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Do only giant stars initiate 'full-on' carbon (and higher element) fusion, even though red giants on the larger end of the spectrum create carbon and oxygen via producing helium per the CNO cycle?

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  • $\begingroup$ Welcome to physics SE. I do not fully understand your statements. Thus the answer would be incomplete. $\endgroup$ – jaromrax Jan 22 at 21:21
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No, even stellar-mass stars will produce helium in the proton-proton cycle, and this will normally produce enough helium to begin a helium-burning stage late in life. Of course many stars, including the Sun, will move between one of these being dominant; currently the Sun is mostly p-p, but will likely become dominated by CNO as its internal temperature rises - it's just below the crossover point of $17\times10^6$ now, at around $15.7\times 10^6\ \mathrm{K}$.

The heavier elements are created in different processes, and most of those do require a more massive star. For the periods leading up to these events, the more sedate parts of the cycle, this Wiki article has a good overview.

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I try to give a brief overview, since the question is not much clear to me:

Carbon is generated in so-called three alpha cycle (three $^4$He participating), which takes place in Red Giants (RG), Asymptotic Giant Branch (AGB) and other heavier stars.

CNO cycle is not producing carbon or oxygen. Carbon is used as a catalyst to create $^4$He and carbon is returned into the environment. CNO cycle has leaks, so some carbon is converted to heavier isotopes (F, Ne ...).

Elements up to iron are generated in cores of heavy stars (can be also blue giants). Lighter stars (like Sun and less) basically end up with carbon cores. This was probably your original question.

Elements above iron (but lighter are also not excluded) are generated by other processes, part of it takes place inside RG and AGB star's intershells and the process is based on neutron captures.

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