n=5 hot r=41.5 cells=5 threads=3
n=6 hot r=267.7 cells=6 threads=1
n=7 hot r=1989.8 cells=7 threads=1
n=8 hot r=15589 cells=8 threads=3
n=5–8 cold (CCW counter-flow)
Toroid n=4 R=6.854 (Fix(T)=φ gate)
GRA Source — from hdgl_analog_v33.cu
gra_rn_closed(n, ω):
Dₙ = √(φ · ω · Fₙ · 2ⁿ · ∏Pₖ, k<n)
Shell radii = Dₙ · norm (norm=D4→φ⁴)
Cells/shell = n (T-steps to fixed point)
Threads = Pₙ mod 4 (prime entropy injection)
Toroid: mode n=4, R=φ⁴, Fix(T)=φ gate
Shell Modes (from code)
n=5 D5=41.5
5 cells · P5=11 threads
n=6 D6=267.7
6 cells · P6=13 threads
n=7 D7=1989.8
7 cells · P7=17 threads
n=8 D8=15589.4
8 cells · P8=19 threads
Live Lattice State
Shell / mode n
—
GRA radius Dₙ
—
Λ_φ depth index
—
Ω resonance
—
S(p) resonance score
—
Gate: S<0.25?
—
Shell radii come from the code.
gra_rn_closed(n) = √(φ·Fₙ·2ⁿ·∏Pₖ) gives D5=773, D6=4988, D7=37074, D8=290470
normalised so D4=φ⁴. Each shell sits at its GRA resonance radius, not phi^n.
Cells per shell = n — each T(X)=1+1/X iteration is one cell. Shell n=5 has 5 T-steps from rim to toroid throat; shell n=8 has 8.
Threads = Pₙ mod 4 — the prime at each mode injects entropy into the angular subdivision, matching the PRIME_TABLE in the field kernel.
Toroid = mode n=4 (Fix(T) gate). S(p)→0 here: destructive interference, X+1=0. Hot/cold annihilate into the null, then N(Φ⁻¹)∈{−1,+1} routes the exit branch.
Cells per shell = n — each T(X)=1+1/X iteration is one cell. Shell n=5 has 5 T-steps from rim to toroid throat; shell n=8 has 8.
Threads = Pₙ mod 4 — the prime at each mode injects entropy into the angular subdivision, matching the PRIME_TABLE in the field kernel.
Toroid = mode n=4 (Fix(T) gate). S(p)→0 here: destructive interference, X+1=0. Hot/cold annihilate into the null, then N(Φ⁻¹)∈{−1,+1} routes the exit branch.