e⁺ ±1 [TTT]
u ±2/3 [TTV]
d ∓1/3 [VTV]
ν 0 [VVV]
■ Flux tubes: 0
R/G/B confine: –
String tension σ: 0.18 GeV²
κ (bag constant): 0.145 GeV/fm
RGB↔MCY diagonal axis · drag:rotate · scroll:zoom · pinch:zoom
⏸ PAUSED
⬡ SOLVED ⬡
R-Cube returns to ground state
|ν⟩=|VVV⟩ at MCY corner · |e⁺⟩=|TTT⟩ at RGB corner
All color charges confined · Proton permutation identity
⟨eiθ−λΞ|Я⟩ → identity permutation
|ν⟩=|VVV⟩ at MCY corner · |e⁺⟩=|TTT⟩ at RGB corner
All color charges confined · Proton permutation identity
⟨eiθ−λΞ|Я⟩ → identity permutation
⟁ SOLUTION FOUND ⟁
A significant QCD state has been reached.
Press CONTINUE to proceed with the simulation.
Press CONTINUE to proceed with the simulation.
Hamiltonian / Classical Scale
~10⁻³–10⁹ m · Ω ≈ 1 boundary
Rishon TTV Notation · RGB-centric
| Particle | Rishon | Charge | Face |
|---|---|---|---|
| e⁺ | TTT | +1 | RGB corner |
| ū | T̄T̄V | −2/3 | R face |
| u | TTV | +2/3 | R face |
| d̄ | T̄V̄T̄ | +1/3 | G face |
| d | VTV | −1/3 | G face |
| ν | VVV | 0 | MCY corner |
Color gluons: R→G · G→B · B→R
Generations: 2nd/3rd same RGB, different Greek (μ,τ / s,c / ε,ε')
Confinement: Only color-neutral combinations form observable hadrons
R-cube rule: No valid state has an isolated color sticker
Proton: uud = TTV+TTV+VTV → net charge +1 = e⁺ corner
Generations: 2nd/3rd same RGB, different Greek (μ,τ / s,c / ε,ε')
Confinement: Only color-neutral combinations form observable hadrons
R-cube rule: No valid state has an isolated color sticker
Proton: uud = TTV+TTV+VTV → net charge +1 = e⁺ corner
Single Color Operators
ΨR
R-color exch.
R U R' U'
ΨG
G-color exch.
U R U' R'
ΨB
B-color exch.
F U F' U'
Gluon Exchange (Color Swap)
R↔G
R↔G gluon
R U R' U' F U F' U'
G↔B
G↔B gluon
U F U' F' U R U' R'
B↔R
B↔R gluon
F R F' R'
Charge Type Operators
Ψ+2/3
u-type quark
R U R' U' R U2 R'
Ψ−1/3
d-type quark
R' D' R D
Ψ0
ν-type neutrino
U R U' R' U L' U' L
WYE operators = composite R-cube move sequences encoding color-charge exchange.
Each Ψ maps to a specific gluon vertex in the QCD interaction graph.
Ψ⁺ = ū quark creation · Ψ⁻ = d̄ quark creation · Ψ⁰ = neutrino exchange
Each Ψ maps to a specific gluon vertex in the QCD interaction graph.
Ψ⁺ = ū quark creation · Ψ⁻ = d̄ quark creation · Ψ⁰ = neutrino exchange
Quarter Turns
R
R'
U
U'
F
F'
L
L'
D
D'
B
B'
Half Turns
R2
U2
F2
L2
D2
B2
RGB-centric Singmaster notation:
R=Red · U=Green(Up) · F=Blue(Front)
L=Dark Red (x−) · D=Cyan(Down) · B=Yellow(Back)
p = prime (counterclockwise) · 2 = 180°
R=Red · U=Green(Up) · F=Blue(Front)
L=Dark Red (x−) · D=Cyan(Down) · B=Yellow(Back)
p = prime (counterclockwise) · 2 = 180°
■ Confinement / Mass Gap
▶
Clay Millennium Problem — $1M unsolved
SU(3) gauge theory predicts no free color charges.
V(r) = −(4α_s/3r) + σr [Cornell potential]
σ ≈ 0.18 GeV² [string tension]
R-cube analog: isolated sticker = unconfined charge → forbiddenOnly white (RGB or MCY or pair) states are observable.
▶ Test Confinement ⚡ Flux Tube Demo
■ Asymptotic Freedom
▶
At high energy (small r), α_s → 0. Quarks behave as free particles.
At low energy (large r), α_s → strong coupling → confinement.
Rapid moves = weak coupling; slow moves = strong regime.
▶ α_s Running Test
At low energy (large r), α_s → strong coupling → confinement.
α_s(μ) = 12π / [(33−2n_f)ln(μ²/Λ²_QCD)]
Λ_QCD ≈ 200 MeV [QCD scale parameter]
R-cube: move speed ↔ coupling constant α_sRapid moves = weak coupling; slow moves = strong regime.
