Documentation | 1QCD Research Portal

§1 Overview

The 1QCD Geometric Model

The 1QCD model establishes a geometric, manipulable physical model for Quantum Chromodynamics by mapping the eight first-generation Standard Model fermions onto the eight corners of an RGB colour cube. Every face rotation of the cube corresponds to a gluon exchange operator; the cube's 48-element symmetry group contains the SU(3) colour symmetry as a subgroup.

The project addresses a long-standing gap in theoretical physics pedagogy: lattice QCD and Feynman diagrams are either numerical or perturbative. Neither provides a real-time, physically intuitive model of quark confinement, flux tube dynamics, and colour charge permutation that a researcher can literally rotate and inject operators into.

Colour scheme: This lab uses the Standard Model RGB/CMY scheme. Particles carry R/G/B colour charge; anti-particles carry C̄ (cyan = anti-red), M̄ (magenta = anti-green), Ȳ (yellow = anti-blue). Not the RYB artist's wheel — the physics RGB cube.

§2 Particle Mapping

Fermion → Cube Vertex (1-to-1)

The 8 corners of the unit cube [0,0,0]–[1,1,1] map exactly onto the 8 first-generation fermions. The white corner [1,1,1] carries the RGB mixture and represents the electron / proton (the central e cubie). The black corner [0,0,0] is the vacuum / neutrino.

Vertex	Particle	Type	Colour	Electric Charge	Rishon	Chirality
[1,1,1]	e / proton	Lepton centre	RGB White	−1	TTT	↻ RH
[1,0,0]	u	Up quark	Red	+2/3	VTT	↻ RH
[0,1,0]	u	Up quark	Green	+2/3	TTV	↻ RH
[0,0,1]	u	Up quark	Blue	+2/3	TVT	↻ RH
[0,1,1]	d̄	Anti-down	C̄ (anti-R)	−1/3	T̄V̄T̄	↺ LH
[1,0,1]	d̄	Anti-down	Ȳ (anti-B)	−1/3	V̄T̄T̄	↺ LH
[1,1,0]	d̄	Anti-down	M̄ (anti-G)	−1/3	T̄T̄V̄	↺ LH
[0,0,0]	νe	Neutrino	Colourless	0	VVV	—

§3 Colour Scheme

RGB / CMY Standard Model Palette

The lab uses Standard Model RGB (not RYB artist's wheel). Six 60° sectors surround the cube centre, alternating particle (RGB) and anti-particle (CMY) charge sectors. Green is oriented straight down so the G-up quark corner sits symmetrically.

Colour	Hex	Charge Type	Sector Angle	Anti-colour
Red	#ff2200	+Particle	0°	Cyan (C̄)
Green	#00ee44	+Particle	120°	Magenta (M̄)
Blue	#2244ff	+Particle	240°	Yellow (Ȳ)
Cyan	#00ffff	−Anti-particle	60°	Red
Magenta	#ff00ff	−Anti-particle	180°	Green
Yellow	#ffff00	−Anti-particle	300°	Blue

The floor conic gradient rotates 180° when a LH (anti-particle) sequence is detected, shifting the R/G/B sectors to C̄/M̄/Ȳ. Background colour shift (full MCY mode) is planned for a future feedforward implementation.

§4 WYE Operators

The WYE Operator Algebra

Three primary operators span the WYE algebra, each corresponding to a Standard Model quantum number and a face move on the RGB cube. Primed variants (W′ Y′ E′) are inverse / left-handed moves that produce anti-particle sequences.

W

WEAK ISOSPIN

90° rotation of the Up face (U). Permutes the Red and Green u-quark corners.

→ Singmaster: U Prime: W' → U'

Y

HYPERCHARGE

90° rotation of the Right face (R). Permutes the Green and Blue u-quark corners.

→ Singmaster: R Prime: Y' → R'

E

GENERATION JUMP

90° rotation of the Left face (L). Introduces a generation-scale excitation; each E adds one generation.

→ Singmaster: L Prime: E' → L'

< | >

KET DELIMITERS

Bra/ket characters trigger a step-pause in the animation sequence. | is the inner separator.

