Gay MCP

Gay-MCP Skill: Deterministic Color Generation

Status: ✅ Production Ready Trit: +1 (PLUS - optimistic/generative) Principle: Same seed → Same colors (SPI guarantee) Implementation: Gay.jl (Julia) + SplitMixTernary (Ruby)

Overview

Gay-MCP provides deterministic color generation via SplitMix64 + golden angle. Every invocation with the same seed produces identical colors, enabling:

1. Parallel computation: Fork generators, get same results
2. Reproducibility: Colors are functions of (seed, index)
3. GF(3) trits: Each color maps to {-1, 0, +1}

Core Algorithm

SplitMix64:
  state = (state + γ) mod 2⁶⁴
  z = state
  z = (z ⊕ (z >> 30)) × 0xBF58476D1CE4E5B9
  z = (z ⊕ (z >> 27)) × 0x94D049BB133111EB
  return z ⊕ (z >> 31)

Color Generation:
  L = 10 + random() × 85    # Lightness: 10-95
  C = random() × 100        # Chroma: 0-100
  H = random() × 360        # Hue: 0-360
  trit = hue_to_trit(H)     # GF(3) mapping

Constants

GOLDEN = 0x9E3779B97F4A7C15  # φ⁻¹ × 2⁶⁴
MIX1   = 0xBF58476D1CE4E5B9
MIX2   = 0x94D049BB133111EB
MASK64 = 0xFFFFFFFFFFFFFFFF

MCP Server

The Gay MCP server provides these tools:

Commands

# Start MCP server
julia --project=@gay -e "using Gay; Gay.serve_mcp()"

# Generate palette
just gay-palette seed=1069 n=12

# Test determinism
just gay-test

API (Ruby)

require 'splitmix_ternary'

# Create generator
gen = SplitMixTernary.new(1069)

# Get color at index
color = gen.color_at(42)
# => { L: 45.2, C: 67.8, H: 234.5, trit: -1, index: 42 }

# Generate trits
gen.next_trit  # => -1, 0, or +1

# Split for parallelism
child = gen.split(7)  # Independent child generator

API (Julia)

using Gay

# Set seed
Gay.gay_seed(1069)

# Get color
color = Gay.color_at(42)

# Generate palette
palette = Gay.palette(12)

# Golden thread
colors = Gay.golden_thread(steps=10)

Tripartite Streams

Three independent streams with GF(3) = 0:

streams = SplitMixTernary::TripartiteStreams.new(seed)

triplet = streams.next_triplet
# => { minus: -1, ergodic: 0, plus: 1, gf3_sum: 0, conserved: true }

Trit Mapping

Hue 0-60°, 300-360° → +1 (PLUS, warm)
Hue 60-180°         →  0 (ERGODIC, neutral)
Hue 180-300°        → -1 (MINUS, cold)

Out-of-Order Proof

proof = SplitMixTernary.prove_out_of_order(seed)
# => { 
#      ordered_equals_reversed: true,
#      ordered_equals_shuffled: true,
#      proof: "QED: Math is doable out of order"
#    }

Integration with Unworld

Colors are derived, not temporal:

# Seed chaining
next_seed = Unworld.chain_seed(current_seed, color[:trit])

# Derive color
color = Unworld.derive_color(seed, index)

Example Output

╔═══════════════════════════════════════════════════════════════════╗
║  GAY.JL: Deterministic Color Generation                          ║
╚═══════════════════════════════════════════════════════════════════╝

Seed: 0x42D

─── Palette (12 colors) ───
  1: #D8267F (trit=+1)
  2: #2CD826 (trit=0)
  3: #4FD826 (trit=0)
  ...

─── Out-of-Order Proof ───
  Indices: [1, 5, 10, 20, 50]
  Ordered = Reversed: true
  Ordered = Shuffled: true
  QED: Math is doable out of order

Specter Navigation Integration (NEW 2025-12-22)

Gay-MCP colors integrate with Specter-style path navigation for correct-by-construction caching:

Color as Navigator Type

# Each navigator gets a deterministic color from seed
nav_color = Gay.color_at(hash(typeof(nav)), 1)

# TupleNav preserves GF(3) across path
path = (ALL, pred(iseven), FIRST)
#       trit mapping: +1, 0, -1 → sum = 0 ✓

Benchmark Integration

Colors visualize benchmark results:

• Red (#D82626): >10x overhead (needs optimization)
• Green (#26D826): 1-2x overhead (acceptable)
• Blue (#2626D8): <1x overhead (faster than baseline!)

Specter Path Coloring

# Colorize a navigation path
colored_path = map(enumerate(path)) do (i, nav)
    color = Gay.color_at(hash(typeof(nav)), i)
    (nav=nav, color=color)
end

Skill Name: gay-mcp Type: Deterministic Color Generation / Navigation Coloring Trit: +1 (PLUS) GF(3): Conserved via tripartite streams SPI: Guaranteed (same seed → same output) Specter: Path coloring for visualization