audit-arithmetic

Assume there is at least one arithmetic or boundary bug in this code.

Audit for:

• Off-by-one errors
• Incorrect inequality direction (< vs <=, > vs >=)
• Overflow / underflow (int, long, specifically nanoTime arithmetic)
• Implicit narrowing or widening conversion
• Incorrect rounding or truncation
• Sign errors
• Sentinel value collisions (can a valid value equal a sentinel?)
• Counter drift (can a counter diverge from the quantity it tracks over a long-running cache?)
• Timer wheel bucket arithmetic (modular arithmetic, wrap-around)
• Frequency sketch counter saturation and reset arithmetic
• Hill climber / adaptive sizing: window vs main partition adjustment; the density and probe-verdict log-ratios (ln((x+ε)/(y+ε))), the probation-capacity denominator (max(1, maximum − windowMaximum − mainProtectedMaximum)), the saturated 4·maximum sample period, and the stride/commitment rung tables (percentage calculations, rounding, overshoot, oscillation)
• FrequencySketch table size calculation (ensureCapacity rounding to power of two, interaction with maximumSize)
• Weight delta computation in UpdateTask (sign conventions, can intermediate sums overflow when weights are near Integer.MAX_VALUE?)

For each suspected issue:

• Provide a concrete input (specific key, value, weight, time values)
• Show step-by-step evaluation through the code
• Show expected vs actual behavior
• If it requires billions of operations, state the count needed

Ignore style and performance. Only report high-confidence defects supported by evaluation traces.