Research Documentation

A 1-1 Correspondence between Cube Algebra and QCD Field Theory

Sections

1. Particle-to-Vertex Mapping

The core of this simulation is the mapping of the 8 fundamental particles of the 1st Generation Standard Model to the 8 vertices of a Euclidean cube. This ensures that every manifold rotation corresponds to a quantum state change.

VERTEX [X,Y,Z] PARTICLE ROLE COLOR CHARGE
[0,0,0]e-LeptonYellow (Leptonic)
[1,1,1]νeNeutrinoWhite (Neutral)
[1,0,0]uQuarkRed
[0,1,0]uQuarkGreen
[0,0,1]uQuarkBlue

2. Shubart Operator Logic

Unlike standard cube turns, Shubart Operators focus on the Long Axis and Short Axis of the manifold. These represent the $SU(3)$ Lie Algebra transformations.

The Wye Operator (120°)

A 120-degree spin around the [1,1,1] vertex (the Neutrino corner). This operator permutes the Red, Green, and Blue quarks without disturbing the leptonic center, representing a 3-way gluon exchange.

  • Input: WYE_OP button or manual W notation.
  • Speed: Adjustable from 50ms (quantum) to 3000ms (stable).

3. Algebraic Syntax

The custom notation engine processes three distinct states of a hadronic interaction:

< Setup | Interaction | Inverse >

Syntax Example: <RYB|G2O-P-|B-Y-R->

  • | : Triggers a "Lattice Pause" (Default 3sec) to identify steady-state positions.
  • - : Represents a 90° counter-clockwise phase shift (Prime).
  • Inverse : The final segment (e.g., B-Y-R-) is automatically validated to ensure the manifold returns to the Proton Steady State.

4. Tensor Export Protocol

Researchers can extract the exact spatial coordinates of all particles after any rotation sequence. This is essential for verifying the Lattice Field Strength.

CSV Format: Columns include Particle_ID, X_Coord, Y_Coord, Z_Coord, and Hex_Color.