E47 FLOW AS A SINGLE 125 × 125 SPECTRAL MATRIX MACHINE

The spin-2 triple tensor carrier is diagonalized by total Casimir sectors. The selector K=(C−6I)(C−30I) isolates the 47-dimensional kernel W₂⊕W₅; Q=K² generates a positive contraction whose discrete and continuous limits are exactly P₄₇.

Symbolic matrix flow

V₂ ⊗ V₂ ⊗ V₂ ≅ V₁₂₅

C ≔ (J₁ + J₂ + J₃)²
V₁₂₅ = W₀ ⊕ W₁ ⊕ W₂ ⊕ W₃ ⊕ W₄ ⊕ W₅ ⊕ W₆
dim(W₀,…,W₆) = (1, 9, 25, 28, 27, 22, 13)

C = diag(0·I₁, 2·I₉, 6·I₂₅, 12·I₂₈, 20·I₂₇, 30·I₂₂, 42·I₁₃)

K ≔ (C − 6I)(C − 30I)
K = diag(180·I₁, 112·I₉, 0·I₂₅, −108·I₂₈, −140·I₂₇, 0·I₂₂, 432·I₁₃)

E₄₇ ≔ ker(K) = W₂ ⊕ W₅
dim(E₄₇) = 47

P₄₇ = diag(0·I₁, 0·I₉, I₂₅, 0·I₂₈, 0·I₂₇, I₂₂, 0·I₁₃)

Q ≔ K²
Q = diag(32400·I₁, 12544·I₉, 0·I₂₅, 11664·I₂₈, 19600·I₂₇, 0·I₂₂, 186624·I₁₃)

ρₘᵢₙ = 11664
ρₘₐₓ = 186624
ε★ = 1⁄99144
ρ★ = 15⁄17

ℛε ≔ I − εQ
limₙ→∞ ℛεⁿ = P₄₇

ẋ = −Qx
limₜ→∞ exp(−tQ) = P₄₇

Ωᶜ = 47⁄125 = 0.376
𝒟 ∘ ℰ = idℋ

Executed certificate

E47 FLOW AS A SINGLE 125 × 125 SPECTRAL MATRIX MACHINE
======================================================

dim(V)                  = 125
σ(C)                    = [0, 2, 6, 12, 20, 30, 42]
multiplicities          = [1, 9, 25, 28, 27, 22, 13]
K sector eigenvalues    = [180, 112, 0, -108, -140, 0, 432]
Q sector eigenvalues    = [32400, 12544, 0, 11664, 19600, 0, 186624]
dim ker(K)              = 47
rank(P47)               = 47
Ωc                      = 0.376000000000000
ρ_min                   = 11664
ρ_max                   = 186624
ε*                      = 1.0086339062373921e-05 = 1/99144
ρ*                      = 0.882352941176471 = 15/17
||R^300 − P47||₂        = 5.612e-14

VALIDATION
[PASS] dim(V₂⊗V₂⊗V₂) = 125
[PASS] σ(C) exact
[PASS] Casimir multiplicities exact
[PASS] K = (C−6I)(C−30I)
[PASS] Q = K²
[PASS] dim ker(K) = 47
[PASS] rank(P₄₇) = 47
[PASS] P₄₇² = P₄₇
[PASS] P₄₇† = P₄₇
[PASS] KP₄₇ = 0
[PASS] QP₄₇ = 0
[PASS] ρₘᵢₙ = 11664
[PASS] ρₘₐₓ = 186624
[PASS] ε★ = 1/99144
[PASS] ρ★ = 15/17
[PASS] ℛⁿ → P₄₇
[PASS] Ωᶜ = 47/125

OVERALL: PASS

Core identity:
lim n→∞ (I − εK²)^n = lim t→∞ exp(−tK²) = P47

limₙ→∞ (I − εK²)ⁿ = limₜ→∞ exp(−tK²) = P₄₇

OVERALL: PASS