Update README.md

Author: dgerosa

README.md

@@ -8,40 +8,29 @@
 The current version (v2) of `precession` is described in 
 - *Efficient multi-timescale dynamics of precessing black-hole binaries.*
 D. Gerosa, G. Fumagalli, M. Mould, G. Cavallotto, D. Padilla Monroy, D. Gangardt, V. De Renzis.
+[PRD 108 (2023) 024042](https://journals.aps.org/prd/abstract/10.1103/PhysRevD.108.024042)
 [arXiv:2304.04801](https://arxiv.org/abs/2304.04801)
 
+The implementation of eccentricity is described in
+- *Spin-eccentricity interplay in merging binary black holes.*
+G. Fumagalli, D. Gerosa.
+[PRD 108 (2023) 124055](https://journals.aps.org/prd/abstract/10.1103/PhysRevD.108.124055).
+[arXiv:2310.16893](https://arxiv.org/abs/2310.16893)
+
 The previous implementation (v1) is described in
 - *PRECESSION: Dynamics of spinning black-hole binaries with python.*
-D. Gerosa, M. Kesden. PRD 93 (2016)
-[124066](http://journals.aps.org/prd/abstract/10.1103/PhysRevD.93.124066).
+D. Gerosa, M. Kesden.
+[PRD 93 (2016) 124066](http://journals.aps.org/prd/abstract/10.1103/PhysRevD.93.124066).
 [arXiv:1605.01067](https://arxiv.org/abs/1605.01067)
 
-Note that v2 and v1 are *not* backward compatible; they are different codes. Unless you are maintaining a legacy pipeline, we highly reccommend using the new code. It is faster, more accurate, and provides more functionalities.
-
-### precession.eccentricity
+Note that v2 and v1 are *not* backward compatible; they are different codes. Unless you are maintaining a legacy pipeline, we highly reccommend using the new code. It is faster, more accurate, and provides more functionalities. 
 
-The `precession` package models the dynamics of circular precessing black hole binaries. To evolve binaries on eccentric orbits, we provide an extension: `precession.eccentricity`. This module is designed to mirror the functionality of the main `precession` package while accounting for orbital eccentricity.
-
-The eccentric extension is described in:
-- *Eccentric extension: Amaldi proceeding.*
-G. Fumagalli \&  D. Gerosa 
-[arXiv:2508.????](https://arxiv.org/abs/2304.04801)\\
-
- and is based on 
- - *Spin-eccentricity interplay in merging binary black holes*
-G. Fumagalli \&   D. Gerosa 
-[arXiv:2310.16893](https://arxiv.org/abs/2310.16893)
-
-
-<br />
-
-
-`precession` and `precession.eccentricity` are released under the MIT licence. You may use `precession` and `precession.eccentricity` as you like but should acknowledge our work. When using the code in any published work, please cite the papers above. The codes have been used in a variety of studies in gravitational-wave and astronomy black-hole binary dynamics, follow the citations to those papers for more. 
+`precession` is released under the MIT licence. You may use `precession` as you like but should acknowledge our work. When using the code in any published work, please cite the papers above. The codes have been used in a variety of studies in gravitational-wave and astronomy black-hole binary dynamics, follow the citations to those papers for more. 
 
 The code is distributed under git version control at
 - [github.com/dgerosa/precession](https://github.com/dgerosa/precession)
 
-The documentation (v2 and eccentric extension) is available 
+The documentation (v2) is available 
 - [dgerosa.github.io/precession](https://dgerosa.github.io/precession)
 
 The v1 documentation is archived at [this link](https://htmlpreview.github.io/?https://github.com/dgerosa/precession/blob/precession_v1/docs/index.html).
@@ -55,8 +44,10 @@ A short tutorial is provided in [the documentation](https://dgerosa.github.io/pr
 The code is developed and maintained by [Davide Gerosa](www.davidegerosa.com). Please report bugs and suggestions using github.
 
 
+The main code deals with quasi-circular black-hole binaries and is accessible via `import precession`. The functionalities to study eccentric binaries are in the `eccentricity` submodule, which we reccommend importing as `import precession.eccentricity as precession`.   
+
 #### Change log
-- *v2.0.1* Extension of the code to work with eccentric orbits. See [arXiv:2508.????](https://arxiv.org/abs/2304.04801)
+- *v2.1.0* Extension to eccentric orbits. See [arXiv:2508.04801](https://arxiv.org/abs/2304.04801)
 - *v2.0.0* New code, not backward compatible. See [arXiv:2304.04801](https://arxiv.org/abs/2304.04801)
 - *v1.0.3* Python 3 support. Updated final-spin formula.
 - *v1.0.0* First public release. See [arXiv:1605.01067](https://arxiv.org/abs/1605.01067).