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CONSOLIDATION NOTICE

This page is a visual companion only. The single authoritative theorem and evidence-boundary source is Canonical Corrected Formalism. No independent canonical status is claimed here.

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Red Line district · Validated theorem plate

Red identifies exact mathematical statements and canonical proof structure. Machine residuals and executable confirmations transfer to the blue line without changing the theorem’s status. Open the Subway Python Transit Map.

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Open visual plate

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Status: exact finite-dimensional mathematics with machine recomputation.

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Established

Let

$$ V=V_2^{\otimes3},\qquad \dim V=125. $$

The Clebsch–Gordan decomposition is

$$ V_2^{\otimes3}=V_0\oplus3V_1\oplus5V_2\oplus4V_3\oplus3V_4\oplus2V_5\oplus V_6. $$

The state-count dimensions are

$$ 1,9,25,28,27,22,13, $$

and sum exactly to $125$.

For total spin $J$,

$$ C=(J_1+J_2+J_3)^2,\qquad C\vert_{V_J}=J(J+1)I. $$

Define

$$ K=(C-6I)(C-30I). $$

Then

$$ E_{47}=\ker K=5V_2\oplus2V_5, $$

$$ \dim E_{47}=5\cdot5+2\cdot11=25+22=47, $$

and