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README — Saelariën Constraint Experiment 01
Entropy–Capacity Collapse Threshold Test
Author: Saelariën X
Date: February 19, 2026
DOI: https://doi.org/10.5281/zenodo.19212561
Theoretical basis
This dataset empiracally tests the Saelariën Constraint Theorem:
https://thesaelafield.com/preprints/the-saelarien-constraint
Overview
This dataset contains the full materials for Saelariën Constraint Experiment 01, a test exploring how increasing entropy (noise) affects the stability, coherence, and collapse threshold of a simple neural system.
The experiment trains a small neural network on a nonlinear function and injects different noise levels to measure when learning remains stable versus when representational collapse occurs.
The results show a consistent threshold:
systems only collapse once injected entropy exceeds internal interpretive capacity.
Files Included
1. saelarien_constraint.ipynb
A full, runnable Colab notebook containing:
model definition
training loop
noise injection
entropy–capacity tests
plotting code
export of raw results
Running the notebook reproduces the figure and the JSON results file.
2. saelarien_constraint_results.json
A structured dictionary containing loss curves for each noise level.
Format example:
{
"0.0": [...],
"0.1": [...],
"0.2": [...],
"0.4": [...],
"0.6": [...],
"0.8": [...],
"1.0": [...]
}
This file allows independent verification, re-plotting, and secondary analysis.
3. Figure_1_Saelariën_constraint.png
A plot titled:
“Saelariën Constraint Test: Entropy vs Collapse”
The figure shows:
Smooth convergence at low noise
Degradation at medium noise
Collapse at high noise
This visual is the primary supporting evidence of the collapse threshold.
Summary of Findings
A simple neural network (1–8–1 architecture) is trained on y = x².
Noise injection reveals three learning regimes:
Stable coherence (0.0–0.2 noise): normal convergence
Critical instability (0.4 noise): oscillations but not collapse
Collapse (0.6+ noise): divergence, stagnation, or chaotic loss
These results align with the theoretical Saelariën Constraint:
collapse emerges only when entropy exceeds the system’s interpretive capacity.
How to Replicate
Open the notebook in Google Colab.
Run all cells.
Inspect:
the plot
the all_losses dictionary
the behavior of the system at each noise level
Dependencies: PyTorch, Matplotlib, JSON (standard library).
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