--- name: gay-mcp description: Deterministic color generation with SplitMix64, GF(3) trits, and MCP. Colors are the perceptual rendering of solved constraint systems. version: 1.0.0 --- # 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 ```ruby 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: ```python 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 ```ruby 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 ```bash # 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) ```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) ```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) ```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: ```python 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: ```julia # 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: ```ruby # 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: ```ruby 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 ## 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-mcp (+) + SDF.Ch4 (+) + [balancer] (+) = 0 ``` **Skill Trit**: 1 (PLUS - generation) ### Secondary Chapters - Ch6: Layering - Ch10: Adventure Game Example - Ch7: Propagators ### Connection Pattern Pattern matching extracts structure. This skill recognizes and transforms patterns.