Hard requirements
Ideas or operations needed to interpret the target at all. Missing one makes the formula or procedure ambiguous.
Learning paths
Start where you are. Build only what you need.
A learning path should not assume that every visitor has the same foundation. MW SysArc maps the concepts a target depends on and distinguishes requirements from helpful support and optional enrichment.
The readiness model
Three kinds of preparation
Strong support
Knowledge that makes the target substantially easier and reduces common mistakes, but can be repaired alongside practice.
Optional enrichment
Extensions, proofs and adjacent concepts that deepen mastery without blocking the immediate calculation.
Example
From a high-school foundation to vector projection
Signed numbers
Coordinates
Right triangles
Components
Dot product
Projection
The path is not a mandatory course sequence. A learner can demonstrate an existing step, skip it and continue. If a mistake reveals a missing dependency, the repair link returns to the smallest useful concept rather than restarting the entire subject.
Calculation remains available. Readiness guidance should help users learn without withholding the practical tool they came to use.
Path design
What makes a learning path useful
A concrete destination
“Compute and interpret a vector projection” is testable. “Understand vectors” is too broad to guide a route.
Canonical repair pages
One maintained explanation should repair each concept. Copying the same lesson across thousands of pages creates drift.
No circular dependencies
The prerequisite graph is checked so a learner is never told that A requires B while B requires A.
Consistent meaning
Intuitive, practical and formal explanations describe the same relationship rather than unrelated examples.
Visible reasons
Each prerequisite explains why it matters, so preparation feels purposeful rather than bureaucratic.
Progress without punishment
Skipping, revisiting and experimenting are legitimate. The path supports agency instead of enforcing one pace.