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2026-10-08 · FIGURE CORRECTION
This visual remains a companion, not authority. The exact $T_z$ weight census is $(1,3,6,10,15,18,19,18,15,10,6,3,1)$; the earlier central bar labels (19,21,19) are erroneous. The current canonical projector statement is $P^{\mathsf T}G=GP$ in the unnormalized basis. $\dim\ker K=47$; the distinct $82$ is $\dim\ker A$ in the Grassmann witness.
Canonical Corrected Formalism — Exact E47 Facts, Numerical Benchmarks, and Evidence Boundaries
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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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Status: exact finite-dimensional mathematics with machine recomputation.
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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
$$ E_{47}=\ker K=5V_2\oplus2V_5, $$
$$ \dim E_{47}=5\cdot5+2\cdot11=25+22=47, $$