Upload app.py

app.py

@@ -209,6 +209,16 @@ This paper aims to extend the Structured Knowledge Accumulation (SKA) framework
             gr.Markdown("### About this App")
             gr.Markdown("The Tensor Net captures the balance between decision probabilities D and entropy gradients \u2207z H, weighted by the knowledge change \u0394Z at each step. When positive, the network is accumulating knowledge in the direction of the entropy gradient. The zero-crossing — marked by dotted vertical lines — signals the onset of structured knowledge accumulation.")
 
+            gr.Markdown("---")
+            gr.Markdown("### Important Note")
+            gr.Markdown(
+                "The layered SKA Neural Network presented here is a discrete approximation (a \u201cshadow\u201d) of the underlying continuous "
+                "[Riemannian Neural Field (RNF)](https://doi.org/10.13140/RG.2.2.35650.24001).\n\n"
+                "It is provided for educational purposes only to illustrate the core mechanism of local entropy reduction through decision shifts \u0394D.\n\n"
+                "The true SKA dynamics and all its deeper properties live in the continuous RNF. "
+                "The layered discretization is useful for teaching and rapid experimentation, but it is not the complete theory."
+            )
+
         with gr.Column(scale=2):
             plot_tensor = gr.Plot(label="Tensor Net per Layer")
             plot_scatter = gr.Plot(label="Tensor Net vs Frobenius Norm")