Constant input of one tenth

Read the equation

The example adds 0.1 on each update. Paired with retention 0.9, this gives equilibrium 0.1/(1−0.9)=1. The same input with no leakage would instead produce unbounded linear growth.

Terms & definitions

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Original context

solving the geometric series gives

An=q1−ρn1−ρ.

By contrast, for an imposed nonleaky rule An+1=An+0.1, threshold two is reached at step 20. That result follows from the nonleakage assumption. It does not establish that all physical or computational loops implement a nonleaky accumulator.

Even positive increments need not produce unbounded accumulation: summable increments such as 2−n have a finite total. A valid crossing theorem needs a condition on the cumulative sum, not just an assertion that data keeps moving.

7.3 Speed can alter timing without creating a new capability

q=0.1