You’ll be able to reconstruct the weather every time you could have 2c consecutive energy sums for ok=a till ok=a+2c-1 (energy sum Sok is x1ok + x2ok + … xnok) of the weather, no matter which a you begin at.
Nonetheless, since PinSketch works in a characterstic-2 area, it holds that (a + b)2 = a2 + b2 (the Freshman’s dream). Due to that, it holds that S2k = Sok2, or in different phrases, we will compute the even energy sums by squaring the half energy sum. Thus, having the odd energy sums between ok=1 and ok=2c-1 (i.e., setting a=1) suffices to reconstruct all energy sums (together with even ones) as much as ok=2c too.
There’s a extra elaborate description within the Miniscript code documentation.