Step-through: Prev / Next in nav bar

σ₁

PAULI / RISHON TOGGLE

Applies a Pauli-matrix-style flip. Used in Rishon TTV decoding to toggle T↔V sub-constituents.

→ Rishon bit flip on active corner

Chirality rule: A sequence is classified as anti-particle (LH) when the number of primed operators exceeds half the total operator count: primes > ops/2. The floor shifts to MCY and quark nodes switch to d̄ corners.

§5 Singmaster Map

WYE → Singmaster Translation

The lab automatically translates WYE operator sequences into standard Singmaster cube notation for rendering via the Roofpig cube engine. The wyeToSingmaster() function performs this:

// wyeToSingmaster — complete translation table
W  → U   // Weak Isospin RH  → Up face CW
Y  → R   // Hypercharge RH   → Right face CW
E  → L   // Generation RH    → Left face CW
W' → U'  // Weak Isospin LH  → Up face CCW
Y' → R'  // Hypercharge LH   → Right face CCW
E' → L'  // Generation LH    → Left face CCW
< | > σ₁ → stripped (step-pause only, not passed to cube)

// Face colour assignments (RGB Std Model)
U: blue    D: green
F: red     B: cyan
R: yellow  L: magenta
    

Lars Petrus Note: Roofpig uses its own internal face labelling (U/D/F/B/R/L). This is not the standard Singmaster colour assignment — it is remapped above to the RGB Standard Model palette. Backface rendering is suppressed via flag=canvas_view_only and CSS overrides.

§6 Ket Notation

Bra-Ket Algebra Input

The input field accepts full Dirac bra-ket notation. The characters < | > pass through to the output display as step-pause delimiters. They do not map to cube moves.

// Syntax: < Setup | Interaction | Inverse >
< W Y | W Y W | W' Y' W' >

// Each "|" triggers a step-pause
// Use Prev / Next in nav bar to step through
// Each operator is highlighted in the Ket display

// Full example — proton RGB cycle:
W Y W                // 3-gluon exchange, RH
W Y E                // 1st generation jump
W Y E E              // 2nd generation (charm, strange)
W' Y' W'             // inverse / anti-particle path
< W Y | W' >        // partial confinement loop
    

§7 Rishon Model

TTV Sub-Constituent Notation

In the Rishon model (Harari/Shupe 1979), quarks and leptons are composed of two types of sub-constituents: T (Tohu, charge +1/3) and V (Vohu, charge 0). Each fermion is a triplet. The 1QCD lab displays the Rishon TTV sequence for every quark corner and uses it as an alternative notation for colour charge.

Particle	Rishon	Colour	Q	Chirality
u	`VTT`	R	+2/3	↻ RH
u	`TTV`	G	+2/3	↻ RH
u	`TVT`	B	+2/3	↻ RH
d̄	`V̄T̄T̄`	Ȳ	−1/3	↺ LH
d̄	`T̄V̄T̄`	C̄	−1/3	↺ LH
d̄	`T̄T̄V̄`	M̄	−1/3	↺ LH

§8 Cornell Potential

V(r) = −κ/r + σr

The Cornell (funnel) potential models the quark-antiquark interaction. At short distances the Coulombic term −κ/r dominates; at large r the linear flux-tube term σr causes confinement.

V(r) = −κ/r + σ·r

  κ = 0.52          // Coulombic strength (dimensionless)
  σ = 0.18 GeV²     // String tension
  r ∈ [0.05, 3.0] fm

// Confinement radius (string breaking):
  r_conf ≈ 1.0–1.2 fm  → CONFINED phase
  r < 0.5 fm           → DECONFINED (asymptotic freedom)
  r > 2.0 fm           → QGP (quark-gluon plasma)

// Stability index mapping:
  r(stab) = 0.1 + (1 − stab/100) × 2.4  fm
    

The live Cornell chart in the left sidebar updates the cyan cursor position after every simulation, mapping the calculated stability index to a physical separation r in femtometres.

§9 Confinement Phases

Phase Detector

After each simulation run the lab classifies the result into one of four confinement phases based on the computed Stability Index and the presence of E (generation-jump) operators.

