🧪 SOPHIALABS // COMPUTATIONAL ARCADE

sLabs Visual Simulation Suite

Interactive 60 FPS computational physics and discrete mathematical micro-labs that bring the foundational axioms and mechanical state machines of SophiaLabs to life.

SIMULATION 02 // FLAGSHIP ARCADE

Spectral Graph Laplacian & Fiedler Slicer

Explore algebraic graph theory, dynamic $L = D - A$ Laplacian matrices, and the Fiedler vector partition algorithm. Watch automated minimal-cut graph bisection cleave monolithic 420-LOC files and cross-plane layer leaks without destructive AST truncation.

ALGEBRAIC CONNECTIVITY λ₂ • ANTI-TRUNCATION • AXIOM 4
LAPLACIAN MATRIX L = D - A
3.0 -1.0 -1.0 -1.0
-1.0 2.0 -1.0 0.0
-1.0 -1.0 3.0 -1.0
-1.0 0.0 -1.0 2.0
λ₂ = 0.0482 // BISECTION CLEAVE ACTIVE

ALL ARCADE SIMULATIONS

Real-time Svelte 5 Runes + Canvas 2D / WebGL
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01
LIVE

Dual-Core Confinement Arena

Yin AST vs. Yang Brownian Particles

Stochastic Brownian reasoning tokens (Yang) confined within harmonic potential wells of AST invariant forcefields (Yin).

✂️
02
FLAGSHIP

Spectral Graph Laplacian & Fiedler Slicer

Topological Codebase Minimal-Cut Decomposition

Explore algebraic graph theory, dynamic L = D - A Laplacian matrices, and the Fiedler vector partition algorithm enforcing Axiom 4.

🪐
03
LIVE

Cosmos 3D Semantic Constellation

High-Density Memory Vector Starfield

Interactive 3D WebGL starfield projecting Nomos Mneme subconscious memory vector embeddings into spatial clusters via cosine similarity.

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04
LIVE

Cybernetic Damped Controller

Oscillation, Damping & Dynamic Remedy

Step-response transfer function oscilloscope demonstrating how Nomos damping parameters (ζ >= 1) and the Revert Invariant prevent multi-turn agent feedback chaos.

⚡
06
ARCADE V2

Transverse Cognitive Walker

Dual-Core Polarity Shift & Quantum Descent

Control an Autonomous AI Agent traversing sovereign execution strata. Shift polarities between Yin Totem and Yang Flux to deflect defects and achieve atomic 2PC sync.

🎛️
07
FLAGSHIP

The sLabs Tactile Hardware Room

7-Invariant Cassettes, CapBAC Floppy Interlock & CRT Oscilloscope

Tactile physical computing room inspired by Felix Rieseberg: 7-Law cassette tapes, 3.5" CapBAC floppy interlock, and Tektronix-style CRT Laplacian oscilloscope.

🦿
08
3D LIVE

Embodied Humanoid & Dexterous Hand Crucible

29-DOF Whole-Body ZMP, 21-DOF 5-Finger Cones & MuJoCo MJCF

Orbit a 3D 29-DOF humanoid and zoom into its 21-DOF 5-finger hand to compare unconstrained VLA tip-over/slip failures against Nomos Dual-Scale Control Barrier Functions across 500 seeds.

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