TL;DR
This paper confirms a conjecture by Gowers and Long by demonstrating that rounding to a delta-net in the special orthogonal group SO(3) does not approximate a group operation.
Contribution
It provides a proof that the delta-net rounding in SO(3) cannot be used as a group operation, resolving a conjecture in the field.
Findings
Rounding to a delta-net in SO(3) is not close to a group operation
The conjecture of Gowers and Long is confirmed
Provides insight into the structure of SO(3) and delta-nets
Abstract
We show that rounding to a delta-net in SO(3) is not close to a group operation, thus confirming a conjecture of Gowers and Long.
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