Skill Graph

SkillPilot represents learning goals and their prerequisites as a shared graph. Educational programmes organise those stable goals into contextual views and learning units. This section explains both the graph and the contracts around it.

Foundations (Single-Source Compendium, EN & DE)

• Complete PDF Compendia: The SkillPilot Graph Definition (English PDF) · Die Graph-Definition von SkillPilot (Deutsches PDF) — generated from the canonical single source with full mathematics, bilingual illustrations, 145-rule enforcement traffic light (Ampelschaltung), and implementation boundaries.
• Graph Definition — Core (§§1–5, EN) · Deutsch (DE): formal goals, relations, prerequisites, frontier, and graph-validity conditions.
• Context, Views, Scope & Goal Types (§§6–10, EN) · Deutsch (DE): canonical layer vs. educational views, personal curriculum scope \(L=\mathrm{Closure}(S)\), understanding/memorisation/assessment goals, time context, and evidence boundaries.
• Learning Units (§§11.1–11.4, EN) · Deutsch (DE): recursively composed educational units, motivational introduction, required outcomes, and completion derived from child units and own obligations.
• Learning-Unit Progression (§11.5, EN) · Deutsch (DE): explicit course dependencies, whole-unit ordering, and the separate choice of access policy.
• Learning-Unit Design Criteria and Examples: the purpose of a unit, criteria for meaningful boundaries and assessments, two worked candidates, and the unit validity rules R1–R5 of 11 November 2026 applied to unit design.
• Optional Acquisition & Time Planning (§12, EN) · Deutsch (DE): multi-period acquisition plans, structural prerequisite witnesses, and workload budgets.
• Assessment-Gated Completion & Implicit Mastery (§13, EN) · Deutsch (DE): direct assessment access, transitive minimality, and globally effective recognition through independent application in valid local learning units (implementation pending). Decision of 4 November 2026. Umsetzungsplan: Lerneinheiten und integrierte Lernkarte.
• Compendium Appendices (B–F, EN) · Deutsch (DE): current implementation status, verification strategy, glossary/symbols, sources, and build reference; for Appendix A see Rule & Milestone Matrix (DE) · English (EN).

Architecture, Media, Goal Book & Interchange (Single-Source Compendium, EN & DE)

• Complete PDF Compendia: Skill Graph Architecture, Media, Goal Book & Package Interchange (English PDF) · Skill-Graph-Architektur, Medien, Lernzielbuch und Paketaustausch (Deutsches PDF)
• General Goal System and Migration (§1, EN) · Deutsch (DE): the separation of goals, programmes, placements, competency axes, and views.
• Node Types (§2, EN) · Deutsch (DE): orientation, understanding, memorisation, and assessment goals.
• View Projection and Goal Placement (§3, EN) · Deutsch (DE): explicit curriculum structure, personal learning scope \(L\), and scope-specific learner views.
• Source And Resource Links (§4, EN) · Deutsch (DE)
• Contentanbindung: Architekturrahmen (§5, DE) · English (EN)
• Human-Readable Source Rationales (§6, EN) · Deutsch (DE)
• Atomic Goal Visualizations (§7, EN) · Deutsch (DE)
• Learning-Goal Book and Evidence-Review Pipeline (§8, EN) · Deutsch (DE)
• Lernzielbuch und lokale Zeitplanung für Lehrkräfte (DE) · English (EN)
• Canonical Gymnasium Rollout Policy (§9, EN) · Deutsch (DE)
• MEM/FWU Roundtrip Plan (§10, EN) · Deutsch (DE)
• Duale Curriculum-Pakete (§11, DE) · English (EN)

See the Concept Documentation Index for didactic concepts and runtime workflows, and the Glossary for shared terminology.

Build Web & PDF Compendia from the Canonical Single Source

All bilingual Web chapters, the 145-rule traffic-light matrix, the bilingual diagrams (00, 08–16), and both LuaLaTeX PDFs are compiled from the canonical single source under docs/concept/skill-graph/source/ (only sources and static original illustrations 01–07 are tracked in Git; generated outputs are built locally and in CI):

python3 docs/concept/skill-graph/build_spec.py --web-and-tex
python3 docs/concept/skill-graph/build_spec.py --all
python3 docs/concept/skill-graph/latex/check-assessment-model.py

The single-source compiler (and compatibility wrapper latex/build-document.py) keeps intermediate LaTeX files under tmp/skill-graph-document/ and writes the generated Markdown pages, bilingual diagram PNGs, and DE/EN PDFs into docs/. Its optional --texmf argument accepts a locally unpacked TeX package tree without changing system packages.

The mathematical reference check exercises full transitive prerequisite demand, local recognition and their boundary cases. It does not implement the runtime feature or establish assessment quality or learner benefit.