Gay Monte Carlo Measurements

---

name: gay-monte-carlo description: Monte Carlo uncertainty propagation with Gay.jl deterministic coloring and Enzyme.jl autodiff for gamut-aware probability distributions. trit: 1 color: "#77DEB1"

Overview

GayMonteCarloMeasurements.jl extends MonteCarloMeasurements.jl with Gay.jl chromatic identity for deterministic color-coded uncertainty propagation.

Core Concepts

Particles as Colored Distributions

using MonteCarloMeasurements
using Gay

# Construct uncertain parameters with color tracking
gay_seed!(0xcd0a0fde6e0a8820)
a = π ± 0.1  # Particles{Float64,2000}

# Propagate through nonlinear functions
sin(a)  # → Particles with full distribution

Enzyme Gamut Learning

using Enzyme

# Learnable colorspace parameters
params = OkhslParameters()

function loss(params, seed, target_gamut=:srgb_boundary)
    color = forward_color(params, projection, seed)
    gamut_penalty = out_of_gamut_distance(color, target_gamut)
    bandwidth_reward = color_distinctiveness(color)
    return gamut_penalty - 0.1 * bandwidth_reward
end

∂params = Enzyme.gradient(Reverse, loss, params, seed)

Features

• Nonlinear uncertainty propagation - Handles x², sign(x), integration
• Correlated quantities - Multivariate particles
• Distribution fitting - fit(Gamma, p) for any Particles
• Visualization - plot(p) shows histogram, density(p) shows KDE
• SPI verification - Fingerprint matching across network

GF(3) Integration

Trit	Role	Operation
+1	PLUS	Generative sampling
0	ERGODIC	Distribution transport
-1	MINUS	Constraint verification

Self-Avoiding Walk

next_color() → visited check
     │
     ├─ fresh → XOR into fingerprint
     │
     └─ collision → triadic fork

Repository

• Source: bmorphism/GayMonteCarloMeasurements.jl
• Seed: 0xcd0a0fde6e0a8820
• Index: 103/1055

Related Skills

• gay-julia - Core Gay.jl integration
• spi-parallel-verify - Fingerprint verification
• fokker-planck-analyzer - Equilibrium analysis

SDF Interleaving

This skill connects to Software Design for Flexibility (Hanson & Sussman, 2021):

Primary Chapter: 4. Pattern Matching

Concepts: unification, match, segment variables, pattern

GF(3) Balanced Triad

gay-monte-carlo (○) + SDF.Ch4 (+) + [balancer] (−) = 0

Skill Trit: 0 (ERGODIC - coordination)

Secondary Chapters

• Ch7: Propagators

Connection Pattern

Pattern matching extracts structure. This skill recognizes and transforms patterns.