Phase	Stability Range	Condition	Physical Interpretation
CONFINED	< 40%	High operator count / many primes	Strong flux tube — quarks cannot separate. RECOVER VACUUM button appears.
DECONFINED	40–85%	Moderate sequence	Hadronic phase — quarks bound but weakly. Normal operating range.
QGP	> 85%	Short / simple sequence	Near-vacuum / quark-gluon plasma analog. Colour charge nearly free.
GUT-SCALE	Any	E operator present	Generation jump detected — GUT-scale energy excitation. Stability −28% per E.

§10 Gluon Exchange

Flux Tube Animation & Gluon Palette

The six gluon exchange buttons in the right sidebar fire direct quark-to-quark colour transitions. Each gluon carries a colour/anti-colour pair. The flux tube canvas renders a Gaussian-width particle stream: narrow at the quark endpoints, thickest at mid-span — physically accurate for the colour-electric flux tube profile.

Gluon	Colour Absorbed	Colour Emitted	Visual
`g(R→G)`	Red	Green	Red→green stream
`g(G→B)`	Green	Blue	Green→blue stream
`g(B→R)`	Blue	Red	Blue→red stream
`g(R→B)`	Red	Blue	Red→blue stream
`g(G→R)`	Green	Red	Green→red stream
`g(B→G)`	Blue	Green	Blue→green stream

§11 Stability Index

Vacuum Stability Calculation

The stability index is computed client-side as a proxy for the vacuum fluctuation magnitude of the input sequence. It feeds the gauge, Cornell chart, and phase detector.

// calcStability(alg) — algorithm
S = 100 − (operator_length × 1.1)
if (E present)  S −= 28   // generation excitation penalty
if (' present)  S −= 14   // LH/inverse penalty
if (σ₁ present) S −= 8    // Pauli toggle penalty
S = clamp(S, 2, 100)

// Example:
"W Y W"     → len 3 → S = 96.7%  → QGP
"W Y E W Y" → len 5 → S = 39.5%  → CONFINED (E penalty)
"W' Y' W'"  → len 3, 3 primes → S = 58.7% → DECONFINED
    

§12 Tensor Export

Data Export Protocol

Every simulation is recorded server-side via record_tensor.php and indexed in the tensor tracker database. The full history is available at history.php.

Field	Type	Description
`sequence`	string	Raw WYE operator input string
`dirac_string`	string	Full bra-ket notation (preserved)
`rotation_state`	string	Singmaster-translated sequence
`gen`	int	Generation number (E count + 1)
`stability_index`	float	Computed vacuum stability %
`is_sol`	bool	1 if stability ≥ 95% (solved state)
`is_gut_scale`	bool	1 if E operator present

Use the Export Log button in the left sidebar to download the current session log as a .txt file. Full CSV tensor export is available from history.php.

§13 Examples

Worked Sequences

Copy any sequence into the Core Lab input field and press EXECUTE:

// ── Proton RGB cycle (3-gluon exchange)
W Y W                         → stab ≈ 96.7% QGP

// ── Baryon triangle (colour-neutral hadron)
W Y W Y W                     → stab ≈ 94.5% QGP

// ── 1st generation step
W Y E                         → stab ≈ 40.3% DECONFINED

// ── Anti-particle path (LH)
W' Y' W'                      → LH, MCY floor, stab ≈ 59.3%

// ── Full bra-ket interaction notation
< W Y | W Y W | W' Y' W' >    → step through with Prev/Next

// ── GUT-scale excitation
W Y E E W                     → GUT-SCALE, stab ≈ 12.5% CONFINED

// ── Pauli Rishon toggle
W σ₁ Y                        → T↔V sub-constituent flip
    

1QCD Research Documentation

The 1QCD Geometric Model

Fermion → Cube Vertex (1-to-1)

RGB / CMY Standard Model Palette

The WYE Operator Algebra

WYE → Singmaster Translation

Bra-Ket Algebra Input

TTV Sub-Constituent Notation

V(r) = −κ/r + σr

Phase Detector

Flux Tube Animation & Gluon Palette

Vacuum Stability Calculation

Data Export Protocol

Worked Sequences