>No, it shows an older law m+m > F+m (just as n+m > r+m), replaced by analogy in most compounds , etc., (compare f>s seen in alt. in parfa U; *parsa > parra L; and acc. pl. *-emF > -e:s L; etc.). All this before pH>f occurred, etc.
> This thread from 2008, in which evidence was presented for Kluge's assimilation in Celtic, got me thinking that the peculiar present stem of Latin <mitto:> 'I send', against <mi:si:> 'I sent' and <missus> 'sent', might be analyzed the same way. Old Latin <cosmittere> (Paul. Fest.) for <committere> 'to join, entrust to, commit' shows that the Proto-Indo-European root began with *sm-.
>It has been identified by some as *smeit- 'to throw', recognized in Avestan <mae:þ-> 'to throw', <hamista-> (*ham-[h]mista-) 'downcast, oppressed', etc. (Pokorny, IEW 968). The fricative in <mae:þ-> suggests that the Iranian words in fact reflect PIE *smeith2-, from which Lat. *mititus rather than <missus> would be expected, and the gemination in <mitto:> is not adequately explained.
>Not really difficult; this is the clearest and only acceptable explanation.
> De Vaan (Et. Dict. of Lat. and the Other Itc. Lgs. s.v., 2008) dismisses <cosmittere> as untrustworthy and argues instead for derivation from PIE *meith2- 'to exchange, remove'. This root is supported by Sanskrit <methete> 'he becomes hostile, quarrels' (i.e. 'exchanges blows'), Germanic *maidaz 'changed, abnormal' (Old English <gema:d> 'insane, mad'), Lat. <mu:to:> 'I (ex)change, remove', and other words. De Vaan places South Picene <meitims> nom. sg., <meitimúm> acc. sg. 'monument' here also. Again however the root-final laryngeal should give Lat. *mititus; there is no basis for dropping it to get *meit- going into Proto-Italic. De Vaan at least recognizes the difficulty of deriving <mittere> from *mi:tere by the so-called littera-rule (i.e. -V:C- replaced by -VCC-, dialectal as explained below) since there is no trace of *mi:tere.