Finite resources and macroscopic consequence

The finite graph uses $|V|$ payload qubits, at most $|V|-1$ successful CNOTs, $|V|$ flags, and at most $|E|$ one-shot timers. Parent records can be stored with at most four choices per non-root site on the square lattice. Exact real-valued timers are an ideal resource; finite clock precision must be reported separately.

For ${\Lambda }_L$, these counts are $N_L$ and $M_L$. An OTOC Hadamard test may prepare the system maximally mixed and measure the real trace of

It requires a specified controlled-unitary implementation and inverse circuit access. Purifying the maximally mixed input uses $N_L$ additional qubits; a test ancilla adds one. The test has a bounded binary score with mean $C_{\tau }(x,t)$. Its implementation time is not the growth time $t$.