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Learning-Unit Progression and Access Policy (§11.5)

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Compendium: §§1–5 Core · §§6–10 Context · §§11.1–11.4 Units · §11.5 Progression · §12 Planning · §13 Implicit Mastery · Appendices B–F · Appendix A (Rules & Ampel)

11.5. Prerequisites and the Limits of a Unit Sequence

Two kinds of prerequisites must be kept distinct:

  • An atomic requires edge targeting a competence requires that competence alone rather than completion of its entire owning unit.
  • A whole-unit prerequisite is an explicitly authorized dependency between complete learning units: it requires full completion of the predecessor unit and belongs to the course composition contract outside the base relations \(C\) and \(R\).

Neither the compiler nor the coach may conflate those two statements.

The unit hierarchy itself must be acyclic. Anyone who further claims an indivisible whole-unit sequence – in which each unit is completed in full before the next begins – must also validate the projected unit-dependency graph. Atomic acyclicity alone does not suffice: for \(a \to b \to c\) with \(\Own(U) = \{a, c\}\) and \(\Own(V) = \{b\}\), unit \(U\) depends on \(V\) via \(a \to b\) while \(V\) depends on \(U\) via \(b \to c\). Grouping produces a mutual block cycle, so \(U\) and \(V\) admit no indivisible whole-unit order; resolving that finding requires re-scoping the unit boundary or explicitly permitting interleaved acquisition rather than inferring silent unit locks from atomic edges.

The atomic normal form \(R \subseteq A \times A\) and its ordered migration from Section 3 remain in force: secure complete atomic prerequisites first, remove redundant non-atomic edges second, and transitively reduce the atomic relation last. That rule implies no automatic minimality rule for a separate whole-unit prerequisite relation yet to be specified.

Access Profile Still Undecided

A domain acquisition order is not yet a technical access gate. Whether and when a whole-unit prerequisite enforces a hard technical entry lock – a unit lock – and how deliberate direct assessment attempts behave under it remains undecided. Any such profile requires a separate product decision and host verification; the learning-unit definition itself introduces none.

Only if an explicit gated access profile is later chosen could authorized predecessor units \(\operatorname{Pred}(U)\) define:

\[ \operatorname{Open}(U) = \bigwedge_{V \in \operatorname{Pred}(U)} \operatorname{Cleared}(V), \qquad \operatorname{Cleared}(U) = \operatorname{Open}(U) \land \Complete(U). \]

Here \(\Complete\) records established evidence whereas \(\operatorname{Cleared}\) expresses conditional course policy; neither opening a unit nor computing clearance writes mastery, and this conditional illustration does not settle whether direct assessment attempts remain open inside a locked unit.

Sources: Learning Units; Learning-Unit Progression and Access Policy; Graph Definition; Assessment-Gated Completion and Implicit Mastery.