Discussion and mathematical release

The advance over a generic history-dependence observation is a bound covering every strategy in a specified alternative class. The necessary class restriction is not optional: uncounted retained information or advance query access can invalidate the result.

The standard RAC supplies the core separation. Its sequential implementation does not require earlier-bit copies in the mathematical controller. Its delay, complete-record, and statistical certificates remain conditional on their stated assumptions.

The environmental question has a different boundary. A winning Markovian qubit and a causal-break witness generated by classical hidden memory give explicit counterexamples to two stronger interpretations.