Math Academy-style pedagogy validation

Is the curriculum sound?

Each check below is a falsifiable claim about the prerequisite graph. Together they form a benchmark you can re-run after any edit to see whether the graph still holds up against the report’s recommendations.

Nodes

Edges

Hours

14.1h

Pass

Warn

Fail

Verdict

All hard checks pass — soft warnings remain.

Connectivity
No isolated nodes, no orphan leaves, every node reachable from a root, no cycles.
0 issues
Forward phase ordering
Every prereq comes from an earlier or same phase. Detects out-of-order edges that would gate a Week 1 skill on a Week 11 skill.
0 backward edges
Multiple entry points
At least three roots so a learner has multiple ways into the graph.
2 roots
Details
- Roots: paths-to-knowledge, principle-of-locality
Capstone & thread termini
All terminal nodes (no dependents) are accounted for in the curriculum's known apex/thread-terminus list; unexpected leaves suggest missing edges.
1 terminal
Details
- 1 terminal nodes, all expected (1 metacognitive apex + 0 thread termini)
14-hour short-course coverage
Sum of estimated hours across all lessons should reach the 4-week / 14-hour goal (3.5 hrs/week × 4 weeks).
14.1h
Details
- 14.1h estimated · target 14h
Phase balance
Every 1-week phase should hold at least 4 lessons so the short course doesn't collapse onto one phase.
4/4 phases ≥ 4
Details
- Week 1: reason: 8 nodes
- Week 2: reality: 5 nodes
- Week 3: constructor theory: 4 nodes
- Week 4: applied reason: 5 nodes
No single-point bottleneck
With only 2 roots, foundational singing nodes can legitimately gate 85%+ of downstream learning. Past 85% is a watch-list, past 99% (single-rooted graph) is a chokepoint.
3 foundational nodes
Details
- paths-to-knowledge gates 91% of downstream nodes
- fallibilism gates 82% of downstream nodes
- role-of-evidence gates 77% of downstream nodes
Reasonable longest path
The deepest chain from a root shouldn't exceed ~14 nodes — too long means the user must master many things in serial before reaching anything new.
max depth 8
Details
- synthesis-capstone: depth 8
- information-substrate: depth 7
- rationality-in-business: depth 7
Practice nodes reachable
Every interactive practice drill should sit within 12 steps of a root. The curriculum spans 12 weeks; capstone pieces can be deep, but no node should be unreachable.
all reachable
Details
- All practice nodes within 12 steps of a root.

Source: src/lib/learning/pedagogy-benchmark.ts