for programming the cosmic microwave background parameters at the Planck scale. With each increment to the simulation clock-rate, a set of Planck units (mass, length, time, charge) are added. The mass-space parameters increment linearly, the electric parameters in a sqrt-progression, thus for electric parameters the early universe transforms most rapidly. 

Cite: "Programming cosmic microwave background parameters for Simulation Hypothesis modeling".
download: doi:10.13140/RG.2.2.31308.16004/7

• Cosmic microwave background in a Planck unit universe
  wiki: Planck unit universe
  

3. Simulating gravity via Planck scale n-body particle-particle orbital pairs

Gravitational orbits are the time-averaged sum of rotating particle-particle orbital pairs at the Planck scale. Every particle is connected to every other particle by a circular orbital, forming an n-body `universe' wide lattice of discrete rotating particle-particle orbitals with particles at the orbital poles. In Planck unit terms, each particle-particle orbital rotates 1 unit of Planck length per unit of Planck time (v = c) in hyper-sphere coordinates.  

Cite: "3. Gravitational orbits emerge from Planck scale n-body rotating orbital pairs".
download: doi:10.13140/RG.2.2.11496.93445/17

• Gravitational and atomic orbitals from particle-particle orbital pairing
  wiki: Gravitational orbital
  

4. Quantized atomic orbital transitions derived via a hyperbolic spiral (classical physics)

The orbital is a physical unit of momentum identical to the photon albeit of inverse phase. Furthermore it is the orbital radius (the Bohr radius) which is treated as the physical structure, while rotating it pulls the electron with it creating the orbit.

Cite: "4. H atom n level Bohr radii correlate with pi via a hyperbolic spiral".
download: doi:10.13140/RG.2.2.23106.71367/9

• Atomic orbitals
  wiki: orbitals#atomic
  
  wiki: alpha spiral