📝 docs(paper): draft

paper/paper.bib

@@ -0,0 +1,94 @@
+@misc{array-api,
+  author = {Array API Consortion},
+  title  = {Array API Standard},
+  url    = {https://data-apis.org/array-api/latest/index.html},
+  year   = {2021}
+}
+
+@article{astropy:13,
+  adsnote       = {Provided by the SAO/NASA Astrophysics Data System},
+  adsurl        = {https://ui.adsabs.harvard.edu/abs/2013A&A...558A..33A},
+  archiveprefix = {arXiv},
+  author        = {{Astropy Collaboration} and {Robitaille}, Thomas P. and {Tollerud}, Erik J. and {Greenfield}, Perry and {Droettboom}, Michael and {Bray}, Erik and {Aldcroft}, Tom and {Davis}, Matt and {Ginsburg}, Adam and {Price-Whelan}, Adrian M. and {Kerzendorf}, Wolfgang E. and {Conley}, Alexander and {Crighton}, Neil and {Barbary}, Kyle and {Muna}, Demitri and {Ferguson}, Henry and {Grollier}, Fr{\'e}d{\'e}ric and {Parikh}, Madhura M. and {Nair}, Prasanth H. and {Unther}, Hans M. and {Deil}, Christoph and {Woillez}, Julien and {Conseil}, Simon and {Kramer}, Roban and {Turner}, James E.~H. and {Singer}, Leo and {Fox}, Ryan and {Weaver}, Benjamin A. and {Zabalza}, Victor and {Edwards}, Zachary I. and {Azalee Bostroem}, K. and {Burke}, D.~J. and {Casey}, Andrew R. and {Crawford}, Steven M. and {Dencheva}, Nadia and {Ely}, Justin and {Jenness}, Tim and {Labrie}, Kathleen and {Lim}, Pey Lian and {Pierfederici}, Francesco and {Pontzen}, Andrew and {Ptak}, Andy and {Refsdal}, Brian and {Servillat}, Mathieu and {Streicher}, Ole},
+  doi           = {10.1051/0004-6361/201322068},
+  eid           = {A33},
+  eprint        = {1307.6212},
+  journal       = {\aap},
+  keywords      = {methods: data analysis, methods: miscellaneous, virtual observatory tools, Astrophysics - Instrumentation and Methods for Astrophysics},
+  month         = oct,
+  pages         = {A33},
+  primaryclass  = {astro-ph.IM},
+  title         = {Astropy: A community {P}ython package for astronomy},
+  volume        = {558},
+  year          = 2013
+}
+
+@article{astropy:22,
+  adsnote       = {Provided by the SAO/NASA Astrophysics Data System},
+  adsurl        = {https://ui.adsabs.harvard.edu/abs/2022ApJ...935..167A},
+  archiveprefix = {arXiv},
+  author        = {{Astropy Collaboration} and {Price-Whelan}, Adrian M. and {Lim}, Pey Lian and {Earl}, Nicholas and {Starkman}, Nathaniel and {Bradley}, Larry and {Shupe}, David L. and {Patil}, Aarya A. and {Corrales}, Lia and {Brasseur}, C.~E. and {N{\"o}the}, Maximilian and {Donath}, Axel and {Tollerud}, Erik and {Morris}, Brett M. and {Ginsburg}, Adam and {Vaher}, Eero and {Weaver}, Benjamin A. and {Tocknell}, James and {Jamieson}, William and {van Kerkwijk}, Marten H. and {Robitaille}, Thomas P. and {Merry}, Bruce and {Bachetti}, Matteo and {G{\"u}nther}, H. Moritz and {Aldcroft}, Thomas L. and {Alvarado-Montes}, Jaime A. and {Archibald}, Anne M. and {B{\'o}di}, Attila and {Bapat}, Shreyas and {Barentsen}, Geert and {Baz{\'a}n}, Juanjo and {Biswas}, Manish and {Boquien}, M{\'e}d{\'e}ric and {Burke}, D.~J. and {Cara}, Daria and {Cara}, Mihai and {Conroy}, Kyle E. and {Conseil}, Simon and {Craig}, Matthew W. and {Cross}, Robert M. and {Cruz}, Kelle L. and {D'Eugenio}, Francesco and {Dencheva}, Nadia and {Devillepoix}, Hadrien A.~R. and {Dietrich}, J{\"o}rg P. and {Eigenbrot}, Arthur Davis and {Erben}, Thomas and {Ferreira}, Leonardo and {Foreman-Mackey}, Daniel and {Fox}, Ryan and {Freij}, Nabil and {Garg}, Suyog and {Geda}, Robel and {Glattly}, Lauren and {Gondhalekar}, Yash and {Gordon}, Karl D. and {Grant}, David and {Greenfield}, Perry and {Groener}, Austen M. and {Guest}, Steve and {Gurovich}, Sebastian and {Handberg}, Rasmus and {Hart}, Akeem and {Hatfield-Dodds}, Zac and {Homeier}, Derek and {Hosseinzadeh}, Griffin and {Jenness}, Tim and {Jones}, Craig K. and {Joseph}, Prajwel and {Kalmbach}, J. Bryce and {Karamehmetoglu}, Emir and {Ka{\l}uszy{\'n}ski}, Miko{\l}aj and {Kelley}, Michael S.~P. and {Kern}, Nicholas and {Kerzendorf}, Wolfgang E. and {Koch}, Eric W. and {Kulumani}, Shankar and {Lee}, Antony and {Ly}, Chun and {Ma}, Zhiyuan and {MacBride}, Conor and {Maljaars}, Jakob M. and {Muna}, Demitri and {Murphy}, N.