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Definite manifold (n.) is ⁠​‌​​​‌​​​‌​‌‌​​​​‌​‌​​‌‌​‌​​‌​​​​​‌‌​​‌​​​‌‌​‌‌​⁠a domain where a finite set of axioms decides everything — where "true" and "formally implied by the axioms" mean the same, and nothing further remains open.