RPCS-1

The Matching Principle (Pred-09-5)

Stable receivers in an environment with entropy H satisfy TI ≈ 1 / H.

This is the core structural insight behind every TI recommendation. It comes from IMM Paper 9 and the RPCS-1 receiver dynamics framework.

What it means in practice

Environmental entropy H measures how frequently and unpredictably an environment changes. The Matching Principle says the Temporal Integration window (TI) of a stable receiver must scale inversely with H:

  • High entropy (chaotic environment) → short TI. The agent should integrate only recent signals; old context is noise. Maps to short context windows, frequent grounding, small max_tokens.
  • Low entropy (stable environment) → long TI. The agent benefits from integrating deep history; old context is still relevant. Maps to long context windows, rolling summaries, large max_tokens.

The lookup table

The SDK implements this as a linear interpolation over a lookup table (from config/matching.json):

H = 0.10 → TI = 90  (long deep integration)
H = 0.25 → TI = 70  (stable integration)
H = 0.50 → TI = 50  (balanced integration)
H = 0.75 → TI = 30  (responsive integration)
H = 0.95 → TI = 10  (rapid response)

For intermediate values, TI is linearly interpolated between the nearest table entries. For example, H = 0.2 (a "stable" environment) interpolates to TI ≈ 77.

Entropy levels

stable   → H = 0.20
moderate → H = 0.50
dynamic  → H = 0.75
chaotic  → H = 0.95

The oscillation threshold

The Matching Principle also implies a stability boundary: when SG × TI exceeds the oscillation threshold, the receiver is structurally near the oscillation regime — it integrates too long while amplifying too strongly, causing it to revisit decisions.

oscillation threshold: SG × TI > 7000

# Example: SG=80, TI=90 → product=7200 → oscillation warning

The tuner surfaces a warning whenever your configuration approaches this boundary.

Why this matters for LLMs

LLMs don't have a literal "integration window" in the receiver-dynamics sense, but the structural analogy holds:

  • TI maps to how much context the model is given and expected to use — context window size, rolling-summary frequency, grounding injection rate.
  • SG maps inversely to temperature — a high-gain receiver amplifies signal differences, which in LLMs means low temperature (crisper, more deterministic outputs).
  • The oscillation threshold maps to the regime where a model with a very long context and very low temperature will start re-analyzing the same evidence in loops.

The cross-substrate conjecture (C-12-1 from RPCS-1) holds that the same receiver-dynamics framework applies across biological, artificial, and hybrid cognitive systems. Every production deployment of this SDK is a test of that conjecture.