How it works
How TheoremPath organizes learning, claims, and evidence.
Last reviewed: April 30, 2026
TheoremPath does not treat a topic page as one large article. It breaks the page into reviewable objects: prerequisite edges, claim records, source roles, diagnostic items, evidence notes, and practice work. That makes the site easier to audit and easier to improve.
See the public evidence page for representative Lean wrappers and display rules, or the Lean verification dashboard for the full manifest.
Operating rule
The site is useful only if the same underlying objects serve the article, the diagnostic, the source trail, and the proof record. Prose explains the object; it does not replace it.
- Dependencies
- What must be known first
- Claims
- Exact statement, assumptions, failure modes
- Sources
- What supports the claim, and how strong it is
- Diagnostics
- Which skill each question tests
- Evidence
- Source checks, Lean scope, review state
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.
Diagrams, demos, and project work are supporting material. They are included when they clarify a concept, not because every topic needs an interactive surface.
System loop
From a learning goal to the next useful prerequisite.
This is the core mechanism behind diagnostics and future public evidence displays.
- 01
Target
Start with a theorem or paper goal
Name the thing the learner wants to understand, then expose the prerequisites it depends on.
- 02
Diagnose
Map answers to skills
Q-matrix links connect each diagnostic item to the definitions, claims, and techniques it tests.
- 03
Ground
Attach claim evidence
Claim records keep statements, assumptions, failure modes, and source roles together.
- 04
Verify
Record exact proof scope
Lean entries name the theorem declaration and the scope they actually verify.
- 05
Route
Recommend the next prerequisite
The study path uses graph edges and evidence state, not page-level guesses.
Evidence records
These records make the system inspectable. They say what is supported, what is formally checked, and what should be rechecked.
Claim record
Statement, assumptions, failure modes, changed fields, dependent claims.
Makes corrections claim-level instead of trusting or rewriting an entire page.
Source support
Source role, locator, authority tier, support status.
Separates canonical support from context, examples, and informal references.
Lean mapping
Declaration name, import path, proof scope, check status.
Counts only exact-scope wrappers as Lean evidence for a governed claim.
Diagnostic item
Question ID, mapped skills, answer evidence, difficulty signal.
Lets the system explain which prerequisite is blocking a learner.
Review queue
Reverse dependencies from changed sources, claims, or proofs.
Shows what needs revalidation before public trust indicators change.
Current verification boundary
A missed answer
Maps to the prerequisite skill it tests, then points to the shortest useful review path.
A changed claim
Keeps its own assumptions, sources, version history, and re-review state.
A Lean proof
Counts only for the exact theorem scope recorded in the Lean mapping.
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.
Source authority is tracked separately from source support. Canonical textbooks, peer-reviewed papers, arXiv preprints, authoritative documentation, and informal sources should not carry the same review weight.
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.
Claim trust
The trust unit is a claim, not a whole page. A theorem, definition, empirical result, or algorithmic statement can have its own assumptions, failure modes, source roles, and review state.
Claim records are versioned at the claim level. When a source, assumption, Lean wrapper, or statement changes, dependent claims can be queued for re-review without rewriting an entire topic page.
Source-checked means a reviewer attached source-location support. A formal Lean statement means a scoped declaration exists. Lean verified is stronger: it requires a generated Lean mapping from CI with no sorry or admit.
Some governed claims have source-check records or Lean-verified wrappers, but most of the corpus is still reviewed by source trails, assumptions, and correction workflow. TheoremPath is not Lean verified as a site. A single proof artifact does not give a topic page a public badge.
Adaptive learning boundary
The current adaptive layer uses question evidence, a Q-matrix, graph prerequisites, and interpretable mastery updates. Learner estimates should name the amount of evidence behind them.
The system does not present a single quiz run as a fixed ability score. Recommendation policies are treated as experiments: shown, clicked, completed, and ignored events matter.
Practice
Practice pages collect worked derivations, implementations, simulations, ablations, plots, paper maps, and short reports. See Practice and Projects.