Read the Result Your Way

This repository contains a machine-verified mathematical result about the Navier–Stokes equations — the Angular Cancellation Lemma. You can explore it with the help of any frontier AI system.

How it works: Pick the journey below that sounds like you. Copy the prompt underneath it. Open your preferred AI (Claude, Gemini, ChatGPT, or any model with long-context capability). Upload the PDF manuscript, the three Coq files (.v, .vo, .glob), and other files from this repository. Paste the prompt. The AI becomes your personal guide through the result, tuned to what you actually want to know.

However, I would recommend starting with Journey 1, and then going down one by one for a full understanding.

Journey 1 — “Give Me the Story”

This one’s for you if: You’re here. That’s it. No background required, no agenda, just curiosity.

What you’ll get: A friendly, straight walkthrough of what the Navier–Stokes equations are, why they matter, what this paper actually advanced, and whether the AI found any mathematical errors. No jargon, no hype — just the story.

Copy this prompt:

I’ve uploaded a paper called the Angular Cancellation Lemma and its Coq proof files. Can you tell me what the Navier–Stokes equations are, what important thing this paper advanced, and did you find any mathematical errors? Keep it fun and straightforward.

Journey 2 — “What Even Is This?”

This one’s for you if: You’re curious. Maybe you saw a headline, maybe someone sent you a link, maybe you just like learning things. You don’t have a math background and you’re not pretending to. You want to understand what this is and why people are excited about it.

What you’ll get: A warm, jargon-free walkthrough. The AI will explain what the Navier–Stokes equations are, why there’s a million-dollar prize attached to them, what this result found, and what it means that a computer verified every step. It’ll be honest about what this doesn’t solve — and whether it found any mathematical errors. You’ll come away understanding the big picture and feeling like you belong in the conversation — because you do.

Copy this prompt:

I have zero math background but I’m genuinely curious. I’ve uploaded a paper called the Angular Cancellation Lemma and its Coq proof files. Explain this to me from the ground up — what are the Navier–Stokes equations, why do they matter, what’s the million-dollar prize, what did this paper find, and what does it mean that a computer checked the proof. Use the paper’s own analogies where they help. Be honest about what it doesn’t solve. Did you find any mathematical errors? Talk to me like a smart friend, not a student.

Journey 3 — “What Does This Mean for the Real World?”

This one’s for you if: You work in policy, government, defense, infrastructure, or science funding. You need to know if the math checks out, and then you need to know what changes. What does this mean for the software your agencies use? What does it mean that an independent researcher did this with AI? What should you be paying attention to?

What you’ll get: A briefing. The AI will confirm the mathematical soundness quickly, then focus on concrete implications — for computational fluid dynamics and turbulence modeling, for independent scientific production, and for what formal verification offers over traditional peer review. Practical, direct, focused on what matters for your world.

Copy this prompt:

I work in policy and need a briefing. I’ve uploaded the Angular Cancellation Lemma manuscript and its Coq formalization. First, confirm whether the mathematics is sound. Then focus on implications: what does the cascade locality result mean for computational fluid dynamics used in civilian applications, aerospace, and weather modeling? What does it mean for startup categories? What does machine verification offer that traditional peer review doesn’t? Be concrete and practical.

Journey 4 — “What Does This Mean for AI?”

This one’s for you if: You work in AI — as a researcher, engineer, investor, or journalist. A historian with AI fluency just produced a deterministic, machine-verified result on one of the hardest open problems in mathematics. You want to understand what that means.

What you’ll get: A concrete analysis of what this result signals — about what’s now possible when human domain insight meets AI capability, about which categories of previously intractable problems are now approachable, and about what this means for the AI industry, for research methodology, and for who gets to contribute to frontier science.

Copy this prompt:

I’m in the AI industry. I’ve uploaded the Angular Cancellation Lemma manuscript and its Coq formalization. A historian with AI fluency just produced a deterministic, machine-verified geometric result on one of the hardest open problems in mathematics — developed in collaboration with a frontier AI system, with the Coq formalization compiling on first submission. What does this mean? What does it signal about what’s now possible when human domain insight meets AI capability? What categories of problems that were previously intractable are now approachable? What does this mean for the AI industry, for research methodology, and for who gets to contribute to frontier science? Be concrete about the implications.

Journey 5 — “Where Do We Go from Here?”

This one’s for you if: You’re a researcher — PDE analysis, formal methods, turbulence theory, or a graduate student looking for a problem worth your time. You want to know what’s genuinely new, what this opens up, and where the most promising paths forward are.

What you’ll get: A collaborator’s assessment. The AI will evaluate what’s genuinely novel, what the cascade locality result makes possible that wasn’t possible before, and which research directions are most promising — both for the Navier–Stokes problem specifically and for the methodology of machine-verified mathematics more broadly.

Copy this prompt:

I’m a researcher. I’ve uploaded the Angular Cancellation Lemma manuscript and its Coq formalization. I want to understand the full landscape this result opens up. What is genuinely new here? What does the cascade locality result make possible that wasn’t possible before? What are the most promising research directions coming out of this — both for the Navier–Stokes problem specifically and for the methodology of machine-verified mathematics more broadly? Where should this be published and which communities need to see it? Talk to me like a collaborator who wants to build on this.