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SCALAR · ALGEBRAIC QUANTUM SCALAR FIELDS
What scalar field survives the algebra?
$V_2^{\otimes 3}\rightarrow C\rightarrow K\rightarrow E_{47}\rightarrow P_{47}\rightarrow \phi$
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LIVE MINI AI LAB
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SCALAR · Algebraic Quantum Scalar Fields · live interface
SCALAR · Algebraic Quantum Scalar Fields · live interface
SCALAR is the FIELD stage between Fold and Murmuration. Fold asks what survives transformation; SCALAR lifts the selected finite algebra into a deterministic scalar-field visualization; Murmuration then asks how structure moves and reorganizes.
Mini AI Labs — Unified Interface Portal · The Mathematical City — Recursive Intelligence / E47
$V=V_2^{\otimes 3},\qquad \dim V=125$
$C=J_{\mathrm{tot}}^2$
$K=(C-6I)(C-30I)$
$E_{47}=\ker K=E_6\oplus E_{30},\qquad \dim E_{47}=47$
$P_{47}=\text{orthogonal spectral projector onto }E_{47}$
$\Omega_c=\frac{\operatorname{Tr}P_{47}}{125}=\frac{47}{125}$
$\Gamma_\varepsilon=I-\varepsilon K^2$
The reference finite-dimensional certificate is MC-AQSFT-E47-20260825. The implementation uses the canonical stationary step $\varepsilon_*=1/99144$ and stability ceiling $1/93312$.
The visualization convention sets
$L:=-\Delta,\qquad K_{\mathrm{field}}=(L-6)(L-30).$
Each displayed plane-wave component is assigned $|k|^2=\lambda$ for a Casimir shell $\lambda$. The terminal E47 field contains only the $\lambda=6$ and $\lambda=30$ shells, so $K_{\mathrm{field}}\phi=0$ term-by-term in the declared visualization construction.
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EVIDENCE BOUNDARY
The continuum plane-wave lift is a deterministic visualization map from the finite E47 algebra. It is not asserted here to be a uniquely derived physical spacetime model. The exact evidence resides in the finite spectral core; the field display is the typed visualization layer.
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