A hybrid architecture for representing and visualizing axiomatic dependency structures across multiple mathematical subjects. Supports both static Mermaid subgraphs and interactive full-graph exploration.
| Subject | Foundations | Derived Items | Notes |
|---|---|---|---|
| Euclid's Elements | Postulates, Common Notions, Definitions | 464 Propositions (13 books) | Geometric constructions |
| Peano Arithmetic | 5 axioms, definitions | Theorems | Successor, induction |
| Other number systems | Axioms (integers, rationals, reals) | Theorems | Construction sequences |
| Number theory | Definitions, lemmas | Theorems | Divisibility, primes |
| Algebra | Group/ring/field axioms | Theorems | Abstract structures |
| Hilbert's geometry | 5 groups of axioms | Theorems | Grundlagen der Geometrie |
| Tarski's geometry | Betweenness, congruence relations | Theorems | First-order, decidable |
| Analysis | Completeness, continuity axioms | Theorems | Real analysis, limits |
Each discourse includes metadata (created, lastUpdated, version, license, authors, methodology, citation) and sources (primary texts, digital editions, commentaries). Nodes can reference sources via sourceRef.
| Phase | Deliverable |
|---|---|
| 1 | Schema + Euclid Props 1–6 JSON; Mermaid generator script |
| 2 | Euclid Book I full JSON; static pages for Books I–IV |
| 3 | Interactive viewer (single discourse) |
| 4 | Peano Arithmetic, Hilbert Geometry JSON |
| 5 | Multi-discourse index; cross-discourse navigation |
| 6 | Tarski, Analysis, other subjects |
Programming Framework · Mathematical Dependency Graphs Design · 2026