The Spelling of Cannot

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To distinguish it from the emphatic "can NOT"?
e.g.  A) "She cannot sing."  [neg. ASSERTION]
                  vs.
       B) "She can not [NOT] sing." (1.DENIAL [She does not have my
permission to
           do so] or 2. DISAGREEMENT [I disagree with your assertion that she
can.])

I think, thus, that this spelling distinction (cannot/can not) reflects, or,
rather, parallels the pragmatic distinction between asserted (new) vs.
presupposed (familiar) information and, most importantly, the scope of
negation.  In (A), the scope is the lexical verb, "sing."  The presupposed or
familiar information, the subject "she," is not included; only the singing is
under the scope of negation .  The subject, "she," might have the ability, or
permission, to do engage in other activities.  In (B), the scope of negation
is ambiguous in that its boundary can be any or all of the affirmative
statement [both presupposed and asserted information].  Consequently, the
scope of negation can be either  the presupposed information [subject,
"she,"] as in, NOT She can sing [Someone else is able to or has permission
to'], or the entire proposition [The speaker disagrees with the assertion
that "she" can sing], or only the new, asserted information, e.g. NOT can
sing [The subject either does not have the ability or has not been granted
permission to do so].
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