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-# SilverSight Symbolic Regression — Design Document
-
-## Principle
-
-**No external imports.** Use existing SilverSight infrastructure:
-- `EquationShape` + `classifyEquation` — structural classification
-- `spectral_profile` — 8D spectral features
-- `chaos_game` — IFS contraction search
-- `sidon_address` — deterministic addressing
-- `qubo/` — binary optimization
-
-## Architecture
-
-```
-Input: (X, y) data points
-  ↓
-1. Generate candidate expression trees
-  ↓
-2. Classify each with classifyEquation → Hachimoji state
-  ↓
-3. Compute spectral profile for each expression
-  ↓
-4. Apply linear scaling (solve for a, b)
-  ↓
-5. Compute fitness = BIC(scaled_expression, data)
-  ↓
-6. Use chaos game to navigate state space
-  ↓
-7. Use QUBO to select optimal expression
-  ↓
-Output: Best expression with R² score
-```
-
-## Missing Pieces (to implement)
-
-### 1. Expression Tree Data Structure
-
-```python
-@dataclass
-class ExprNode:
-    op: str           # '+', '-', '*', '/', 'sqrt', 'sin', 'cos', 'log', 'exp', 'x', 'const'
-    left: Optional['ExprNode']
-    right: Optional['ExprNode']
-    value: Optional[float]  # for const nodes
-    depth: int = 0
-    size: int = 0
-```
-
-### 2. Linear Scaling (Keijzer 2003)
-
-Given expression g(x) and target y, solve:
-```
-f(x) = a·g(x) + b
-where a, b = argmin Σ(f(x_i) - y_i)²
-```
-
-Closed-form solution:
-```
-a = cov(g, y) / var(g)
-b = mean(y) - a·mean(g)
-```
-
-### 3. BIC Fitness
-
-```
-fitness = n·ln(MSE) + k·ln(n)
-where:
-  n = data points
-  k = tree complexity (weighted: var=1, const=3)
-  MSE = mean squared error after linear scaling
-```
-
-### 4. Chaos Game Search
-
-Use existing `chaos_game.py` to navigate expression space:
-- Each expression maps to a spectral profile
-- Spectral profile maps to a Sidon address
-- Chaos game contracts toward good expressions
-
-### 5. ε-Lexicase Selection
-
-Select on individual data points, not aggregate fitness:
-- For each data point, keep only expressions within ε of best
-- This preserves behavioral diversity
-
-### 6. Operator Diversity via Hachimoji States
-
-- Φ (trivial): simple expressions (x, x², √x)
-- Σ (symmetric): balanced expressions (x·y, x+y)
-- Λ (quantified): expressions with constants
-- Π (complex): deep expressions (sin(1/x), exp(x²))
-- Ω (contradiction): degenerate expressions (constant, NaN)
-
-Force diversity by requiring expressions in multiple Hachimoji states.
-
-## Implementation Plan
-
-### Phase 1: Core Infrastructure
-1. `python/expr_tree.py` — expression tree data structure
-2. `python/linear_scaling.py` — Keijzer linear scaling
-3. `python/bic_fitness.py` — BIC fitness function
-
-### Phase 2: Search
-4. `python/chaos_game_search.py` — chaos game navigation
-5. `python/lexicase_selection.py` — ε-lexicase selection
-
-### Phase 3: Integration
-6. `python/symbolic_regression.py` — main entry point
-7. `tests/test_symbolic_regression.py` — verification
-
-### Phase 4: QUBO Enhancement
-8. Use QUBO to select optimal expression from candidates
-9. Use Hachimoji states to enforce diversity
-
-## Key Advantage Over GP-ELITE
-
-GP-ELITE uses genetic programming (random mutation + crossover).
-SilverSight uses **chaos game** (deterministic IFS contraction) + **Hachimoji states** (structural classification).
-
-This means:
-- Deterministic: same input → same output
-- Structured: expressions are classified by type, not just fitness
-- Efficient: chaos game contracts faster than random search
-
-## Test Cases
-
-1. **Kepler's Third Law**: T = a^1.5 from 8 planets
-2. **Simple polynomial**: y = 2x² + 3x + 1
-3. **Trigonometric**: y = sin(x) + 0.5·cos(2x)
-4. **Exponential**: y = exp(-x²)
-5. **BMCTE entropy**: H(p) = f(N, p) from experiment data