{
  "question": "a chaotically stirred, diffusing tracer: its exact state at K=1e18 stirrings, and its eternal fate",
  "gates": [
    {
      "gate": "exact_by_construction",
      "oracle_vs_1000_explicit_steps": "byte-identical"
    },
    {
      "gate": "end_of_time",
      "K": "1e18",
      "clock_fold_us": 29,
      "full_field_ms": 4.1,
      "cells": 259081,
      "float_simulation_dies_at_step": 34
    },
    {
      "gate": "stretching_rate",
      "lambda": "phi^2 = (3+sqrt5)/2 (exact algebraic integer)"
    },
    {
      "gate": "verdict",
      "spectral_gap": 0.5814,
      "fate": "mixes to uniform -- certified, not simulated"
    }
  ],
  "field_sha256_prefix": "11a7d53f8aef1180",
  "note": "509^2-lattice demonstration of the capability; one workstation"
}