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Rex St. John
demolive

Generative Chains

Six browser demos working through one question — what a blockchain looks like when the thing doing the work is a generative model. Proof of Generation, a Lean proof chain over open Erdős problems, and two experiments in grown rather than drawn structure.

Claude Code / WebGL / Lean

Demo

Two essays I wrote in 2023 argued that generative models were going to end up inside consensus mechanisms, and I never built anything to go with them. These are the demos I owed that argument: six single-file pages, no build step, each one taking a piece of the idea as far as it goes before it breaks.

The through-line is one claim. A generative model's output depends on its exact weights, so the hash of an output is a commitment that only that model can satisfy. Artwork Chain tests it directly — every block is a painting made from one verse of Genesis plus the hash of the block before it, and a fine-tuned knockoff cannot reproduce a single one.

Turn that into work and you get Proof of Generation: a machine paints a secret prompt and broadcasts only the hash, and the miners race to find a prompt that paints the same image. Prompt Mining runs the race; Request for Art plots it, with near misses gathering toward the center. Both also show the flaw, which is the honest part — real image models are noisy, so a miner can find the right prompt and still miss the hash.

Challenge Vaults is what happens when you fix that by swapping the noisy model for a perfect checker. The puzzles become open Erdős problems stated in Lean and the kernel gives an exact yes or no. That idea outgrew this repo and is now its own project.

Living Rules and Bloom Chain go the other direction — from chains of blocks to grids of cells, where one local rule produces structure at every scale and a language model decides what gets grown.

These are concept demos. Every model, network, prover and result is simulated in the browser, nothing touches a real chain, and the Lean statements are simplified sketches. The ten Erdős problems are real and were open as far as I know; erdosproblems.com has the current status.

Screens

  • The Artwork Chain demo, showing block 5 of a chain where each block is a painting generated from a verse of Genesis plus the previous block's hash, with the canonical model's verification passing and a knockoff model available to test against
    Artwork Chain. Each block is a painting made from one verse plus the hash before it. The canonical model reproduces it exactly; the fine-tuned knockoff fails. The weights are the key.
  • The Prompt Mining demo, with a hidden target painting on the left reduced to a broadcast hash, and twelve miners generating candidate paintings from noun-verb-noun prompts, with counters for possible prompts, guesses this round and guesses per second
    Prompt Mining — the Proof of Generation demo. One machine paints a secret prompt and broadcasts only the hash. Twelve miners race to find a prompt that paints the same image; first match mints it and sets the next puzzle.
  • The Request for Art demo, a radial scatter plot with twelve miners around the rim and the requested artwork at the center, each generated attempt landing in a ring according to how many words of the prompt it got right
    The same race as a scatter plot. Attempts land closer to the center the nearer they get, and only an exact match reaches the middle — which is also where the idea breaks.
  • The Living Rules demo, a circular dish of cells organized into pink and violet membranes and dividing colonies, beside the rule that produced them shown as three sensing rings and a growth response curve
    Living Rules. One tiny rule per cell — look at three distances, then grow or shrink. Nobody drew these shapes; a search found rules whose cells organize themselves.
  • The Bloom Chain demo, showing a many-colored flower grown from cellular automata, with a breakdown of which living rule was assigned to the petals, center, stem and leaves
    Bloom Chain. Describe something, and Claude picks a living rule for each part and grows it. Each new prompt is handed the previous answer, so the scene evolves link by link.