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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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OPEN LIVE INTERFACE

THE MATRIX is the live Grok App Builder runtime — Circuit · MPS · E47 · Tools · Atlas. This is the standalone City OS instrument: the same quantum object as the original in-page site Matrix, not a second lab and not a cycle laboratory.

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THE MATRIX · QUANTUM CIRCUIT INSTRUMENT

How does a finite qubit register compute?

A browser-native statevector lab on $(\mathbb{C}^2)^{\otimes n}$, $n \le 8$: live column evolution, Born collapse with classical $cX$/$cZ$, CHSH, 3-qubit bit-flip QEC, BB84, MPS truncation, and the E47 algebraic witness.

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quantum-matrix.html

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LIVE INTERFACE

The embed above is the original site Matrix (in-page). The standalone City OS lab is this Grok App Builder instrument: live preview, shots, QFT/CP, teleport, CHSH, QEC, MPS, E47, Atlas.

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Research mandate

THE MATRIX is the Mini AI Labs quantum-circuit instrument. It sits with The Cube — E47 Geometric Computation and SIGILLUM — Forty-State Spectral Computer as a selected system: The Cube interrogates the 125-state carrier; SIGILLUM interrogates the 40-state seal; THE MATRIX interrogates an $n$-qubit statevector.

$$ (\mathbb{C}^2)^{\otimes n} \longrightarrow U_{\mathrm{col}} \longrightarrow \lvert\psi\rangle \longrightarrow M,\; cX,\; cZ $$

Mathematical spine

• Carrier: $n \le 8$ qubits, complex amplitudes, $\|\psi\|^2 = 1$.
• Live preview: unitaries apply immediately; measure and classically-controlled $cX$/$cZ$ wait for Collapse.
• Gates: $H,X,Y,Z,S,T$, $R_x,R_y,R_z$, CNOT, SWAP, $CP(\theta)$, $cX$, $cZ$, Measure.
• Presets: Bell, GHZ, W, QFT3, Deutsch, kickback, Grover2, teleport, bit-flip encode.
• Tools: CHSH (Alice $\{Z,X\}$, Bob $\pm \pi/4$), 3-qubit majority QEC, BB84, MC-OCTET-PACKET-1.0.
• MPS: adjacent-bond SVD with transfer-norm $\langle\psi\vert\psi\rangle$.
• E47 witness: $\Omega_c = 47/125$, $\varepsilon_* = 1/99144$, $\rho_* = 15/17$. Display of SPECTRA's algebraic object; the UI does not add a theorem.

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EVIDENCE BOUNDARY

THE MATRIX is an E0/E1 classical statevector simulator. CHSH, teleport, QEC, and BB84 are pedagogical reconstructions on simulated qubits, not a quantum device. E47 constants are inherited from SPECTRA's finite-dimensional algebra and stay at that evidence class.

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City connections

• Mini AI Labs — Advanced Research Interface — public research interface; THE MATRIX is a selected quantum-circuit instrument, not a cycle laboratory.
• SPECTRA — Structure Lab — 125-dimensional spectral algebra; THE MATRIX does not inherit SPECTRA's E0/E1 kernel authority.