Invariant Grammar Slide Deck is retained as a noncanonical visual/interpretive artifact and does not supersede this citizen's canonical E0/E1 theorem or proof links.
Two exact drift points are binding. First, slide 2 writes $\psi_{n+1}=\tfrac12(\psi_n+\phi^{-5}\psi_{n-1})$ and then labels $\phi^{-5}/2\approx0.3002831060$ as its fixed point. For a constant fixed point $\psi_{n+1}=\psi_n=\psi_{n-1}=x$, the displayed recurrence gives $x=\tfrac12(1+\phi^{-5})x$, hence $x=0$ because $\phi^{-5}\ne1$. The stated nonzero fixed point therefore requires an additional operation/normalization not written on the slide.
Second, the deck repeatedly promotes $47/125$ to a universal physical, linguistic, thermodynamic, collapse, and consciousness threshold. Those claims remain outside the certified boundary. The canonical result is the normalized rank of the E47 Casimir-selected sector, $\Omega_c=\operatorname{rank}P_{47}/125=47/125$, plus the explicitly validated finite-dimensional projector/contraction theorems. No universal phase-transition law follows from that rank ratio alone.
The deck also uses the sequence Σ → K → Ψ → Γⁿ → Λ → Ω → ℑ; this is retained as presentation grammar only. Executable contraction remains $\Gamma=I-\varepsilon K^2$ with $\Gamma^n\to P_{47}$, and any semantic or physical interpretation requires an explicitly typed map after projection.
The submitted diagonal witness used raw representation labels $j=0,1,2,3,4,5,6$ as if they were Casimir eigenvalues, then applied $K=(C-6I)(C-30I)$. That construction has nullity 13, not 47, because the eigenvalue 30 block is absent.
The corrected typed chain is
$$ j\longmapsto \lambda_j=j(j+1)\longmapsto C=\operatorname{diag}(\lambda_j)\longmapsto K=(C-6I)(C-30I). $$
With multiplicities $(1,9,25,28,27,22,13)$, the selected sectors are $j=2$ and $j=5$, giving
$$ \dim\ker K=25+22=47, \qquad \Omega_c=47/125. $$
This update corroborates the existing citizen and records a new typed correction identity: representation labels are not interchangeable with Casimir eigenvalues. No duplicate E47 citizen is created.
Open the canonical E47-Kartekeya executable validation monograph and transit charter
The packet preserves the exact finite chain
$V_2^{\otimes3}\to C\to K=(C-6I)(C-30I)\to E_{47}=\ker K\to P_{47}$
and the validated limits
$e^{-tK^2}\to P_{47}$ and $(I-\varepsilon K^2)^n\to P_{47}$.
Agent routing must retain the correction that direct $I-\varepsilon K$ iteration is not generally contractive.