§ 03 · Matrix math · Overview
Matrix math
The arithmetic AI runs on, and the reason Pearl can mine with it
On this page 2 sections
Bitcoin miners prove their work by hashing. Pearl miners prove theirs by multiplying matrices: the same arithmetic that runs AI models. That’s Pearl’s central idea, proof of useful workProof of useful work: Proof of work whose computation can also be useful. Pearl's is matrix multiplication, the main math inside AI models, though the rules do not check that the matrices mean anything., and this group is the math underneath it.
You don’t need more than school arithmetic to follow it. Every page starts with small numbers you can check by hand, then shows the real sizes from Pearl’s mainnet.
What’s in this group?
Read in order. Each page links forward to the mining pages that use it.
| Page | What you’ll learn |
|---|---|
| Matrices | What A and B are, the size rules, and how a matrix becomes bytes and a BLAKE3 fingerprint. |
| Matrix multiplication | Rows times columns, why it costs m·n·k, and the slab-by-slab view that tickets are built on. |
| Integers and quantization | Why entries run from −64 to 64, why sums fit in 32 bits, and how AI numbers become 7-bit integers. |
| Rank and noise | How rank-128 noise is built from a thin matrix and a ±1 selector, removed exactly, and kept honest. |
| GPUs and tiles | How a GPU tiles the work, and why the reference miner’s 2 × 64 hash tile is one thread’s registers. |
| Cheap verification | Freivalds’ trick, and why Pearl uses a zero-knowledge certificate instead. |
Why matrix multiplication?
Three reasons make it a good fit for mining:
- It’s what the world already computes. Most of the cost of running a large AI model is matrix multiplication, so mining can share hardware, and even computations, with AI serving.
- It’s easy to measure. Multiplying m × k by k × n is exactly m·n·k multiply-accumulates, so work can be priced per operation.
- It’s cheap to check, with the right proof. Verification can cost a tiny fraction of the work.
In this group
- 03.01 Matrices Grids of numbers, and the two that every Pearl miner multiplies
- 03.02 Matrix multiplication Rows times columns, one multiply-accumulate at a time
- 03.03 Integers and quantization Small whole numbers in, exact 32-bit sums out
- 03.04 Rank and noise Random enough to stop shortcuts, cheap enough to peel off
- 03.05 GPUs and tiles Thousands of cores, each one holding a lottery ticket
- 03.06 Cheap verification Checking a multiplication is far easier than doing it