Article 1 — Cosmology
Planck Unit Scaffolding Correlates with the Cosmic Microwave Background
Compares a hypothetical Planck-unit universe (sans particles) with the Cosmic Microwave
Background. Using only Planck mass, Planck length, and a spiral geometry as the rule set,
the model derives estimates for the CMB temperature, radiation energy density, and cold
dark matter density consistent with observational values. The Casimir force equation
reduces to the radiation density equation, implying finite universal boundaries.
Article 2 — Relativity
Relativity as the Mathematics of Perspective in a Hyper-Sphere Universe
Relativity is recast as a translation between two coordinate systems: relativistic 3-D
space-time residing on a non-relativistic Planck-unit lattice within an expanding
4-axis hyper-sphere. Because all particles travel at $c$ in the hyper-sphere frame,
motion between particles is relative — and photons, lacking a mass state, travel
only laterally across the surface. Relativity becomes the mathematics of perspective
between these two frames.
Article 3 — Gravity
Gravitational Orbits from N-Body Rotating Particle–Particle Orbital Pairs
A geometric model in which gravitational and atomic orbits emerge from time-averaged
networks of rotating point-to-point orbital pairs. Macroscopic objects are discretized
into Planck-mass points, each forming independent orbital pairs with all other points.
Using only $\alpha$, $\pi$, and Planck units, the model reproduces Kepler's law and
anomalous orbital precession without requiring a gravitational force.
Article 4 — Atomic Physics
Geometrical Origins of Quantization in H-Atom Electron Transitions
A geometric reformulation of Planck units and fundamental constants using an
integer-valued unit-number map $\theta$ and a small set of dimensionless generators
($\pi, \Omega, \alpha$). An exhaustive integer-space search over admissible
unit-number assignments collapses onto a unique equivalence class characterised by
the base-15 rail $3M + 2T = -15$, selecting the canonical representative
$M=15$, $T=-30$.
Article 5 — In Progress
Photon-Orbital Hybrid Model
Work in progress — exploring the geometry of photon-to-orbital momentum exchange,
the W-axis synthesis, and the dual-domain (matter/radiation) model. Simulation code
and preliminary results are available in the orbitals/atomic section.
Work in progress
🌀 Related Code
Article 6 — Evidence
Do Anomalies in the Physical Constants Constitute Evidence of Coding?
The geometric framework yields a unified table of constants of the form
$x^\theta i^p y^q$, where cancellation rules enforce dimensionless invariants.
Joint improbabilities are reported for the dimensionless-combination suite, the
dimensioned-constant suite, and electron-parameter reconstruction — interpreted
through a Minimum Description Length lens as evidence of compact coding.
Article 7 — Quarks
Geometric Origin of Quarks — The Mathematical Electron Extended
Embedded within the mathematical electron formula $\psi = 4\pi^2 q^3$ are geometrical
objects with Planck-unit attributes. The fine-structure constant $\alpha$ and $\Omega$
combine into a magnetic monopole geometry $q$ (units: ampere·metre), giving the electron
a $q^3$ internal structure suggesting quarks are related to monopoles. A quark model
constructed from these objects yields down ($D$, charge $-\tfrac{1}{3}e$) and
up ($U$, charge $+\tfrac{2}{3}e$) quarks, with implications for matter–antimatter
asymmetry.