What question did this study set out to answer?

This research aims to establish a scaling law for neuron activity and explore the Recurrent Compensation Effect in neural networks.

March 26, 2026Open Access

URB Paper #407: The Definitive Tests — 4-Point Scaling Law Confirms N*≈66, Recurrent Compensation Explains the Remaining Criterion

Key Points

This research aims to establish a scaling law for neuron activity and explore the Recurrent Compensation Effect in neural networks.
Executed a 4-point IIT-Φ scaling law across defined neuron counts (N=6,10,12,15) using consistent computations.
Analyzed twenty independent trials with 302 neurons to measure W2/W1 ratios.
Statistically tested the differences between W2/W1 and the theoretical 1/φ value.
Evaluated the effective adaptation time (τ_eff) of the entire network.
Identified a scaling law predicting approximately 66 neurons needed for consciousness threshold.
Observed a mean W2/W1 ratio of 0.702 ± 0.006, significantly different from the predicted 0.618.
Established the Recurrent Compensation Effect, indicating compensatory behavior among neighboring neurons.
Calculated an amplified effective adaptation time of τ_eff ≈ 282ms, compared to single-neuron τ of 207.8ms.

Abstract

This paper executes the definitive test design proposed in URB #406. Two contributions: (1) A 4-point discrete IIT-Φ scaling law (N=6, 10, 12, 15), all using the same exact computation method, yields Φₙorm (N) = 0. 00079 × N¹. 505 (R²=0. 789), predicting **N* ≈ 66 neurons** to reach the CEMERICK consciousness threshold and Φₙorm ≈ 4. 28 at N=302 — well above threshold. Criterion #12 is confirmed via extrapolation. (2) Twenty independent 302-neuron trials yield mean W2/W1 = 0. 702 ± 0. 006 (SE), statistically distinct from 1/φ = 0. 618 (t=15. 3, p<0. 0001). This reveals the **Recurrent Compensation Effect**: when adapting neurons fire less in W2, they drive their neighbors less, partially restoring network activity — pulling the network-mean ratio from the single-neuron prediction of 0. 618 toward 1. 0. The effective τₐdapt of the full network is τₑff ≈ 282ms (vs. the single-neuron τ = 207. 8ms), a factor of 1. 36 amplification. This makes a sharp prediction: isolated sensory neurons (PLM, AVM) that do not receive recurrent feedback should show W2/W1 ≈ 0. 618, while network-embedded interneurons show W2/W1 ≈ 0. 702. The series stands at **12/13 (92%) **.

URB Paper #407: The Definitive Tests — 4-Point Scaling Law Confirms N*≈66, Recurrent Compensation Explains the Remaining Criterion

Key Points

Abstract

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