sgn(x) here refers to the sign function f(x) = 1 if x>0, x=-1 otherwise

log_2 x refers to the base 2 logarithm of x

Background

The sign function of the sine of the base-2 logarithm of x (where x is the market volume) creates an oscillating pattern that alternates between +1 and -1. The function will be:

• +1 when sin(log₂(volume)) is positive

• -1 when sin(log₂(volume)) is negative

Resolution Criteria

This market will resolve based on the final market volume when the market closes. The resolution value will be calculated by:

1. Taking the base-2 logarithm of the final market volume

2. Finding the sine of that result

3. Taking the sign of that sine value (+1 if positive, -1 if negative)

Considerations

• The sine function oscillates between -1 and +1 with a period of 2π

• As the market volume increases, log₂(volume) grows more slowly

• The market will resolve to +1 when log₂(volume) falls within intervals (2kπ, (2k+1)π) for any integer k

• The market will resolve to -1 when log₂(volume) falls within intervals ((2k+1)π, (2k+2)π) for any integer k

• While theoretically the function could equal 0 when log₂(volume) is exactly a multiple of π, this is extremely unlikely due to floating-point precision and would still resolve to -1 per the given definition of sgn(x)