Is the curriculum sound?

• 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: red-flag-screen, pulse-clap

• 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.

  16 terminal
  Details

  • 16 terminal nodes, all expected (1 metacognitive apex + 15 thread termini)

• 70-hour curriculum coverage

  Sum of estimated hours across all KPs should reach the 3-month / 70-hour goal (5–6 hrs/week × 12 weeks per the source report).

  69.8h
  Details

  • 69.8h estimated · target 70h

• Phase balance

  Every 2-week phase should hold at least 4 KPs so the curriculum doesn't collapse onto one stretch.

  6/6 phases ≥ 4
  Details

  • Weeks 1-2: foundation: 10 nodes
  • Weeks 3-4: onset & solfège: 10 nodes
  • Weeks 5-6: vowels & SOVT: 10 nodes
  • Weeks 7-8: scale, intervals & dynamics: 10 nodes
  • Weeks 9-10: bridge & range: 10 nodes
  • Weeks 11-12: a cappella & repertoire: 10 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.

  5 foundational nodes
  Details

  • red-flag-screen gates 97% of downstream nodes
  • alignment-and-release gates 93% of downstream nodes
  • silent-breath-hiss gates 92% of downstream nodes
  • hum-onset gates 90% of downstream nodes
  • speaking-center gates 87% 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 17
  Details

  • rescue-drill-selection: depth 17
  • harmony-over-drone: depth 16
  • self-diagnosis: depth 16

• 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.

  19 too deep
  Details

  • major-pentachord (depth 13)
  • third-echo (depth 13)
  • fourth-fifth-echo (depth 14)
  • glide-to-landing (depth 14)
  • two-syllable-legato (depth 14)
  • two-phrase-memory (depth 13)
  • one-octave-scale-fragment (depth 14)
  • tonic-dominant-arpeggio (depth 15)
  • degrees-against-drone (depth 13)
  • five-note-melisma (depth 15)
  • phrase-transposition (depth 14)
  • call-response-variation (depth 15)
  • a-cappella-resolve-tonic (depth 14)
  • verse-breath-plan (depth 14)
  • unison-with-guide (depth 15)
  • harmony-over-drone (depth 16)
  • song-from-memory (depth 15)
  • self-diagnosis (depth 16)
  • rescue-drill-selection (depth 17)

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