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Perhaps I’m misinterpreting, but the article seems to claim Milanovitch cycles are based on eccentricity only instead of “ variations in eccentricity, axial tilt, and precession.” [0] That precession is more prominent seems to refine not repudiate Milanovitch.

A fun factlet is that precession is the artistic topic of a sculpture at the Hoover Dam:

While Polaris is our North Star, Hansen’s terrazzo floor points out that the North Star of the ancient Egyptians, as they built the great pyramids, was Thuban. And in about 12,000 years, our North Star will be Vega. [1]

0. https://en.wikipedia.org/wiki/Milankovitch_cycles

1. https://medium.com/the-long-now-foundation/the-26-000-year-a...

This Hoover Dam trivia appears in the 2014 Richard Linklater film "Boyhood". From the script:

  MASON
  Yeah, in just a few years that's you

  (Indicates girls)
  And that's gonna be me

  He subtly indicates the Man Alone guy, stil1 sitting at his
  booth, giving a lecture of some kind, with data, etc.

  MAN ALONE IN BOOTH
  ...Also inlaid into the terrazzo floors was a star map, a celestial map of 
  heavenly bodies so accurately displayed that one could chart the
  procession of the Pole Star fourteen thousand years into the future, such
  that future generations upon...(Continuing Indistinct Under)

  SHEENA (O.S.)
  I wonder what his deal is. I mean, he obviously has money to eat here.

  MASON (O.S.)
  He just said. He's a UT professor, tenure and everything.
Seems likely and there's good correlation. I guess the previous theory about CO2 being involved was wrong.

https://www.carbonbrief.org/explainer-how-the-rise-and-fall-...

What, the part in your link that clearly states:

    These ice ages are triggered and ended by slow changes in the Earth’s orbit. 
How, exactly, does that invalidate the insulative properties of the atmosphere also playing a minor role:

    But changing atmospheric concentrations of CO2 also plays a key role in driving both cooling during the onset of ice ages and warming at their end. 
Even the primary article discussing the orbital parameters embraces the physical fact that multiple factors are at play, some playing a larger part than others.
(comment deleted)
CO₂ does play a role but it is not leading temperature changes, instead the atmospheric CO₂ concentration increases when the oceans warm up due to ${reasons} which in turn can lead to an increase in surface temperature - as to whether this is the case depends on many other factors like ocean currents, cloud coverage and more. The opposite is true as well, cooler oceans absorb more CO₂ which leads to a decrease in atmospheric CO₂ concentration which in turn can (but does not have to, see above) lead to a surface temperature decrease.