PIR Evolver Engine

Overview

The PIR Evolver Engine applies Prime Integer Relations to financial time-series data. It detects market regime shifts by measuring how far a return sequence deviates from Thue-Morse equilibrium — the same mathematical framework that detects structural health issues in our TPNN neural networks.

How PIR Regime Detection Works

Step 1: Extract Return Sequences

Price data is converted to return sequences per asset. The Thue-Morse sequence assigns deterministic signs based on bit-count parity — no randomness, no fitting, no parameters to tune.

Step 2: Compute Balance Gap

The signed power-sum residual measures how far the return sequence is from Thue-Morse equilibrium. Zero means perfect equilibrium (stable regime). Non-zero means structural shift detected.

Step 3: Compute Pattern Area

The shoelace area of the signed cumulative path. Low area = well-structured trend. High area = scattered, uncertain regime. This is the entropy measure — it captures the "shape" of the return sequence.

Step 4: Classify Regime

Balance gap magnitude and pattern area classify the market into four states:

• Bullish — low balance gap, low pattern area, positive returns
• Range — low balance gap, low pattern area, flat returns
• Transition — high balance gap, high pattern area, direction uncertain
• Bearish — low balance gap, low pattern area, negative returns

Momentum Rebalancer

The engine applies regime detection to a top-16 crypto momentum strategy:

• Detect regime shifts via balance gap spikes
• Adjust position sizing based on regime confidence score
• Risk-adjusted allocation across BTC, ETH, SOL, AVAX, and 12 more assets
• Rebalance on regime transitions, not on fixed time intervals

Why PIR Works Here

Markets have structural equilibria — trends, ranges, and consolidation patterns. PIR captures the mathematical "shape" of the return sequence. When that shape breaks Thue-Morse balance, a regime change has occurred. This is not pattern matching or machine learning — it is a deterministic mathematical test that runs in O(n) time.

SignalO Integration

The PIR Evolver Engine powers SignalO, our live signal feed product. SignalO exposes the engine's regime detection as a real-time subscription service with push alerts, API access, and historical replay. See SignalO for the product page.

Educational Disclaimer

PIR regime detection is an experimental mathematical framework. Markets are complex adaptive systems and no signal can predict future performance. The PIR Evolver Engine and SignalO are educational and research tools, not financial advice.