Multi-Modal Audio & Video Synthesis: Timestamped Chunking & LaTeX Math Extraction

University lectures and technical webinars contain dense spoken formulas, fast transitions between whiteboard proofs, and colloquial professor explanations. Standard speech-to-text models produce continuous walls of unformatted text without logical chapter breaks.

Extracting usable study notes requires three synchronized processing stages: acoustic silence-aware segmentation, phonetic speech-to-text with specialized mathematical vocabulary prompting, and post-processing mathematical normalization into LaTeX syntax.

When a speaker says "the integral from zero to infinity of e to the minus x squared dx equals square root pi over two," standard transcription outputs broken text. The pipeline has to convert spoken mathematical phrasing into standard LaTeX notation:

$$\int_{0}^{\infty} e^{-x^2} \, dx = \frac{\sqrt{\pi}}{2}$$

Render the LaTeX server-side with KaTeX so a study card never reflows on the client, and give every card a clickable timestamp back into the recording.