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ENGAGE DENSITY
Launch Density — Quantum Topological Visualizer
Public interactive runtime for tomographic reconstruction, E47 spectral gating, field/state visualization, and reconstruction diagnostics.
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Density is the application / measurement interface downstream of the E47 spectral core. It turns the selector-projector formalism into an interactive tomography workflow while keeping the mathematical layer separate from physical or clinical validation.
$\text{truth phantom}\to\text{angular projections}\to\text{sinogram}\to\operatorname{ART}^{(n)}\to P_{47}\text{ gate}\to\text{residual / profile}$
Related City interfaces: SPECTRA — Algebraic Visualization Lab · Spectra Fold — Levinthal Contraction Visualizer · Murmuration — Topological Data Swarm Lab
| Panel | What it exposes |
|---|---|
| Truth phantom $\Omega(x,y)$ | Reference target for reconstruction. |
| ART reconstruction | Iterative algebraic reconstruction from sampled projections. |
| $P_{47}$ coherence gate | Selected-subspace filtering layer tied to the E47 projector grammar. |
| Error map | $ |
| Sinogram | Eight informational angular views at $45^\circ$ spacing, $0^\circ\ldots315^\circ$. |
| 3D slices | Interactive XY, XZ, and YZ orthogonal sections. |
| Radial coherence profile | Truth versus ART versus gated output. |
The interface exposes the SU(2) sector decomposition $J=0,\ldots,6$ and highlights the selected sectors $J=2$ and $J=5$:
$\dim E_6=25,\qquad \dim E_{30}=22,\qquad \dim E_{47}=25+22=47.$
The selector is
$$ K=(C-6I)(C-30I),\qquad \ker K=E_6\oplus E_{30}=E_{47}. $$
The dissipative state flow is
$$ \dot\rho=-K^2\rho, $$
with exact polynomial projector
$$ P_{47}(C)=\frac{C(C-2)(C-12)(C-20)(C-31)(C-42)}{1{,}814{,}400}. $$
The finite carrier has
$$ \dim\mathcal H=125,\qquad \Omega_c=\frac{47}{125}=0.376. $$