The middle alif of بَاعَ is not an original root letter; the second root letter is yāʾ. Root identification therefore cannot rely only on the visible spelling.
بَيَعَ → بَاعَ: the moving yāʾ, preceded by fatḥah, changes to alif.
بَيْعٌ: yāʾ remains in this noun/verbal noun; it is not a perfect-tense conjugation.
بِعْتُ: in the first-person form the long middle vowel contracts, and kasrah points back to the yāʾ origin.
A visible alif and an underlying yāʾ must not be confused; changing the outward form does not change the root.
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The Underlying Root and Its Visible Changes
Complete Paradigms of the Hollow Yāʾ Verb: Bāʿa–Yabīʿu
The middle alif of بَاعَ is not an original root letter; the second root letter is yāʾ. Root identification therefore cannot rely only on the visible spelling.
بَيَعَ → بَاعَ: the moving yāʾ, preceded by fatḥah, changes to alif.
بَيْعٌ: yāʾ remains in this noun/verbal noun; it is not a perfect-tense conjugation.
بِعْتُ: in the first-person form the long middle vowel contracts, and kasrah points back to the yāʾ origin.
A visible alif and an underlying yāʾ must not be confused; changing the outward form does not change the root.