Dynamic coherence management
E₄₇ Kernel
Finite SU(2) carrier V₂⊗3. Selector K = (C − 6I)(C − 30I). Transient modes contract; the 47-dimensional kernel is the invariant sector the Citadel projects into.
- n
- 8
- occupancy
- 1.00000
- start Ω
- 0.564
Tnx = P x + Ωcn (I − P)x. Complement amplitudes fall as (47/125)n. Occupancy of an isotropic vector starts near Ω_c and locks to 1.
dim V
125
dim ker K
47
transient
78
Ω_c
47/125 = 0.376
λ_min⁺
11,664
λ_max
186,624
ε*
1.009e-5
Selector
K = (C − 6I)(C − 30I)
Casimir spectrum
Multiplicities [1, 9, 25, 28, 27, 22, 13] sum to 125. Kernel sectors sit at C = 6 and C = 30 (25 + 22 = 47).
C=0
1
C=2
9
C=6
25
C=12
28
C=20
27
C=30
22
C=42
13
Projector
P₄₇ = N Nᵀ. P² = P = P†, tr P = 47, KP = 0.
Contraction
Γ = I − ε K², 0 < ε < 1/93312. Γⁿ → P₄₇.
Ratio
Ω_c = 0.376 is the isotropic occupancy of the kernel, not a free parameter.