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<a href="https://storage.googleapis.com/regal-scholar-453620-r7-podcast-storage/mathematics-processes-database/mathematics-database-table.html">← Mathematics Database</a>
<a href="discourse-schema.json">Schema (JSON)</a>
<a href="MATHEMATICAL_DEPENDENCY_GRAPHS_DESIGN.md">Design (Markdown)</a>
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<h1>Mathematical Dependency Graphs — Design Document</h1>
<h2>Overview</h2>
<p>A hybrid architecture for representing and visualizing axiomatic dependency structures across multiple mathematical subjects. Supports both static Mermaid subgraphs and interactive full-graph exploration.</p>
<h2>Scope: Target Subjects</h2>
<table>
<tr><th>Subject</th><th>Foundations</th><th>Derived Items</th><th>Notes</th></tr>
<tr><td><strong>Euclid's Elements</strong></td><td>Postulates, Common Notions, Definitions</td><td>464 Propositions (13 books)</td><td>Geometric constructions</td></tr>
<tr><td><strong>Peano Arithmetic</strong></td><td>5 axioms, definitions</td><td>Theorems</td><td>Successor, induction</td></tr>
<tr><td><strong>Other number systems</strong></td><td>Axioms (integers, rationals, reals)</td><td>Theorems</td><td>Construction sequences</td></tr>
<tr><td><strong>Number theory</strong></td><td>Definitions, lemmas</td><td>Theorems</td><td>Divisibility, primes</td></tr>
<tr><td><strong>Algebra</strong></td><td>Group/ring/field axioms</td><td>Theorems</td><td>Abstract structures</td></tr>
<tr><td><strong>Hilbert's geometry</strong></td><td>5 groups of axioms</td><td>Theorems</td><td><em>Grundlagen der Geometrie</em></td></tr>
<tr><td><strong>Tarski's geometry</strong></td><td>Betweenness, congruence relations</td><td>Theorems</td><td>First-order, decidable</td></tr>
<tr><td><strong>Analysis</strong></td><td>Completeness, continuity axioms</td><td>Theorems</td><td>Real analysis, limits</td></tr>
</table>
<h2>Metadata & Sources</h2>
<p>Each discourse includes <strong>metadata</strong> (created, lastUpdated, version, license, authors, methodology, citation) and <strong>sources</strong> (primary texts, digital editions, commentaries). Nodes can reference sources via <code>sourceRef</code>.</p>
<h2>Hybrid Architecture</h2>
<ol>
<li><strong>Canonical JSON</strong> — One file per discourse, source of truth</li>
<li><strong>Mermaid generator</strong> — Filter by book/chapter, output subgraph</li>
<li><strong>Interactive viewer</strong> — Full graph with zoom, search, highlight</li>
<li><strong>Index/Registry</strong> — Catalog of all discourses with metadata</li>
</ol>
<h2>Implementation Phases</h2>
<table>
<tr><th>Phase</th><th>Deliverable</th></tr>
<tr><td>1</td><td>Schema + Euclid Props 1–6 JSON; Mermaid generator script</td></tr>
<tr><td>2</td><td>Euclid Book I full JSON; static pages for Books I–IV</td></tr>
<tr><td>3</td><td>Interactive viewer (single discourse)</td></tr>
<tr><td>4</td><td>Peano Arithmetic, Hilbert Geometry JSON</td></tr>
<tr><td>5</td><td>Multi-discourse index; cross-discourse navigation</td></tr>
<tr><td>6</td><td>Tarski, Analysis, other subjects</td></tr>
</table>
<h2>References</h2>
<ul>
<li>Euclid's Elements: <a href="http://www.perseus.tufts.edu/hopper/text?doc=Perseus:text:1999.01.0086">Perseus Digital Library</a></li>
<li>Heath, T.L. <em>The Thirteen Books of Euclid's Elements</em> (1908, 2nd ed.)</li>
<li>Hilbert: <em>Grundlagen der Geometrie</em> (1899)</li>
<li>Tarski: <em>What is Elementary Geometry?</em> (1959)</li>
<li>Peano: <em>Arithmetices principia</em> (1889)</li>
</ul>
<p style="margin-top:2rem;color:#666;font-size:0.9rem;">Programming Framework · Mathematical Dependency Graphs Design · 2026</p>
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