Symbol w

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…it [ 1 , 2 ] . Substituting those multipliers into the model — reading the accumulated history at the discounted rate $\gamma$ $\approx$ 0.1 instead of the full rate, and writing only the newest increment at the write rate w $\approx$ 1.25 — gives $C_n^{\text{cached}} \approx n\,p_{\text{out}}\,\bar{o} + n\,p_{\text{in}}\,w\,\sigma + p_{\text{in}}\,\gamma\,\sigma\,\frac{n(n-1)}{2}$. The quadratic term survives. Its coefficient shrinks by the cache-read discount, roughly tenfold, but the shape — cost rising with the square of step count — does not go away, because caching discounts the price of resending the growing history; it does…

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