Welcome to the Unified Pipeline Sandbox. This document tests all features of the newly consolidated processor.js.

1. Mathematical Rendering
- 1.1 Inverse Kinematics
2. Academic Citations
3. Syntax Highlighting
4. GitHub Flavored Markdown (GFM)
5. Summary Collapsibles

1. Mathematical Rendering

This section verifies that remark-math and rehype-katex correctly compile academic block equations.

1.1 Inverse Kinematics

Let's look at the Pseudo-Inverse Jacobian matrix equations. Inline math works perfectly, such as the error term $\Delta X$ .

Here is the Damped Least Squares continuous block proof:

J^{\dagger} = J^T (J J^T + \lambda^2 I)^{-1}

\Delta q = J^{\dagger} \Delta X

2. Academic Citations

This section verifies that rehype-citation successfully hooks into our CSL engine.

According to research into robot dynamic arrays, computing joint torques $\tau$ requires continuous tracking of the mass inertia matrix, Coriolis, and gravity vectors. This theory was thoroughly proven by Mark Spong (Spong et al., 2006). The deeper generalized joint matrices also depend heavily on the end-effector constraints (Siciliano et al., 2008).

3. Syntax Highlighting

This section tests prismjs code highlighting injections.

import { processMarkdown } from './markdown/processor.js';

export async function parseText(content) {
    const { contentHtml, headings } = await processMarkdown(content);
    return contentHtml.length > 0;
}

import numpy as np

def inverse_kinematics(jacobian, delta_x):
    # Calculate pseudo-inverse
    j_pseudo = np.linalg.pinv(jacobian)
    return np.dot(j_pseudo, delta_x)

4. GitHub Flavored Markdown (GFM)

Testing GFM tables.

Parameter	Type	Description
$q$	Vector	Joint angles
$\tau$	Vector	Joint torques

5. Summary Collapsibles

Testing rehype-collapsible details blocks.

Click to view hidden code

It works! The native <details> HTML5 element gracefully expands.

Test completed successfully! The Table of Contents to the right should have mapped all 5 sections cleanly with proper intersection observer highlights.

Siciliano, B., Sciavicco, L., Villani, L., & Oriolo, G. (2008). Robotics: modelling, planning and control. Springer Science & Business Media.