What is the reason for breaking the meem in the word "يومئذ" (yawmaʾidhin) in Surat Al-Ma'arij, verse 11, and would the meaning differ if the meem were opened (i.e., pronounced with a fatha)?

The word "yawma'idhin" (يومئذٍ) in Surat Al-Ma'arij is not the only instance where Hafs recites with a kasra on the letter meem. He also recites "wa min khizyi yawma'idhin" (وَمِنْ خِزْيِ يَوْمِئِذٍ) in Surat Hud with a kasra on the meem. The reciters differed regarding the meem in "yawma'idhin" in three places: Surat Sa'ala Sa'il (Al-Ma'arij), Hud, and An-Naml. The reason for thera on the meem, for those who recited with it, is considering "yawm" (يوم) to be genitive due to annexation (idafa). As for the fathah, its reason is the annexation of "yawm" to an indeclinable noun (idh - إذ). There is no difference in meaning between the kasra and the fathah, but the difference lies in the grammatical inflection (i'rab) and indeclinability (bina').