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PR: Levin-Levity Skill for BB(6) WEV Extraction

Summary

Adds the levin-levity skill synthesizing Leonid Levin's algorithmic complexity theory with playful mutual ingression of minds for BB(6) prediction market coordination.

The Duality

LEVIN (-1)  ←→  LEVITY (+1)
     \          /
      \        /
       ERGODIC (0)
         ↓
   Nash Equilibrium
  • LEVIN: Convergence, compression, Kolmogorov complexity
  • LEVITY: Exploration, expansion, serendipitous discovery
  • ERGODIC: Nash equilibrium extracting WEV from their mixing time differential

World Extractable Value (WEV)

World Strategy τ_mix Cost
W_Nash (uncoordinated) Solo provers years 100 human-years
W_Opt (market-coordinated) $BEAVER prediction market months 10 human-years

WEV = 90 human-years of extractable proof effort

GF(3) Triad

Skill Trit Role
busy-beaver-oracle +1 Generate lower bound proofs
levin-levity 0 Nash equilibrium + WEV pricing
prediction-market-oracle -1 Market-making

Sum: 0 ✓ GF(3) CONSERVED

Key Features

  1. Levin Search: Universal algorithm weighted by 2^(-|p|)
  2. Kolmogorov Rewards: BEAVER_REWARD = log₃(BB(n)) × MULTIPLIER
  3. LEVITY-LEVIN Game: Best response dynamics for synthesis scheduling
  4. WEV Extraction: Arbitrage between market and proof mixing times

Files Changed

  • skills/levin-levity/SKILL.md - Main skill specification
  • README.md - Updated with BB(6) Oracle Triad documentation

Related Work

  • /busy-beaver-oracle/BEAVER_TOKENOMICS.md
  • /src/triplet_1_week2_nash_solver.jl
  • Thread T-019b77ab-df84-7480-9387-33977beb9b2b (BB(6) WEV analysis)

Checklist

  • GF(3) conservation verified
  • Seed 1069 signature included
  • Nash equilibrium dynamics documented
  • WEV extraction mechanism specified
  • Kolmogorov complexity rewards formula defined

"In the mutual ingression of minds, the shortest proof finds itself."