~A. and {Norman}, Henrik and {O'Steen}, Richard and {Oman}, Kyle A. and {Pacifici}, Camilla and {Pascual}, Sergio and {Pascual-Granado}, J. and {Patil}, Rohit R. and {Perren}, Gabriel I. and {Pickering}, Timothy E. and {Rastogi}, Tanuj and {Roulston}, Benjamin R. and {Ryan}, Daniel F. and {Rykoff}, Eli S. and {Sabater}, Jose and {Sakurikar}, Parikshit and {Salgado}, Jes{\'u}s and {Sanghi}, Aniket and {Saunders}, Nicholas and {Savchenko}, Volodymyr and {Schwardt}, Ludwig and {Seifert-Eckert}, Michael and {Shih}, Albert Y. and {Jain}, Anany Shrey and {Shukla}, Gyanendra and {Sick}, Jonathan and {Simpson}, Chris and {Singanamalla}, Sudheesh and {Singer}, Leo P. and {Singhal}, Jaladh and {Sinha}, Manodeep and {Sip{\H{o}}cz}, Brigitta M. and {Spitler}, Lee R. and {Stansby}, David and {Streicher}, Ole and {{\v{S}}umak}, Jani and {Swinbank}, John D. and {Taranu}, Dan S. and {Tewary}, Nikita and {Tremblay}, Grant R. and {de Val-Borro}, Miguel and {Van Kooten}, Samuel J. and {Vasovi{\'c}}, Zlatan and {Verma}, Shresth and {de Miranda Cardoso}, Jos{\'e} Vin{\'\i}cius and {Williams}, Peter K.~G. and {Wilson}, Tom J. and {Winkel}, Benjamin and {Wood-Vasey}, W.~M. and {Xue}, Rui and {Yoachim}, Peter and {Zhang}, Chen and {Zonca}, Andrea and {Astropy Project Contributors}},
+  doi           = {10.3847/1538-4357/ac7c74},
+  eid           = {167},
+  eprint        = {2206.14220},
+  journal       = {\apj},
+  keywords      = {Astronomy software, Open source software, Astronomy data analysis, 1855, 1866, 1858, Astrophysics - Instrumentation and Methods for Astrophysics},
+  month         = aug,
+  number        = {2},
+  pages         = {167},
+  primaryclass  = {astro-ph.IM},
+  title         = {The {A}stropy Project: Sustaining and Growing a Community-oriented Open-source Project and the Latest Major Release (v5.0) of the Core Package},
+  volume        = {935},
+  year          = 2022
+}
+
+@software{jax:18,
+  author  = {Bradbury, James and Frostig, Roy and Hawkins, Peter and Johnson, Matthew James and Leary, Chris and Maclaurin, Dougal and Necula, George and Paszke, Adam and VanderPlas, Jake and Wanderman-Milne, Skye and Zhang, Qiao},
+  date    = {2018},
+  title   = {{{JAX}}: Composable Transformations of {{Python}}+{{NumPy}} Programs},
+  url     = {http://github.com/jax-ml/jax},
+  version = {0.4.35}
+}
+
+@article{numpy:2020,
+  author    = {Charles R. Harris and K. Jarrod Millman and St{\'{e}}fan J.
+               van der Walt and Ralf Gommers and Pauli Virtanen and David
+               Cournapeau and Eric Wieser and Julian Taylor and Sebastian
+               Berg and Nathaniel J. Smith and Robert Kern and Matti Picus
+               and Stephan Hoyer and Marten H. van Kerkwijk and Matthew
+               Brett and Allan Haldane and Jaime Fern{\'{a}}ndez del
+               R{\'{i}}o and Mark Wiebe and Pearu Peterson and Pierre
+               G{\'{e}}rard-Marchant and Kevin Sheppard and Tyler Reddy and
+               Warren Weckesser and Hameer Abbasi and Christoph Gohlke and
+               Travis E. Oliphant},
+  doi       = {10.1038/s41586-020-2649-2},
+  journal   = {Nature},
+  month     = sep,
+  number    = {7825},
+  pages     = {357--362},
+  publisher = {Springer Science and Business Media {LLC}},
+  title     = {Array programming with {NumPy}},
+  url       = {https://doi.org/10.1038/s41586-020-2649-2},
+  volume    = {585},
+  year      = {2020}
+}
+
+@software{quax:23,
+  author = {Kidger, Patrrick},
+  date   = {2023},
+  title  = {{{Quax}}: {{JAX}} + multiple dispatch + custom array-ish objects},
+  year   = {}
+}
+
+@article{unxt:2025,
+  author    = {Starkman, Nathaniel and Price-Whelan, Adrian M. and Nibauer, Jake},
+  doi       = {10.21105/joss.07771},
+  journal   = {Journal of Open Source Software},
+  number    = {107},
+  pages     = {7771},
+  publisher = {The Open Journal},
+  title     = {unxt: A Python package for unit-aware computing with JAX},
+  url       = {https://doi.org/10.21105/joss.07771},
+  volume    = {10},
+  year      = {2025}
+}

