If a theory works, it works for all applications from all perspectives. This still does not prove a theory, just proves it is difficult to disprove the theory. Arrhenius' greenhouse gas equation is a result of his attempting to develop a theory that carbon dioxide causes the ices ages. His theory didn't make it but was revived to explain global warming. Warming caused by CO2 correlates with concentrations somewhat, but there are exceptions. So Arrhenius' equations are not close enough to be a solid theory. To understand why, the true magnitude of the impacts on the atmosphere and oceans need to be better understood. As the magnitude of one impact decreases more much smaller impacts by other physical variables become more significant. It becomes a very interesting puzzle, resembling chaotic changes due to unknown impacts. Chaos is explainable. The inertia of one process does not match the inertia of another. That causes the slower process to over run its ideal equilibrium for conditions set by the changing faster process. So if chaos is explainable, it may be calculable to a degree that it may be predictable.
A stumbling block to predicting chaotic patterns is that the data available is not perfect. It has its own chaotic nature. To make sense when comparing two chaotic data sets, a common initial state is required. The one biggest hurdle in climate science it that initial state, the Ice Ages.
The solar cycles have the greatest correlation with temperature over the Ice Ages, but the degree of change in solar impact is smaller than required to produce the estimated temperature change of the ice ages. Something is wrong if the chaotic nature of climate is to be determined to a degree that it is predictable. That out of range value is the Vostec ice cores.
One of the more significant orbital variables that changes the solar impact on Earth's climate is axial tilt. The Earth tilt changes a few degrees over a period of 14,000 years. As the angle of tilt changes, the wobble on the axis changes. Both of these orbital changes are internal to the Earth/Moon orbital system. Changes in solar output and changes in the distance from the sun during orbit are external factors. The internal factors are key to understanding climate.
The ice ages are characterized by ice, of course, huge glaciers that covered larger portions of the northern hemisphere. That change in the mass distribution and the altitude of the mass changes the tilt and wobble of the Earth. As ice mass builds in the Canadian region and upper United States, the center of rotation shifts toward that center of mass. This region has the greatest impact on rotation because it has a higher average altitude and sufficient land surface area to support the mass.
At the southern polar region, the Antarctic continent is more nearly centered with the current center of rotation. Once the accumulated northern hemisphere ice mass is great enough, the southern pole shifts away from the center of the Antarctic continent. When the maximum tilt occurs, the precipitation patterns change. More ice builds on the Antarctic continent and more rain falls in the region of Siberia. Since Siberian rivers drain to the Arctic ocean, when those rivers are blocked by glacial ice, the Siberian region become a huge inland lake. That lake changes the precipitation pattern in the Northern hemisphere, increasing the rate of snow and ice accumulation in the Canadian/US region.
What happens at this point is that the region that the Antarctic and the Arctic draw their moisture from changes. As the Australian land mass become cooler with the shift, the average temperature of the oceans feeding the Southern pole decreases. This changes the average temperature and CO2 concentration recorded in the Vostec ice cores. The question becomes, how indicative of global average temperature are the ice core records?
During interglacial periods, the ice cores indicate that CO2 concentration was about 280PPM and that temperatures were about 8 degrees warmer. The concentration of CO2 can be calculated to be approximately controlled by a water temperature of 300K degrees. That is an example, not something that should be taken as a solid value. During a glacial period, the CO2 concentration is approximately 190PPM. That can be calculated to be associated with an average water temperature of 280K degrees, also an approximation. So during an interglacial, the moisture provided to the Antarctic could be supplied more by the mid latitudes and during a glacial period, more by the lower latitudes. That agrees with the shift of the southern pole from the center of the Antarctic land mass to the Eastern edge where more moisture from cooler oceans would be included in the average precipitation.
If this is the case, the the Vostec ice cores are telling a different story than commonly reasoned. That the average temperature of the Antarctic is not changing as much, the average temperature of the oceans providing the moisture is changing. A subtle but distinct difference.
At a maximum glacial period, the inertial mass of the Antarctic and the Arctic regions are competing. A large portion of the stabilizing mass in the Arctic region is the water contained in the Siberian region. Once the maximum inertial forces of the Northern and Southern poles coincide, the likelihood of instability of the glacial dams blocking the outflow of the Great Siberian Lake reaching a breaking point increases. Once that happens, the draining of the region changes the mass balance adding to the tilt and wobble of the Earth's rotation. This decreases the probability of the Great Siberian Lake reforming sufficiently to restore the pseudo-stable axial rotation.
This possibility leads to new possibilities. At the maximum tilt, the geomagnetic field would shift slowly as the internal dynamo tries to find its new equilibrium. The draining of the Great Siberian Lake alters the internal dynamics forcing the internal dynamo to seek a new equilibrium. If the rate of change is enough at the maximum axial tilt, the shift can cause a geomagnetic reversal.
The main question involving CO2 is how much impact it has. Without including positive feed backs, the impact from 190PPM to 420PPM is approximately 2.5 C degrees. The decrease in CO2 with such a small change in temperature by ocean absorption is much smaller. So the CO2 concentration in the Vostec ice cores is unlikely due to a change in global temperature, more likely a change in biological CO2 utilization and glacial sequestering.
If this theory is correct, that internal variability determines the ice ages, then the impact of man on climate is significant and significantly different than theorized. Man has more impact on the rotational tilt of the Earth by removing accumulating snow ans ice than on the atmospheric physics. The balance of both should be considered.