Upload README.md with huggingface_hub

README.md

@@ -117,6 +117,18 @@ Kronecker coefficients are central to:
 - **MCP Server**: `mcp.bigcompute.science` (22 tools, no auth)
 - **AGENTS.md**: [Contribution guide](https://github.com/cahlen/idontknow/blob/main/AGENTS.md)
 
+## Understanding This Data
+
+Symmetric groups describe all the ways you can rearrange a set of objects. Kronecker coefficients answer the question: when you combine two of these rearrangement patterns, what patterns do you get?
+
+Each character table lists the "partitions" of n (ways to write n as a sum, like 5 = 3+2 = 2+2+1) and the character values that describe each rearrangement pattern. For S20, there are 627 partitions; for S30, there are 5,604; for S40, there are 37,338. The Kronecker coefficient g(lambda, mu, nu) for three partitions tells you how many times the pattern nu appears when you combine patterns lambda and mu. A value of 0 means "never"; a value of 1 means "exactly once."
+
+A concrete example from S20: given three specific partitions of 20, the Kronecker coefficient might be 14, meaning those two patterns combine to produce the third pattern in 14 distinct ways.
+
+These numbers grow fast. At S30, there are 26.4 billion nonzero coefficients -- this is the largest complete Kronecker table ever published. At S40, even the character values exceed what a 64-bit integer can hold (the largest is 5.9 times 10^22), so the full Kronecker table requires a special 128-bit GPU kernel that has not been built yet.
+
+Why does anyone outside pure math care? Geometric Complexity Theory, one approach to the famous P vs NP problem, needs exactly these coefficients. Computing them at scale is a prerequisite for that research program. Kronecker coefficients also show up in quantum information theory, where they describe entanglement structure.
+
 ## Citation
 
 ```bibtex