There are emerging tools such as Remotion, which allow users to create videos based on their instructions. However, when it comes to professional-grade mathematics and physics, Remotion lacks the rigor and accuracy that Manim offers, a library originally developed by 3Blue1Brown. I conducted a test using Manim to produce a video that illustrates the Mills-Yang … Continue reading Try Manim to Create Math Video

I've built a basic data science AI agent already so would be great to learn from other similar agents, this one ai-data-science-team/examples/README.md at master · business-science/ai-data-science-team is a good reference. The structure mainly is at Dive to the sql_database_agent.py to view how it leverage LLM to write sql queries. It calls upon a sql tool … Continue reading AI Data Science Team Git Repo

Skills are essentially reusable prompt templates that encode project-specific knowledge. Instead of explaining "use Bun APIs, not Node fs" every time, you write it once in a skill. The LLM automatically loads it when relevant. OpenCode intentionally supports Claude Code's .claude/skills/ directory structure, so skills written for Claude Code work in OpenCode too. This is … Continue reading OpenCode’s Skill System

There are three main locations storing prompts: Each prompt type serves a different purpose: agents configure specialized AI behaviors, session prompts set global LLM instructions, tool prompts define how tools should be used, and command templates provide command structure. 1. Agent Prompts (/agent/) generate.txt - Meta-prompt for generating new agents /agent/prompt/ (5 files): title.txt - Generate message titles summary.txt - Create PR-style summaries compaction.txt - Compress conversation history explore.txt - Fast codebase exploration 2. Session Prompts (/session/prompt/) - 12 files Provider-specific: anthropic.txt, beast.txt, gemini.txt, qwen.txt, … Continue reading Three Kinds of Prompts Used in OpenCode

Large codebases are like onions - layers upon layers. You don't need to understand everything. Focus on: Entry points - where does execution start? Core domain - what's the main business logic? Interfaces - how do users/systems interact? Everything else is implementation detail you can explore when needed. 1: Start with Entry Points: Always find … Continue reading Navigate a Large Codebase – OpenCode

OpenCode is a an open-source AI coding agent - essentially a terminal-based AI assistant for software development. It's comparable to Claude Code, but open-sourced and provide-agnostic. It's been attracting lots of community adoption now. Core Architecture Pattern: OpenCode uses a hierarchical agent model with two tiers: Primary Agents - User-facing, switchable via Tab key, there … Continue reading Open-Source AI Coding Agent – OpenCode

The Dirac adjoint is needed to replace ψ† so Lorentz-invariant physics is kept.

In 1920s, Pauli faced the problem to solve properties of electrons: Magnetic behavior like a tiny bar magnet Two-valued “intrinsic” angular momentum (spin up / spin down) Spectral line splittings (Zeeman effect) that orbital angular momentum alone could not explain So Pauli needed a mathematical object that: Acts like angular momentum But has only two … Continue reading How Did Pauli Derive the Pauli Matrices

For vectors, Lorentz transformations preservexaxax^a x_a For spinors, the key object is the gamma matrices inside the Dirac equation:(iγa∂a−m)ψ=0(i\gamma^a \partial_a - m)\psi = 0 So by this intuitive guessing and trying, K is found. To make it more concrete:

The algebra defines the symmetry. The representation tells you what kind of physical thing carries that symmetry. The Lie algebra su(2)\mathfrak{su}(2)su(2) is like a universal rotation engine. A representation answers: “Rotation of what?” Spin-1/2 rep → rotates electron spin states Spin-1 rep → rotates vectors in space Higher reps → describe higher spin particles