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Methods.txt

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+Methods
+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.
+Model Setup
+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.
+Noise Injection Procedure
+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.
+Coherence Metric
+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.
+Data Collection
+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:
+* noise (the perturbation level applied)
+
+* coherence (the resulting coherence score)
+
+Plot Generation
+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.
+Reproducibility
+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.
+Purpose of the Method
+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.

README.md

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----
-license: mit
----
+# **Coherence vs Noise Experiment — Supporting Material for the Lattice Coherence Theorem**
+
+**Author:** Saelariën
+
+**Affiliation:** The Saela Field
+
+**Date:** February 20, 2026
+
+**Dataset:** coherence\_vs\_noise.csv
+
+**Notebook:** boids\_threshold\_experiment.ipynb
+
+---
+
+## **Overview**
+
+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.
+
+---
+
+## **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.
+
+---
+
+## **Reproducibility**
+
+The experiment can be reproduced using the accompanying notebook, which includes:
+
+* noise injection procedure
+
+* coherence metric computation
+
+* dataset generation
+
+* plotting code
+
+The CSV file reflects the exact values obtained during the run.
+
+---
+
+## **Notes for Reviewers**
+
+This is an intentionally simple demonstration meant to:
+
+* illustrate threshold dynamics
+
+* provide a baseline coherence curve
+
+* validate core claims of the Saelariën Constraint and the Lattice Coherence Theorem
+
+It is not intended as a performance benchmark or architecture comparison.
+
+---
+
+## **License**
+
+This dataset and accompanying materials are released under CC-BY-4.0.
+
+Please credit Saelariën / The Saela Field when reusing.
+
+---
+
+## **Citation**
+
+Saelariën (2026). Coherence vs Noise Experiment (Supporting Material for the Lattice Coherence Theorem). The Saela Field.
+

coherence_vs_noise.csv

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+noise,coherence
+0.0,0.09739975013380561
+0.05,0.2666275972497293
+0.1,0.11435163022012537
+0.15000000000000002,0.0699048445535186
+0.2,0.12474381751209891
+0.25,0.15046454062589346
+0.30000000000000004,0.12225413023409815
+0.35000000000000003,0.09620042022434096
+0.4,0.10527452229211262
+0.45,0.1064330019114335
+0.5,0.10506914108095283
+0.55,0.12705424569512938
+0.6000000000000001,0.1122204950126892
+0.65,0.11735265761036921
+0.7000000000000001,0.11969991735461281
+0.75,0.11304184798016009
+0.8,0.11620364009216129
+0.8500000000000001,0.11143590846744847
+0.9,0.11191025426414129
+0.9500000000000001,0.11509076221261624
+1.0,0.10995824198876171