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Scale Invariance

Murmuration patterns persist across sample sizes from 1,000 to 1,000,000 curves

Small Sample 1,000 curves
Medium Sample 10,000 curves
Large Sample 100,000 curves
Very Large Sample 1,000,000 curves

What is Scale Invariance?

The murmuration patterns don't depend on sample size. Whether you analyze 1,000 or 1,000,000 curves, the same oscillating wave structure appears.

Why It Matters

Scale invariance suggests the patterns are fundamental to elliptic curves, not statistical artifacts. Larger samples simply make the waves clearer.

Noise Reduction

With more curves, random fluctuations average out, revealing the underlying mathematical structure more precisely.

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