Lab
142 explorable, interactive pieces — every concept we write about, made tangible.
Bradley-Terry vs. majority voting over pairwise comparison rounds. Five nodes with hidden quality scores compete; a malicious node is down-ranked by BT while majority voting is captured. Reference: Fortytwo GPQA Diamond — BT 85.90%, majority 68.69%.
Semaphore's double-signal defense, explorable: send transactions to spend month-scoped nullifiers PBH-style, replay a spent proof to watch the gate revert with the real contract errors, and roll the month to see the external nullifier change reset the quota.
Forward passes through a small feed-forward network, animated: signals ripple layer to layer, weights set the glow, and activations heat the neurons they reach.
Two random vectors in high dimensions are almost always near-orthogonal. Slide dimension d from 3 to 8192 and watch a sphere of random directions collapse onto the equator — the geometry behind DiFR's random-projection activation fingerprints.
Interactive diagram of the five-step LLM IP protocol: embed a statistical fingerprint, commit it with Poseidon, register on-chain, prove ownership with a ZK proof, enforce via smart contract. Select an attack scenario to see which steps are vulnerable.
An interactive Merkle tree: click any leaf to watch its hash cascade hop by hop to the root, with the sibling hashes that form the inclusion proof highlighted along the way — four hashes prove one of sixteen leaves.
The KZG polynomial commitment scheme, stepped through. Pick an evaluation point z on the cubic P(x) = x³−2x²−x+2 to watch the opening proof π materialize, see the pairing check pass, then corrupt π to make it fail — and read why 50,000 gas ($0.067) is all Ethereum needs to verify any such claim.
Explore how Uniswap v4's 14-bit permission bitmap maps to pool lifecycle callbacks. Toggle bits or select preset patterns to see which hook functions fire for each operation.
A glowing marker performs literal gradient descent over a 3D loss landscape — analytic gradients, momentum, and a fading trail. Drag to orbit the terrain; click anywhere on it to drop a new starting point.
Train a model on its own output, generation after generation. Each step draws a finite sample of size M and refits — so the tails starve first and the curve collapses toward a spike. Toggle replace vs accumulate: replace drives σ̂ toward zero, accumulate holds it. A copy of a copy of a copy.
Proof sizes for six ZK schemes at 1,000 computation steps — hover or tap a row to see the trust model, setup requirement, and primary source. Folding-based IVC (Nova, HyperNova) holds constant; batch STARKs and separate Groth16 proofs grow with depth.
An agentic audit swarm's load-bearing stage: hypothesis particles leave the contract and hold at the falsifier gate while a proof-of-concept runs — hallucinated findings burst into debris, executable ones pass into the report. Tap a code line to plant a bug and watch the swarm catch it.