Earth's Obliquity Today
Today, on January 28, 2024 at noon, Earth's axial tilt, or mean obliquity was 23.43615° or 23°26'10.1".
Earth's mean obliquity today is about 0.00001°, or 0.04", less than 30 days ago.
The Arctic and Antarctic circles today are 1.2 m (4 ft) closer to the poles, and the Tropic of Cancer and Tropic of Capricorn are equally closer to the equator than 30 days ago.
Earth: The living planet
The Tilt Changes
In a repeating cycle that lasts about 41,000 years, Earth's axial tilt oscillates between 22.1 and 24.5 degrees. This change in obliquity is caused by gravitational forces from the Sun, the Moon, and other planets.
Acts Like Two Spinning Tops
Axial precession can be described as a slow gyration of Earth's axis about another line intersecting it. A complete wobble of Earth's axis takes around 26,000 years. It outlines the shape of a pair of cones or two spinning tops connected at the tips, which would be at the center of Earth.
Ancient Discovery
Greek astronomer Hipparchus of Nicea is historically credited as the man who first proposed that Earths axis gradually shifts, though very slowly. Hipparchus made his discovery around 130 BCE, based on comparisons of astronomical observations more than a century apart.
https://www.timeanddate.com/astronomy/axial-tilt-obliquity.html
Is this what you're talking about by polar shift and oval pattern? Or something else?