Scheduling problems in the three-field notation $\alpha \mid \beta \mid \gamma$ are formalized as assemblies of independent fields, so that every problem is a problem in its own right and the relations between problems follow from relations between the values of single fields.

A kernel fixes what a schedule is. A field over a kernel is a restriction of its instances, a constraint module that adds data and a condition on schedules, or an objective. A specification chooses one value in every field and determines a problem. If one specification is field by field a special case of another, the data maps of the fields combine into an embedding of the first problem into the second, which is sound whenever every field is. Two families of fields cover the problems: one in which every job is a sequence of operations, for parallel machines and shops with and without preemption, and one for serial and parallel batching. Their fields cover machine environments, processing times, numbers of machines and jobs, machine sets, release dates, deadlines, precedence constraints in sixteen classes with time lags, communication and transportation delays, a transport robot, a server with setup times, batch setups, no-wait, no-idle, forbidden times, high multiplicity, and sixteen objectives. Maximizing the smallest machine load and scheduling with rejection are formalized as problems of their own.

The construction is carried out for The Scheduling Zoo. All 747 of its problems are specifications. Three of the 614 relations in its data come from two rules of its notation that do not hold; with the two rules corrected the data has 612 relations, and all are proved: 566 as special cases and 34 as reductions of decision versions, each checked by evaluation, and 12 encodings that change the instance, proved one by one. The general theorems also relate pairs of problems of the zoo that its data does not relate.

Instances and schedules are read as words of natural numbers, every field written through its view, the meaning its constraints use, so that the word of an instance of a special case is also a word of its image. Against this reading, 950 results of the zoo are stated in terms of running times on the word RAM, P and NP-hardness, fixed-parameter tractability and W[t]-hardness, as defined in registered formalizations, and the open questions of the zoo are posed as pairs of competing propositions. Proved transfer theorems carry results along the relations: algorithms go down along special cases and hardness goes up, and hardness also goes along the threshold steps between objectives, along the encodings of machine sets, and from the standard encoding to high multiplicity. Strong hardness, with numbers polynomial in the length of the input, is distinguished from plain hardness throughout. Proved from the words up, building on registered formalizations: Smith's rule decides $1 \mid\mid \sum w_jC_j$ within $O(n \log n)$ instructions plus the length of the input; $1 \mid r_j \mid L_{\max}$ is strongly NP-hard, and para-NP-hard in $p_{\max}$ and in the number of distinct processing times; $P \mid M_j \mid \sum w_jZ_j$ is fixed-parameter tractable in $m + p_{\max}$ and strongly W[1]-hard in $m$; and $FF(1,m) \mid\mid \sum Z_j$ is strongly NP-hard and strongly W[2]-hard in $m$, while $FF(1,m) \mid\mid \sum w_jZ_j$ is solved within $O(W n^m)$, $O(W m^{q_{\max}} n)$ and $O(W 2^{\chi} n)$ instructions, $W$ the total weight.