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coherence-threshold-experiment

This experiment provides a simple, empirical demonstration of the threshold behavior described in the Lattice Coherence Theorem. The goal was to test how coherence changes as perturbation increases, and whether the system exhibits the predicted sharp transition between a stable regime and a decoherent regime.

The dataset contains coherence measurements for noise levels ranging from 0.0 to 1.0. The resulting curve shows a structured decline in coherence followed by a clear collapse, consistent with the theoretical threshold λ described in the theorem.

For the complete theoretical formulation, see the accompanying Lattice Coherence Theorem PDF or preprint.

DOI:https://doi.org/10.6084/m9.figshare.31223362

Experimental Setup

A small computational model was used to track how increasing noise affects internal coherence. For each noise value, the model processed inputs with a defined level of perturbation, and a coherence metric was computed across internal activation states.

The coherence score represents the mean similarity between internal representations. Higher values indicate stable alignment, while lower values indicate representational breakdown.

Noise was applied as a direct perturbation to the model’s internal state. The experiment prioritizes interpretability and conceptual clarity over complexity.

Dataset Description

The dataset contains two columns:

noise — the magnitude of perturbation applied to the system, ranging from 0.0 to 1.0
coherence — the resulting coherence score for that noise level

Together, these values illustrate the system’s transition from order to disorder as external load increases.

Interpretation of Results

The curve produced by this experiment demonstrates three clear phases:

Stable Regime:

At low noise levels, coherence remains relatively high. The system is able to maintain alignment because interpretive capacity outweighs perturbation.

Threshold Collapse:

Past a certain noise value, coherence drops sharply. This behavior matches the predicted synchrony threshold, where perturbation exceeds the system’s available interpretive bandwidth.

Decoherent Regime:

After the collapse, the system enters a low-coherence domain. Additional noise does not significantly alter coherence, indicating loss of structured internal behavior.

This pattern aligns directly with the inequality formalized in the Lattice Coherence Theorem, where coherence growth occurs only when interpretive capacity exceeds perturbation.