𝐆𝐄𝐎𝐌𝐄𝐓𝐑𝐈𝐂 𝐂𝐎𝐋𝐋𝐀𝐏𝐒𝐄 𝐂𝐎𝐍𝐅𝐈𝐑𝐌𝐄𝐃: 𝐍𝐏-𝐇𝐚𝐫𝐝 𝐒𝐩𝐢𝐧-𝐆𝐥𝐚𝐬𝐬 𝐜𝐨𝐥𝐥𝐚𝐩𝐬𝐞𝐝.

When I published my NP-Hardness preprint, the obvious question was: Is this a property of my specific architecture – or something deeper?

Now I have the answer.

In a new technical appendix, I applied a completely different system to the same data: a classical GMDH network based on the work of Alexei Ivakhnenko (1968) – the forgotten "Father of Deep Learning" who developed self-organizing polynomial networks decades before backpropagation existed.

The result is striking:

❌ R² = -0.0055 across all 98 neurons (zero predictive power)

✅ Full structural connectivity (9 layers, complete pairwise coupling)

✅ Invariant activation (49-50 neurons active per iteration, near-zero variance)

✅ Uniform switching (mean: 48.0 switches per neuron)

Translation: The GMDH network finds nothing to learn – yet the system is fully coupled, perfectly stable, and globally coordinated.

This is the signature of geometric collapse: Structure without function. Coupling without causation. Order without computation.

The information-geometric manifold is not an artifact of my architecture. It is a property of the informational substrate itself.

📄 Appendix DOI: 10.5281/zenodo.17849616

📄 Appendix Link: https://doi.org/10.5281/zenodo.17849616

#Physics #ArtificialIntelligence #InformationGeometry #ComplexityTheory #Research #SpinGlass #TrauthResearch #GMDH #Ivakhnenko #DeepLearning #NPHardness