Most education software can report what lesson a learner completed. It is much less certain about what the learner can still explain, solve, or apply after the interface has moved on.
A local-first, LLM-readable knowledge model that represents concepts, prerequisites, evidence, attempts, and mastery state rather than storing education as a flat sequence of lessons.
The aim. Help learners and AI tutors reason about what is known, what is missing, and what should come next.
01The problem behind the project
Most learning software knows what content it served but not what a learner can actually explain or apply. A graph can expose gaps and support more precise next-step decisions.
MasteryGraph treats learning as a network of capabilities with prerequisites and evidence. Attempts, errors, review history, and demonstrations of competence attach to the graph so that the next step can respond to a learner's actual state rather than a fixed course sequence.
Learners, parents, teachers, curriculum designers, and AI tutors may benefit. Mastery judgments can shape opportunity, so evidence and uncertainty must stay visible.
02How it took shape
A written methodology, graph-oriented content structures, agent-readable documentation, and an applied companion artifact in MasteryMath.
The methodology is expressed as local, inspectable structures that both software and AI tutors can read. MasteryMath serves as the first applied artifact, translating graph ideas into deterministic problems, checking, progress records, and a parent-facing view.
Josiah developed the learning-system ideology and directed the translation from broad mastery ideas into an implementable local-first model.
The methodology is embodied partly in a working SwiftUI companion prototype, but broader learning-outcome validation has not been performed.
03What the project means now
The project does not argue that every form of learning should become a score. Its stronger claim is that educational systems should preserve why they believe a capability is mastered, what evidence would change that belief, and which prerequisite gap explains an error.
A graph does not automatically create good pedagogy, and mastery cannot be reduced safely to a single score without domain-specific evidence.
The useful unit for an AI tutor is not just a lesson; it is a claim about capability attached to evidence and prerequisites.
Publish the methodology with a worked synthetic example and explicitly map which parts MasteryMath currently implements.