The Mathematics Dependency Graph
Every definition, theorem, and proof in the corpus is a canonical object with a stable identity, a kind, a bilingual name, and a certification status. Merged together they form one navigable graph: what rests on what, what is certified, and what still needs authoring across all four courses.
Solid arrows are certified prerequisites between courses. Dashed boxes are prerequisite courses the corpus assumes but does not yet contain. Real Analysis is the keystone gap: every course rests on it.
Choose a course, then a chapter, to see its canonical objects. Filter by kind or search by name.
The graph is honest about what is certified and what is not.
Objects per course
Curriculum gaps
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Missing
Real Analysis Sequences, series, limits, continuity, and the completeness of R are assumed throughout but not yet a course in the corpus. This is the keystone gap.
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Missing
Linear Algebra Vector spaces, dual spaces, and linear functionals support the functional-analytic viewpoint of distributions.
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Assumed
Set Theory and Logic Elementary set notation and logical implication, stated explicitly in the Topology chapter 1 prerequisites.
Each object carries a stable identifier of the form PREFIX-CHNN-KIND-NNN, a course and chapter, a kind, a bilingual name, and a status of extracted, reviewed, or certified.
The depends_on field is the edge set of the fine grained graph. It is authored, never guessed.
The result serves three roles at once: advising, accreditation, and planning.