paper/paper.md

@@ -0,0 +1,138 @@
+---
+title:
+  "coordinax: A Python package enabling calculations with coordinates in JAX"
+tags:
+  - Python
+  - Numerical Computing
+  - Scientific Computing
+authors:
+  - name: Nathaniel Starkman
+    orcid: 0000-0003-3954-3291
+    affiliation: "1,2"
+    corresponding: true
+  - name: Adrian M. Price-Whelan
+    orcid: 0000-0003-0872-7098
+    affiliation: "2"
+affiliations:
+  - index: 1
+    name:
+      Brinson Prize Fellow at Kavli Institute for Astrophysics and Space
+      Research, Massachusetts Institute of Technology, USA
+    ror: 042nb2s44
+  - index: 2
+    name: Department of Physics, Case Western Reserve University, USA
+    ror: 051fd9666
+  - index: 3
+    name: Center for Computational Astrophysics, Flatiron Institute, USA
+    ror: 00sekdz59
+date: October 1 2025
+bibliography: paper.bib
+---
+
+# Summary
+
+`coordinax` is a Python package for coordinate and frame-aware computing with
+JAX [@jax:18], a high-performance numerical library that supports automatic
+differentiation and just-in-time compilation across multiple compute
+architectures. `coordinax` is built on top of `quax` [@quax:23] -- a framework
+for building JAX-compatible array-like objects -- and `unxt` [@unxt:2025] -- for
+handling units and quantities in JAX. With these foundations, coordinax enables
+the definition and transformation of coordinate representations, the
+construction of coordinate frames and frame transformations, and computations
+with coordinates while preserving their associated representations and frames.
+In addition, coordinax supports time-dependent operators on coordinates,
+allowing for straightforward definition of inertial and non-inertial reference
+frames. By providing seamless integration into JAX, coordinax substantially
+extends JAX’s capabilities for scientific applications that require rigorous and
+efficient handling of coordinates.
+
+Scientific research frequently requires transforming between coordinate systems
+and defining reference frames that may be time-dependent or non-inertial.
+`coordinax` provides a principled framework within JAX to represent and carry
+out such operations consistently and efficiently. By leveraging JAX’s automatic
+differentiation, it enables thorough support for these transformations,
+including those involving rotating reference frames, while preserving
+compatibility with gradient-based methods. At the same time, `coordinax` is
+designed to be intuitive and performant, making it straightforward to
+incorporate frame-aware computations into existing JAX workflows.
+
+`coordinax` is designed to be accessible to researchers and developers, offering
+an intuitive interface for defining, transforming, and analyzing coordinate
+frames and their associated data. It supports both straightforward use cases and
+more advanced workflows, making it suitable for a broad community of users.
+Furthermore, `coordinax` leverages multiple dispatch to enable deep
+interoperability with other libraries, currently including `astropy`, and to
+accommodate custom array-like objects within JAX. This extensibility ensures
+that `coordinax` can serve as a foundation for diverse scientific and
+engineering applications, wherever coordinate- and frame-aware computations are
+required.
+
+# Statement of Need
+
+JAX is a powerful tool for high-performance numerical computing, featuring
+automatic differentiation, just-in-time compilation, and support for sharding
+computations. It excels in providing unified interfaces to various compute
+architectures, including CPUs, GPUs, and TPUs, to accelerate code execution
+[@jax:18]. While JAX supports PyTrees -- nested containers of independent arrays
+with some built -- in and user-extendable functionality—there is no intrinsic
