In toto, and as stated, you are not correct.
If you would like to discuss the errors and misunderstandings in each of your points, we can explore them in more detail. Once we have the points clarified then you can revise your questions to reflect more accurate understandings and we can explore those questions.
In follow-up:
P1. Regardless of the source of CO2 (natural or anthropogenic), increases in atmospheric CO2 drives increases in global temperature.
First, there are a few little vocabulary distinctions that are necessary to discuss as a part of making sure that we stay on track. A
Climate Driver is a group of factors and influences that act in concert to impact and influence climate. CO2 ratios are an atmospheric composition factor that directly influences the surface temperatures (among other impacts and influences). CO2 can act in a feedback role, but it can also act as a primary forcing factor. A
climate forcing factor is an influence that directly impacts a specific aspect of climate. In the case of CO2, it acts as a forcing which influences increases (or decreases) in surface temperature due to the nature of how CO2 interacts with radiative energies (predominantly a narrow range of EM frequencies) transiting the atmosphere.
Simplified explanation:
AGW is an example of a climate driver.
Rising CO2 levels are one of the radiative forcing elements that work in association with others to create the AGW climate driver.
P2. As per the paleoclimate data, CO2 levels rise following increases in temperature.
Without considering any other factors, P1 and P2 should lead to a geometric progression (feedback cycle) of increasing temperatures and CO2 levels.
Paleoclimate data reflects instances where CO2 has acted as a feedback factor to both enhance small externally forced environmental temperature increases and decreases (e.g. Milankovitch cycle forcings). In these feedback roles, CO2 equilibration lags temperature changes.
Paleoclimate data also reflects instances where CO2 has acted as a primary forcing factor when natural CO2 reservoirs are induced to release large amounts of stored and previously sequestered CO2 into the atmosphere/active carbon cycle (e.g. the PETM, mid-Cretaceous Warming (~120Mya), Early Jurassic warming (183 Mya), and the modern Anthropocene AGW).
As for “runaway feedback cascades,” CO2 is not a good candidate for this type of effect under conditions of the typical insolation and STP (Standard Temperatures and Pressures) of the Earth’s averaged climate. The more CO2 in the atmosphere, the more CO2 it takes to affect surface temperature increases at STP (changes, significant pressure differences, for instance might result in a situation that more closely reflects your contemplated scenario – e.g. Venus situation – though water vapor probably played a significant role in the early runaway GHG situation on Venus)
If the above points are correct, some questions....
Alec was correct, even with the reframing necessary to make your points more accurately reflect mainstream science understandings, there are some answers to be given with regard to your questions.
Q1. Regardless of the source of CO2, at what point do CO2 levels have to reach to engage this feedback cycle so that it is irrevocable (self-maintaining)? For lack of a better term, I'll call this the Point of No Return. (PoNR).
In reconsidering the actual nature of CO2 and AGW, a similar concern is the fact that many of the same reservoirs that act as the feedback CO2 stores when the climate warms naturally through cyclical patterns such as the Milankovitch cycles, are going to release their reserves according to temperature (irrespective of what is causing that warming). These are the carbon reservoirs of our planet’s soils, waters, shores, and shallow water silts (on and off-shore). This is one of the areas that there is some uncertainty in mainstream climate science understandings. The precise conditions necessary to trigger these reservoirs to release their carbon stores, is not known.
These release conditions are generally referred to as Tipping Points or trigger conditions, and roughly equate to your PoNR.
Q2. Have we reached the PoNR?
Difficult to say, due to the fact that emissions are still increasing and accelerating in increase. Additionally, even short-term equilibration between CO2 (and the various other GHGs (Green House Gases) and other AGW factors) and realized surface temperature takes several decades. So, with the realization that most of the effects we are seeing today are the result of emissions which occurred decades ago, and we still have several decades worth of greatly increased CO2-forced warming already “in the pipeline,” combined with uncertainties in necessary trigger values, it is impossible to say whether or not we have actually reached or surpassed tipping points with the emission effects in the pipeline. I suspect that many of the short-term carbon reservoirs have been triggered into substantive but gradual releases (High latitude soils (permafrost) and lakes, mid-latitude soils and shallow water carbon reservoirs, etc.). Whether or not this is sufficient to reach large scale tipping points, I don’t think anyone can say conclusively at this time.
Q3. What mechanism(s) breaks this feedback cycle so that temperatures and CO2 stop rising?
Humanity is currently emitting ~30GT of CO2 per year (roughly the equivalent of one hundred super-volcanoes (Krakatoa equivalent) erupting every year. The first thing to do when you realize that you are accelerating towards a cliff is to take your foot off the accelerator. Ideally, the first step is to get humanity to a net-zero fossil carbon emission state as quickly as possible. Secondly, you probably want to invest in helping nature to actively drawdown atmospheric carbon into the 300-330ppmv range as quickly as possible. Beyond this, we are looking at a minimum of several centuries of fluctuations that will take a lot of time, money, and dedicated effort to adapt/adjust to, and survive. This is only if we accomplish the first step in the very near future. If we continue at the present rate for more than a few decades without substantive action, things get much worse, much quicker, for much longer, and our choices and options much fewer.
Q4. Related to Q3, what mechanism(s) causes CO2 levels to drop below the PoNR where they cannot restart the cycle?
Perfect stabilization of the Earth’s climate is, at the least, a bit beyond our current level of understanding, our existent technological capacity, and our economic willingness to invest in. That said, there are several viable approaches to reduce future impacts and intensities, with relatively minor shifts in public policy, economic investment, and individual/societal behavioral adjustment. The more time that passes, the fewer choices and options we have and generally the less desirable the outcome.