Proposition: Identical record, different entropy histories

A fixed sector record does not determine a sequential accessible entropy history, even with equal finite output dimensions and the same fixed complete initial state.

Proof. Append qubits $B,R_1,R_2,R_3$, initially in $|0000⟩$, and release $R_j$ at tick $j$.

In the first completion use identity evolution. Accessible prefix entropy is zero at every tick.

In the second, at tick one apply a Hadamard on $B$, followed by CNOT from $B$ to $R_1$. The state on $B{R}_1$ is a Bell pair, so the first accessible entropy is one bit. At tick two swap $B$ and $R_2$. The accessible $R_1{R}_2$ state is now a pure Bell pair, with entropy zero. Tick three is identity.

The entropy sequences are therefore

All factors, initial states, and release dimensions agree. These are designed finite histories, not black-hole histories.