+notion that the contained arrays are collectively an array-like object. As a
+result, operations in JAX remain fundamentally array-based, which poses
+challenges for scientific applications that require structured objects such as
+coordinate data.
+
+Astropy has been an invaluable resource for the scientific community, with over
+10,000 citations to its initial paper and more than 2,000 citations to its 2022
+paper [@astropy:13; @astropy:22]. One of its core sub-packages,
+`astropy.coordinates`, provides a rich framework for defining coordinate
+representations and transforming between reference frames. This functionality
+ensures that scientific calculations involving positions, velocities, and other
+kinematic quantities are expressed consistently within well-defined frames.
+However, despite JAX’s NumPy-like API, it does not provide native support for
+such structured objects, and `astropy.coordinates` cannot be directly extended
+to work with JAX. This gap highlights the need for a solution that integrates
+the expressive power of Astropy’s coordinate framework with the high-performance
+and differentiable computing features of JAX.
+
+`coordinax` addresses this gap by providing a function-oriented
+framework—consistent with the style of JAX—for handling coordinates,
+representations, and frame transformations, with an object-oriented front end
+that will be familiar to users of `astropy.coordinates`. By leveraging `quax`
+and `unxt`, `coordinax` defines coordinate classes that integrate directly with
+JAX functions. Through automatic differentiation, it not only supports
+transformations of positions but also propagates velocities and accelerations
+through those same transformations. Coordinates can further be aggregated into
+phase-space objects, ensuring that positions, velocities, and higher-order
+kinematics transform cleanly across inertial and non-inertial frames. This
+design allows researchers to work directly with coordinate arrays while relying
+on `coordinax` to manage the underlying transformations, preserving both
+performance and conceptual clarity.
+
+# Related Works
+
+`astropy.coordinates` provides a framework for coordinate representations,
+reference frames, and transformations [@astropy:13;@astropy:22], and `coordinax`
+builds on many of the same ideas. Its architecture differs in several key ways:
+it integrates with JAX to support time-dependent operators, automatic
+differentiation through transformations, and consistent propagation of
+velocities and accelerations across inertial and non-inertial frames. The
+transformation system is redesigned around multiple dispatch, making it easier
+to add new representations, frames, and transforms while remaining compatible
+with JAX’s compilation and differentiation. `coordinax` is both a JAX-oriented
+framework for coordinate-aware computing and a test-bed for features that will
+guide future development in `astropy.coordinates`, even as the projects follow
+different implementation paths and timescales.
+
+# Acknowledgements
+
+Support for this work was provided by The Brinson Foundation through a Brinson
+Prize Fellowship grant.
+
+The authors thank the Astropy collaboration and many contributors for their work
+on `astropy`, which has been invaluable to the scientific community. Members of
+the `coordinax` development team are also core developers and maintainers of the
+`astropy` package, and we had `astropy` as our guiding star while developing
+`coordinax`. We also extend our gratitude to Patrick Kidger for his valuable
+communications and guidance on using `quax` to ensure seamless integration of
+`coordinax` with `jax`.
+
+# References

pyproject.toml

@@ -106,7 +106,7 @@ build-backend = "hatchling.build"
 
 
 [tool.codespell]
-skip = ["uv.lock"]
+skip = "uv.lock,paper/paper.bib"
 
 
 [tool.commitizen]