How this is verified
Quadrature is AI-authored under an owner-designed verification system. There is no human-review gate on the mathematics by design — the verification system is the safeguard, and the build fails rather than ships when a claim does not hold.
Two honest axes
The algebra solution, the calculus derivation, the proof that the two agree, the dimensional check, and the closed form the graphs run on are all produced and checked by SymPy. The proof is shown, not asserted — see the proof panel in any lesson.
The physics modeling assumptions — g = −10 (a clean-arithmetic simplification of 9.81), "no air resistance," "point mass" — are an author's claims. They are disclosed, not discharged: you can check the math against SymPy, but you take the model on a textbook's footing. They never enter the derivation record.
What breaks the build
- A failed algebra = calculus proof. Each identity must reduce to zero (
simplify(algebra − calculus) == 0) via a tiered symbolic + high-precision numeric checker. - A non-homogeneous unit. Every expression's dimensions must balance.
- A schema mismatch. Every shipped object is validated against a strict JSON Schema.
- A closed form that drifts from SymPy. The JS the browser runs must reproduce SymPy's own sample values to within one part in a billion (the parity oracle).
- Math that will not render. Every LaTeX string must render with KaTeX.
- A dead formula link or leaked notation. Every in-prose formula reference must resolve to a real reference entry, and generated formula typography must contain no leaked source-notation symbol names.
- A platform-specific name. A scan gate keeps the course provider-agnostic.
The three regimes
"Algebra is just calculus done" is only true for constant acceleration. Every topic declares which of three relationships it is: (1) algebra is calculus evaluated; (2) calculus does what algebra cannot (non-constant forces); (3) algebra-only. A learner always knows which one they are looking at.