Mathematical Dependency Graphs — Design Document

Overview

A hybrid architecture for representing and visualizing axiomatic dependency structures across multiple mathematical subjects. Supports both static Mermaid subgraphs and interactive full-graph exploration.

Scope: Target Subjects

SubjectFoundationsDerived ItemsNotes
Euclid's ElementsPostulates, Common Notions, Definitions464 Propositions (13 books)Geometric constructions
Peano Arithmetic5 axioms, definitionsTheoremsSuccessor, induction
Other number systemsAxioms (integers, rationals, reals)TheoremsConstruction sequences
Number theoryDefinitions, lemmasTheoremsDivisibility, primes
AlgebraGroup/ring/field axiomsTheoremsAbstract structures
Hilbert's geometry5 groups of axiomsTheoremsGrundlagen der Geometrie
Tarski's geometryBetweenness, congruence relationsTheoremsFirst-order, decidable
AnalysisCompleteness, continuity axiomsTheoremsReal analysis, limits

Metadata & Sources

Each discourse includes metadata (created, lastUpdated, version, license, authors, methodology, citation) and sources (primary texts, digital editions, commentaries). Nodes can reference sources via sourceRef.

Hybrid Architecture

  1. Canonical JSON — One file per discourse, source of truth
  2. Mermaid generator — Filter by book/chapter, output subgraph
  3. Interactive viewer — Full graph with zoom, search, highlight
  4. Index/Registry — Catalog of all discourses with metadata

Implementation Phases

PhaseDeliverable
1Schema + Euclid Props 1–6 JSON; Mermaid generator script
2Euclid Book I full JSON; static pages for Books I–IV
3Interactive viewer (single discourse)
4Peano Arithmetic, Hilbert Geometry JSON
5Multi-discourse index; cross-discourse navigation
6Tarski, Analysis, other subjects

References

Programming Framework · Mathematical Dependency Graphs Design · 2026