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# State/Binary quadratic forms are uniquely determined by their values at a superbasis

Proposition: (Binary quadratic forms are uniquely determined by their values at a superbasis) Suppose that $\{ \pm \vec e, \pm \vec f, \pm \vec g \}$ is a lax superbasis. Suppose that $\alpha, \beta, \gamma \in \ZZ$. Then, there exists a unique integer-valued binary quadratic form $Q$, such that: $$Q(\vec e) = \alpha, Q(\vec f) = \beta, Q(\vec g) = \gamma.$$

## Logical Connections

This statement logically relies on the following definitions and statements: Def/Lax superbasis, Def/Binary quadratic form, State/Arithmetic progression rule for binary quadratic forms

The following statements and definitions rely on the material of this page: State/The domain topograph has no circuits

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