| | Methods
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| | This experiment evaluates how coherence changes as perturbation increases within a simple interpretive-driven system. The goal was to produce an empirical demonstration of the threshold behavior described in the Lattice Coherence Theorem, where coherence declines sharply once perturbation exceeds a critical value.
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| | Model Setup
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| | A minimal computational model was used to prioritize interpretability. The system processes a sequence of internal activation states, and coherence is defined as the mean pairwise similarity between these states. This reflects how consistently the system maintains internal structure under increasing load.
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| | Noise Injection Procedure
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| | Noise was applied directly to the system’s internal state. For each trial, a noise value between 0.0 and 1.0 was selected. Perturbation was introduced by adding scaled random noise to the activation states. Each noise level represents an increasing degree of external disturbance.
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| | Coherence Metric
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| | Coherence was quantified using cosine similarity. For each noise value, the model generated a set of internal activations, and coherence was calculated as the mean cosine similarity across all pairs of activations. Higher values indicate stable alignment, while lower values indicate breakdown of synchrony.
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| | Data Collection
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| | The experiment iterated through a range of noise values, computing coherence at each step. The results were recorded in the file coherence_vs_noise.csv, which includes two columns:
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| | * noise (the perturbation level applied)
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| | * coherence (the resulting coherence score)
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| | Plot Generation
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| | A simple plotting script was used to visualize the relationship between noise and coherence. The plot illustrates a structured decline in coherence with increasing noise, followed by a sharp drop that corresponds to the predicted threshold condition.
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| | Reproducibility
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| | All code required to reproduce this experiment is provided in the accompanying notebook. The notebook contains the noise generation procedure, coherence calculation, dataset export steps, and plotting code. Running the notebook in a fresh environment reproduces the CSV and plot exactly.
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| | Purpose of the Method
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| | The intention of this experiment is not to evaluate a specific architecture but to provide a conceptual demonstration of threshold behavior in coherence-driven systems. The simplicity of the model ensures that the observed transition can be clearly attributed to perturbation dynamics rather than model complexity. |
