Recursive Intelligence by Nicholas Kouns
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Canonical K47/125 Formalism — July 2026
This governing section supersedes older draft descriptions below wherever they conflict. Exact mathematics, numerical reproduction, postulates, fits, models, and open obligations are explicitly separated.
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Let $V_2$ be the five-dimensional spin-2 irreducible representation of $SU(2)$ and define
$V:=V_2^{\otimes 3},\qquad \dim V=5^3=125.$
With total Casimir
$`C=(J_x^{\mathrm{tot}})^2+(J_y^{\mathrm{tot}})^2+(J_z^{\mathrm{tot}})^2,$$
the exact decomposition is
$`V_2^{otimes3}cong V_0oplus3V_1oplus5V_2oplus4V_3oplus3V_4oplus2V_5oplus V_6,$$
with spectrum $\{0,2,6,12,20,30,42\}$ and isotypic dimensions $(1,9,25,28,27,22,13)$.
Define
$K:=(C-6I)(C-30I).$
Then
$`E_{47}:=\ker K=W_2\oplus W_5\cong5V_2\oplus2V_5,$$
$`dim E_{47}=25+22=47,$$
and
$\Omega_c:=\frac{\dim E_{47}}{\dim V}=\frac{47}{125}=0.376.$
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Scope lock: $47/125$ is an exact dimension ratio after the discrete choice of the $j=2$ and $j=5$ sectors. It does not by itself determine a dimensional physical scale.
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$P_{47}(C)=\frac{C^6-107C^5+4088C^4-66940C^3+430848C^2-624960C}{1814400}$
satisfies
$P_{47}^2=P_{47}=P_{47}^*,\qquad \operatorname{rank}P_{47}=47.$