What rank for Paris-Saclay?

[UPDATED on 21/05/2024 with the 2021-2023 positions (Figures 1 and 2)]
The Paris-Saclay University was officially created on December 29, 2014, but in some shape or another the project had started as early as 2010 or even in 2008, depending on the point of view. Among the declared goals of this endeavour was improving (by the year 2020) the position of the new university in the Shanghai (ARWU) ranking with respect to the Paris-Sud University, which is the main partner to the project.
In 2020, Paris-Saclay was finally ranked in the ARWU, and it jumps to 14th place overall (and to first place in mathematics!) Congratulations to my (former) colleagues for this tremendous progress!

It is interesting to compare the current and predicted ranking of Paris-Saclay (letters and red error bars).

A) The first prediction was made in 2012 by Dominique Vernay, chair of the Foundation for Scientific Cooperation (FSC) Paris-Saclay Campus (top official of the project at the time), who was confident that the new institution would reach the top 10 "of the most attractive universities in the world" [1,2]. This declaration was generally understood at the time as referring to the ARWU ranking, where the size increase of the institution would have the largest effect.

B) The 2017 objectives of Paris-Saclay were more modest, only aiming for the top 20 of the ARWU ranking. This estimation is supported by 2015 projections that predict a rank between 18 and 26 [1,2]. For reference, the same calculation for the COMUE Sorbonne Universités (resulting from the merger of Université Pierre et Marie Curie (UPMC) and Université Paris-Sorbonne) predicted the 40th place in 2016. Sorbonne Universités was finally ranked in the ARWU in 2018, at the 36th place, dropped to 44 in 2019 and oscillates around 40 since (see the Figure below.) As expected, there is no improvement with respect to the UPMC position.

 

Paris-Saclay and the Sorbonne are joined in the top 50 by the PSL University (ranked 41st) and followed by the University of Paris (ranked 69th). In France the Paris region really dominates this ranking: fifth on the list is Grenoble Alpes Universit, in the 101-150 pack.

Experience as boundary conditions for belief

It is not often that one uses field theory as a metaphor to clarify results from another domain; Quine manages that in Two Dogmas of Empiricism. After discussing the difficulties of defining analyticity and its relation to redutionism he opens section VI by the following image:

The totality of our so-called knowledge or beliefs, from the most casual matters of geography and history to the profoundest laws of atomic physics or even of pure mathematics and logic, is a man-made fabric which impinges on experience only along the edges. Or, to change the figure, total science is like a field of force whose boundary conditions are experience. A conflict with experience at the periphery occasions readjustments in the interior of the field.

Our knowledge is not a one-to-one representation of the world, like a full-scale map unfolded over the territory (see also Borges and Eco on this point.) The two are rather autonomous domains that only meet at the boundary, each with its own "structure".