A high-multiplicity word lists every distinct job once, with its record, release date, weight and due date, preceded by the number of jobs that have them ($StandardReading$). It does not say which job is which, and it has no facts on pairs of jobs.

Theorem. The standard reading determines the answer for every specification with high multiplicity. Two instances written by one high-multiplicity word have the same numbers of jobs and machines and the same global facts, and a bijection between their jobs keeps every record, release date, weight and due date; renaming the jobs along it maps the feasible schedules of one instance to those of the other, at the same cost.

A program reads the standard word of an instance without facts on pairs of jobs and writes the high-multiplicity word of the same instance: for every job it counts the jobs with the same record, release date, weight and due date, and it writes the distinct tuples in increasing order. It runs in polynomial time on every word.

Theorem. Let $s \le t$, where $s$ has the standard encoding, no precedence constraints and no communication delays, and $t$ has high multiplicity. Then NP-hardness goes up from $s$ to $t$, and so does W[t]-hardness for parameters $\kappa_s$ of $s$ and $\kappa_t$ of $t$, if on every instance written by a high-multiplicity word of the lift of an instance $x$ of $s$, $\kappa_t$ is at most a computable function of $\kappa_s(x)$. Being in P goes down from $t$ to $s$, and so does fixed-parameter tractability under the same bound, for a parameter of $s$ computable in polynomial time.

Strong NP-hardness is not carried: a high-multiplicity word can be much shorter than the standard word of the same instance, so numbers that are small for the standard word can be large for the high-multiplicity word.

Theorem. Along $P \mid\mid C_{\max} \to P \mid HM \mid C_{\max}$, NP-hardness and W[t]-hardness for the number of machines go up, and fixed-parameter tractability for the number of distinct processing times goes down. Here the number of distinct processing times of $P \mid\mid C_{\max}$ is computed in polynomial time by writing the high-multiplicity word and computing it there, which fixed-parameter tractability of $P \mid HM \mid C_{\max}$ includes.