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The literal meaning of "sumimasen" in this particular context is "it is not resolved/it is not over", in the sense that whatever transgression has warranted a sumimasen is so terrible that it simply isn't resolved by a mere apology. This is similar to the other popular Japanese apology moushiwake arimasen/gozaimasen, which literally means "there is no excuse," and implies that one is throwing oneself on the mercy of the person to whom the apology is being directed.

The importance of knowing the literal meaning of sumimasen can be seen from the following common expressions:
A: ¤ªÂÔ¤¿¤»¤·¤ÆºÑ¤ß¤Þ¤»¤ó¡ª
A: O-matase-shite sumimasen!
Hon-wait(causative)-(progressive) resolve-negative
B:ºÑ¤ß¤Þ¤»¤ó¤Ã¤Æ¡¢ºÑ¤ß¤Þ¤»¤ó¤ÇºÑ¤à¤â¤ó¤«¡ª
B: Sumimasen tte, sumimasen de sumu mon ka!

Resolve-negative (quote), resolve negative-with resolve (negative emphatic)
Here, A said "I'm sorry for keeping you waiting," to which B replied "Sorry? Sorry isn't gonna cut it!" Sumu is the plain infinitive form of "sumimasen."

Another common expression involving the same verb is:
Âþ¤¸¤ãºÑ¤Þ¤Ê¤¤¤¾
Tada ja sumanai zo!


This literally means "(it) won't be resolved (sumu) simply!" The actual meaning is more of a threat. It could be translated as "this isn't over yet" or "you won't get off easy for this," or even "I'll make you pay for this," depending on the context.