Preface: Etymonline does not answer this question. I (but please tell me if I should not) quote the definitions for the English verbs (Loan words from Latin then Old French) because they did not shift semantically and so equal the Latin definitions.
[5. 'compōnō ' on Wiktionary :] [...] From com- + pōnō (“put”). [...]
- I arrange, compile, compose, make up.
- I construct, build.
- I organize, order.
- I settle.
[6. 'cōnstituō' on Wiktionary :] [...] From con- (“with”) + statuō (“set up; establish”). [...]
- I set up, establish, confirm
- (with infinitive) I decide, resolve.
Abbreviate 'Inanimate Subject(s)' to IS, and any 'direct object' as DO. Consider this syntax:
1. IS
composes \\ constitutesDO.
Replace the verbs in question by definitions 5.1 and 6.1 above:
2. IS
makes up / constructs \\ sets upDO.
2 makes no sense; IS itself (assumed inanimate) cannot cause directly, but IS can cause indirectly through chance and randomness (ie: the Big Bang effect). So if 2's verbs are interpreted causatively as in 3 below, then
3 appears to justify com- as a causative prefix;
but is any of the above correct?
3. IS CAUSES TO BE
made up / constructed \\ set upDO.