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Red Line district · Canonical deductions
Red identifies exact derivations and logically necessary consequences of stated definitions. Numerical confirmations remain blue, while applications and interpretations retain their own district colors. Transfer through the Subway Python Transit Map.
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Evidence rule
This page states only what can be logically extracted from the current mathematical, computational, engineering, and public-source record. It distinguishes established result, proposed interpretation, strategic relevance, and institutional evidence.
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The canonical K47/125 construction contains a finite-dimensional representation-theoretic result that can be stated independently of any defense, biological, cosmological, or consciousness interpretation.
Let
$$ V=V_2^{\otimes 3},\qquad \dim V=125, $$
with diagonal $SU(2)$ action and total Casimir $C$. Its spectrum is
$$ \operatorname{spec}(C)=\{0,2,6,12,20,30,42\}, $$
with state-count multiplicities
$$ (1,9,25,28,27,22,13). $$
Define
$$ K=(C-6I)(C-30I). $$
Then
$$ E_{47}=\ker K=5V_2\oplus 2V_5, \qquad \dim E_{47}=25+22=47. $$
The orthogonal projector $P_{47}$ onto this subspace can be constructed spectrally or numerically. With
$$ A=K^\dagger K=K^2, $$
and a step size satisfying
$$ 0<\varepsilon<\frac{2}{\lVert A\rVert}, $$
the contraction
$$ x_{n+1}=(I-\varepsilon A)x_n $$