Bitcoin consensus rules appear to avoid any notion of approximation or tolerance. Amounts difficulty targets hashes and script evaluation are all defined using bounded integers with explicit overflow and truncation behavior. Even values described as bitstrings are integers modulo fixed powers of two.
Is this purely an implementation choice or is Bitcoin consensus fundamentally an agreement over exact integer equality in a discrete algebraic structure. More specifically does consensus safety rely on the fact that every state transition is a total function over finite integers where equality is unambiguous across implementations and would the introduction of even a single real valued or floating point quantity make validity ill defined in a permissionless setting.
If this framing is meaningful can Bitcoin consensus be modeled as agreement over a discrete structure such as a product of rings with fixed bounds and does this help explain design choices like satoshis integer based difficulty adjustment and halving to an exact zero rather than asymptotic issuance.
