plurigrid ======= description: Gay.jl MCP server integration for deterministic color generation via SplitMix64
origin/feature/skill-connectivity-hub-20251226
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:
- Parallel computation: Fork generators, get same results
- Reproducibility: Colors are functions of (seed, index)
- 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:
| Tool | Description |
|---|---|
color_at |
Get color at specific index |
palette |
Generate N-color palette |
golden_thread |
Golden angle spiral |
reafference |
Self-recognition loop |
loopy_strange |
Generator ≡ Observer |
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
<<<<<<< HEAD Skill Name: gay-mcp Type: Deterministic Color Generation Trit: +1 (PLUS) GF(3): Conserved via tripartite streams SPI: Guaranteed (same seed → same output)
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
origin/feature/skill-connectivity-hub-20251226