epistemic-arbitrage

Epistemic Arbitrage: Propagator-Based Knowledge Synthesis

Epistemic arbitrage exploits knowledge differentials between domains. When concept A in domain X is well-understood, but its isomorphic counterpart A' in domain Y is mysterious, we can arbitrage by transferring understanding.

Core Architecture

Propagator Networks (Radul/Sussman)

A propagator network consists of:

┌─────────┐     ┌─────────────┐     ┌─────────┐
│  Cell A │────▶│ Propagator  │────▶│  Cell B │
│ (known) │     │  (transfer) │     │(derived)│
└─────────┘     └─────────────┘     └─────────┘

• Cells: Containers for partial information
• Propagators: Functions that combine/transform information
• Merging: Monotonic accumulation (information only increases)

SplitMixTernary RNG

For parallel propagation with determinism:

class SplitMixTernary
  GOLDEN = 0x9e3779b97f4a7c15  # Golden ratio constant
  
  def initialize(seed)
    @state = seed
  end
  
  def next_ternary
    # Advance state (SplitMix64)
    @state = (@state + GOLDEN) & 0xFFFFFFFFFFFFFFFF
    z = @state
    z = ((z ^ (z >> 30)) * 0xbf58476d1ce4e5b9) & 0xFFFFFFFFFFFFFFFF
    z = ((z ^ (z >> 27)) * 0x94d049bb133111eb) & 0xFFFFFFFFFFFFFFFF
    z = z ^ (z >> 31)
    
    # Map to ternary: -1, 0, +1
    (z % 3) - 1
  end
  
  def split(index)
    # Create independent child stream
    child_seed = @state ^ (index * GOLDEN)
    SplitMixTernary.new(child_seed)
  end
end

Arbitrage Patterns

Pattern 1: Domain Transfer

# Knowledge in domain A
cell_a = Cell.new(:music, :circle_of_fifths)
cell_a.add_info(:structure, :cyclic_group_12)
cell_a.add_info(:generator, :perfect_fifth)

# Unknown in domain B
cell_b = Cell.new(:number_theory, :modular_arithmetic)

# Propagator transfers structure
propagator = Propagator.new(:domain_transfer) do |source, target|
  if source.has?(:structure)
    target.merge(:structure, source.get(:structure))
    target.merge(:insight, "Z/12Z isomorphic to circle of fifths")
  end
end

propagator.connect(cell_a, cell_b)
propagator.fire!