Methodology
How TheoremPath is organized.
Last updated: April 22, 2026
The site connects topic pages, prerequisite edges, diagnostics, references, practice work, and labs. Each layer has a narrow job.
Dependencies
Topic, definition, theorem, skill
Diagnostics
Question result to repair path
Sources
Citation to role and claim
Practice
Derive, implement, compare
Labs
Change a parameter, watch behavior
Page structure
A topic page starts with a concrete problem and a small set of prerequisites. It then moves through definitions, examples, formal statements, common mistakes, exercises, and links to related topics.
Labs appear when changing a parameter, running a simulation, or stepping through an algorithm teaches the concept better than prose alone.
Topic path
- 1
Problem
↓
- 2
Prerequisites
↓
- 3
Definitions
↓
- 4
Example
↓
- 5
Theorem or algorithm
↓
- 6
Exercise
↓
- 7
Lab
↓
- 8
Next topic
Prerequisite graph
The graph stores typed nodes: topics, definitions, statements, assumptions, equations, skills, exercises, source locations, and content gaps.
Edges are labeled by relationship: prerequisite, application, proof dependency, source grounding, misconception repair, or diagnostic result.
Diagnostics and learner state
Diagnostics map answers to prerequisite areas. A missed question can point to the topic, definition, or skill that explains the miss.
Where learner state is active, the first model uses Performance Factor Analysis over graph edges. New recommendation models are compared against baselines before they become product claims.
Source grounding
A source has a role. It may provide intuition, a formal statement, proof machinery, assumptions, exercises, implementation detail, historical context, or production practice.
The source map records what each reference is used for and where it connects to the topic graph.
The public source map is kept on the References page.
Corrections
Corrections target the smallest broken object: sentence, equation, edge, exercise, source note, or diagram.
Public pages keep claim text, source notes, and graph edges close together so mistakes can be traced and fixed without rewriting the whole page.
Practice
Practice pages collect worked derivations, implementations, simulations, ablations, plots, paper maps, and short reports. See Practice and Projects.