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)

---

Manifesto

The colors are not arbitrary—they are the perceptual rendering of a solved constraint system.

We are building a deterministic, parallelizable, human-adapted coordinate system that renders formal constraints as perceptual reality, in a way that can be:

Property	Mechanism	Verification
Verified	SPI fingerprints, GF(3) conservation	Sheaf cohomology gluing
Merged	Worlding patterns, Möbius inversion	Derangement CRDTs
Learned	Enzyme autodiff, reafference loops	Compression progress

The color IS the proof. The hue encodes the trit. The seed determines the universe.

---

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:

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

Hex Color Output (#RRGGBB)

Convert OkLCH to hex for CSS/web usage:

def oklch_to_hex(L: float, C: float, H: float) -> str:
    """Convert OkLCH to #RRGGBB hex string."""
    import math
    
    # OkLCH -> OkLab
    a = C * math.cos(math.radians(H))
    b = C * math.sin(math.radians(H))
    
    # OkLab -> Linear RGB (simplified)
    l_ = L/100 + 0.3963377774 * a + 0.2158037573 * b
    m_ = L/100 - 0.1055613458 * a - 0.0638541728 * b
    s_ = L/100 - 0.0894841775 * a - 1.2914855480 * b
    
    l, m, s = l_**3, m_**3, s_**3
    
    r = +4.0767416621 * l - 3.3077115913 * m + 0.2309699292 * s
    g = -1.2684380046 * l + 2.6097574011 * m - 0.3413193965 * s
    b = -0.0041960863 * l - 0.7034186147 * m + 1.7076147010 * s
    
    # Clamp and convert to 0-255
    def to_byte(x): return max(0, min(255, int(x * 255)))
    
    return f"#{to_byte(r):02X}{to_byte(g):02X}{to_byte(b):02X}"

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"
#    }

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

---

Skill Name: gay-mcp Type: Deterministic Color Generation Trit: +1 (PLUS) GF(3): Conserved via tripartite streams SPI: Guaranteed (same seed → same output)

---

End-of-Skill Interface

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)

API (Python)

from gay import SplitMixTernary, TripartiteStreams

# Create generator
gen = SplitMixTernary(seed=1069)

# Get color at index (returns dict with L, C, H, trit, hex)
color = gen.color_at(42)
# => {'L': 45.2, 'C': 67.8, 'H': 234.5, 'trit': -1, 'index': 42, 'hex': '#2E5FA3'}

# Generate hex color directly
hex_color = gen.hex_at(42)  # => '#2E5FA3'

# Generate palette as hex list
palette = gen.palette_hex(n=12)
# => ['#D8267F', '#2CD826', '#4FD826', ...]

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

# Split for parallelism (deterministic child)
child = gen.split(offset=7)

# Tripartite streams (GF(3) = 0 guaranteed)
streams = TripartiteStreams(seed=1069)
triplet = streams.next_triplet()
# => {'minus': -1, 'ergodic': 0, 'plus': 1, 'gf3_sum': 0, 'conserved': True}

Integration with discrete_backprop

Color learning via gradient-free optimization:

from gay import SplitMixTernary
from discrete_backprop import DiscreteBackprop

class ColorLearner:
    """Learn optimal color sequences via trit-based backprop."""
    
    def __init__(self, seed: int, target_palette: list):
        self.gen = SplitMixTernary(seed)
        self.target = target_palette
        self.backprop = DiscreteBackprop(dims=3)  # L, C, H
    
    def loss(self, index: int) -> float:
        """Compute color distance to target."""
        color = self.gen.color_at(index)
        target = self.target[index % len(self.target)]
        return sum((color[k] - target[k])**2 for k in ['L', 'C', 'H'])
    
    def step(self, indices: list) -> dict:
        """Discrete gradient step via trit perturbation."""
        losses = [self.loss(i) for i in indices]
        
        # Compute trit-based gradient (Δtrit per dimension)
        gradients = self.backprop.discrete_gradient(
            params=[self.gen.state],
            losses=losses,
            perturbation='trit'  # Use {-1, 0, +1} perturbations
        )
        
        # Chain seed based on gradient direction
        direction_trit = sum(g for g in gradients) % 3 - 1  # Map to {-1, 0, +1}
        self.gen.chain_seed(direction_trit)
        
        return {
            'loss': sum(losses) / len(losses),
            'gradient_trit': direction_trit,
            'new_seed': hex(self.gen.seed)
        }

# Usage
learner = ColorLearner(seed=0x42D, target_palette=[
    {'L': 50, 'C': 80, 'H': 30},   # Target warm
    {'L': 70, 'C': 60, 'H': 150},  # Target neutral
    {'L': 40, 'C': 90, 'H': 240},  # Target cold
])

for epoch in range(100):
    result = learner.step(indices=[0, 1, 2])
    if result['loss'] < 0.01:
        break

Integration with Langevin Dynamics (NEW)

Track which colors affect which noise calls in Langevin training:

# Instrument Langevin noise via color tracking
function instrument_langevin_noise(sde, step_id)
    color = color_at(rng, step_id)
    noise = randn_from_color(color)
    return (color, noise, step_id)
end

# Export audit trail showing cause-effect
audit_log = export_color_trace(
    trajectory=sde_solution,
    seed=base_seed
)
# Shows: step_47 → color_0xD8267F → noise_0.342 → parameter_update

# Verify GF(3) conservation across trajectory
gf3_check(color_sequence, balance_threshold=0.1)

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)

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 }

## r2con Speaker Resources

| Speaker | Handle | Repository | Relevance |
|---------|--------|------------|-----------|
| bmorphism | bmorphism | [r2zignatures](https://github.com/bmorphism/r2zignatures) | Zignature-based function recognition with Gay.jl color integration |
| bmorphism | bmorphism | [Gay.jl](https://github.com/bmorphism/Gay.jl) | Source of deterministic color generation for r2 analysis |
| pancake | trufae | [r2pipe](https://github.com/radareorg/r2pipe) | Scripted access to radare2 for color pipeline integration |
| swoops | swoops | [libc_zignatures](https://github.com/swoops/libc_zignatures) | Signature similarity patterns inform color fingerprinting |

Patterns That Work

• Deterministic color via SplitMix64
• GF(3) trit derivation from hue
• Cross-session fingerprint verification

Patterns to Avoid

• Non-deterministic color generation
• Ignoring seed provenance