The Cube — E47 Geometric Computation

The Cube — unmarked 125-site carrier

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VISUAL SYSTEM · MINI AI LABS

Near-black laboratory. Cyan live · bronze Λ-ghost · mint lock. No type on stills. Record: CITY-LABS-VISUAL-SYSTEM-20260915.

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The Cube · 125-site carrier

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OPEN LIVE INTERFACE

Open The Cube

Geometric computation. 125-site Professor’s Cube carrier. Rank-1 $C_5^3$ Laplacian kernel kept distinct from rank-47 E47.

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THE CUBE · GEOMETRIC COMPUTATION INSTRUMENT

A browser-native educational surface for the 125-site Professor’s Cube carrier, E47 spectral selection, S₃ symmetry bridge, HBr Morse formalism, HFBG-47, and four-dimensional tesseract projection.

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Open The Cube full screen

The Cube · canonical live application

Mathematical spine

Carrier: $\Sigma_5^3$ with $|\Sigma_5^3|=125$ and $\pi(x,y,z)=25x+5y+z$.
E47: $K=(C-6I)(C-30I)$, $E_{47}=\ker K$, $\dim E_{47}=47$, $P_{47}=P_6+P_{30}$.
Contraction: $\Gamma_\varepsilon=I-\varepsilon K^2$ with $\Gamma_\varepsilon^n\to P_{47}$.
Exact bridge: $[C,U_\sigma]=[L,U_\sigma]=[P_{47},U_\sigma]=0$ for $\sigma\in S_3$.
HBr: $V(r)=D_e(1-e^{-a(r-r_e)})^2$ and $E_0/D_e=82/1895$ for the declared corpus values.
Tesseract: a four-dimensional projection visualizer used as an educational representation, separate from the certified finite-dimensional E47 carrier.

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Evidence boundary. The Cube keeps the rank-1 $C_5^3$ Laplacian kernel distinct from the rank-47 E47 spectral kernel. Shared carrier and factor symmetry are displayed as bridges, not identity claims.

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Live system

Canonical live application: garden-king-granite-pixel.grok.me
Source/archive: Google Drive · The Cube — Web App
Python formalism source: The_Cube.py
Browser/reference builds: preserved in Drive for provenance and comparison.