Developed by: Khurram Pervez, Assistant Professor of Mathematics
ΣMath Core is a high-performance mathematical visualization engine that bridges the gap between deep symbolic reasoning and real-time interactive rendering. By leveraging a fine-tuned Qwen2.5-Coder-7B backbone with the NuminaMath-TIR dataset, the model excels at Chain-of-Thought (CoT) reasoning, allowing it to solve complex geometric problems before translating them into interactive code.
The engine utilizes a specialized Resilient Execution Pipeline to render 3D manifolds, animations, and parametric surfaces directly in the browser, optimized specifically for local deployment on NVIDIA hardware.
🚀 The Multi-Stage Pipeline
1. TIR (Thought-Intermediate-Reasoning)
By training on the NuminaMath-TIR dataset, the model follows a rigorous logical path:
Identification: Analyzes the geometric properties of the requested manifold.
Calculation: Determines the necessary vertices, normals, and parametric equations.
Code Synthesis: Generates high-efficiency Python code (Plotly/Matplotlib) using its native Coder capabilities.
2. The Resilient Engine (FastAPI Layer)
To ensure stability during research, the system includes a proprietary processing layer:
Dummy Interception: Captures and silences plt.show() commands to prevent GUI thread blocking on Ubuntu/Linux servers.
Colorscale Transpilation: Automatically maps Matplotlib colormap names (e.g., spring, summer) to Plotly-valid equivalents to ensure 3D renders never fail.
Sandbox Execution: Executes generated code in a safe local scope using your RTX 4060 Ti.
📸 Interactive Visual Samples
Here are examples of advanced parametric surfaces generated in real-time by ΣMath Core v2.0, showcasing the full Thought-Intermediate-Reasoning (TIR) pipeline.
3D Torus Visualization
Full Research Dashboard Interface
Resilient Color Scaling Error Fix
ΣMath Interactive Torus
ΣMath Dashboard
Resilient Colorscale Error
💻 System Configuration
Component
Specification
Compute Engine
NVIDIA GeForce RTX 4060 Ti (16GB VRAM)
Model Format
GGUF (Quantized Q4_K_M)
Context Window
n_ctx=4096 (Optimized for detailed manifold calculation)
