A k-form assigns a (multi)linear, antisymmetric “density” to each point that can be evaluated on k tangent vectors. Density here is a bit abstract, but it  is not a “density” in the physics sense (mass per volume), but you can picture it as an oriented, multilinear measuring device that eats kk tangent vectors and spits out a number telling you “how much kk-dimensional … Continue reading Revisit Differential Forms by Taking Exterior Derivative of 1 form and 2 form

write out the narrative, create a Manim animation for it following the same style as the Yang-Mills video - with sections for: Outro Title/intro Equation breakdown (showing each term appearing) Visual explanations (matrices, commutators, comparing Abelian vs non-Abelian) Physical interpretations then i will record the voice to mp3. combine them with ffmpeg, the final output … Continue reading Learn 3Blue1Brown’s Workflow to Create High Quality Video

Let's start from global U(1) symmetry, A quantum wavefunction for a charged particle is ψ(x)\psi(x) An extra term pops out A miu is not physically observable, so we need to so some math tricks to surface it out In this case, i.e. electromagnetism, the phase change is a simple U(1) group, to extend U(1) to … Continue reading Derive electromagnetism’s Field Strength From Scratch

OpenCode is completely open-sourced and offers several free LLMs, including GLM4.7, which is reported to be quite impressive and comparable to Claude's Sonnet 4.5. It also performs well in math tasks. I'm eager to explore it further and see what other savvy AI users have shared about its use cases. This is provided by David … Continue reading OpenCode Use Cases

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