▶ α_s Running Test
■ Chiral Symmetry Breaking
▶
SU(2)_L × SU(2)_R broken to SU(2)_V at low energy.
Pions (π⁺,π⁻,π⁰) emerge as pseudo-Goldstone bosons.
▶ Chiral Test Seq.
Pions (π⁺,π⁻,π⁰) emerge as pseudo-Goldstone bosons.
⟨q̄q⟩ ≈ −(250 MeV)³ [chiral condensate]
m_π² = 2m_q·|⟨q̄q⟩|/f_π² [Gell-Mann–Oakes–Renner]
R-cube: solved → broken symmetry state; scrambled → restored▶ Chiral Test Seq.
■ SU(3) Group Structure
▶
8 Gell-Mann matrices λ_a (a=1…8) generate SU(3).
Gluons carry color-anticolor: 8 physical gluons.
WYE operators Ψ_R/G/B = generators T³, T⁸, hypercharge Y.
▶ SU(3) Orbit Test
Gluons carry color-anticolor: 8 physical gluons.
[T^a, T^b] = if^{abc} T^c [structure constants]
f^{123}=1, f^{147}=f^{246}=f^{257}=f^{345}=½
R-cube face colors = SU(3) weight diagram corners.WYE operators Ψ_R/G/B = generators T³, T⁸, hypercharge Y.
▶ SU(3) Orbit Test
■ Proton Structure & Spin
▶
Proton = uud. Mass ≈ 938 MeV; Higgs gives <1%.
~99% from QCD binding / gluon field energy.
Flux tubes between quarks ≈ 1 fm, σ ≈ 0.18 GeV².
▶ Proton State ⚡ Show Flux Tubes
~99% from QCD binding / gluon field energy.
uud: TTV⊗TTV⊗VTV → |e⁺⟩=|TTT⟩ corner
Spin crisis: Σ_q Δq ≈ 0.3 ≠ ½
Gluon ang. momentum + orbital L_q account for the rest.Flux tubes between quarks ≈ 1 fm, σ ≈ 0.18 GeV².
▶ Proton State ⚡ Show Flux Tubes
■ Lattice QCD / Hamiltonian
▶
Kogut-Susskind Hamiltonian on a spatial lattice a:
Each face rotation = plaquette operator U_p.
5×5×5 wireframe = extended lattice background.
▶ Plaquette Sweep
H = (g²/2a)Σ_l E²_l + (1/g²a)Σ_p (2−Tr U_p)
a → 0 limit recovers continuum QCD
R-cube = 3×3×3 spatial lattice, a=CUBIE/GAP ≈ 0.88.Each face rotation = plaquette operator U_p.
5×5×5 wireframe = extended lattice background.
▶ Plaquette Sweep
■ Cosmo / QCD Phase Transition
▶
At T ~ 150 MeV (t ~ 10µs after Big Bang): deconfinement.
Quark-gluon plasma → hadron gas (crossover, not 1st order).
Solved state ↔ confined hadron phase (T<T_c).
▶ Phase Transition Demo
Quark-gluon plasma → hadron gas (crossover, not 1st order).
T_c ≈ 155 ± 9 MeV [lattice QCD result]
Baryogenesis: n_B/s ≈ 8.7×10⁻¹¹
R-cube scrambled state ↔ quark-gluon plasma (T>T_c).Solved state ↔ confined hadron phase (T<T_c).
▶ Phase Transition Demo
■ AdS/CFT · String Duality
▶
Maldacena duality: Type IIB strings on AdS₅×S⁵ ↔ N=4 SYM.
Flux tubes in QCD ↔ fundamental strings in AdS bulk.
RGB↔MCY axis = holographic RG flow.
▶ Holographic Demo
Flux tubes in QCD ↔ fundamental strings in AdS bulk.
λ·Ξ₆d in the formula = string coupling × 6D compactification
σ_string = 1/(2πα') [Nambu-Goto action]
R-cube diagonal = AdS₅ bulk radial direction.RGB↔MCY axis = holographic RG flow.
▶ Holographic Demo
LIVE QCD OBSERVABLES
Move Count
0
Color Disorder S
0.000
Flux Tube Energy
0.00 GeV
Plaquette Tr U_p
3.000
α_s (running)
0.118
Color Confinement
CONFINED
Scale Regime
Hamiltonian
Active Flux Tubes
0
Permutation Order
1
WAVEFUNCTION STATUS
|Ψ⟩ = |000⟩ ground state
Color singlet · E_gluon = 0
All Ψ_operators: identity
Color singlet · E_gluon = 0
All Ψ_operators: identity
CORNER PARTICLE STATE
RGB corner: e⁺ [TTT] Q=+1
MCY corner: ν [VVV] Q=0
MCY corner: ν [VVV] Q=0
FLUX TUBE CONTROL