[{"data":1,"prerenderedAt":4},["ShallowReactive",2],{"XLR4BW6qiT":3},"# Gibbs Measures\n\n[![.github/workflows/push.yml](https://github.com/james18lpc/GibbsMeasure/actions/workflows/push.yml/badge.svg)](https://github.com/james18lpc/GibbsMeasure/actions/workflows/push.yml)\n[![Gitpod Ready-to-Code](https://img.shields.io/badge/Gitpod-ready--to--code-blue?logo=gitpod)](https://gitpod.io/#https://github.com/james18lpc/GibbsMeasure)\n\nThe purpose of this repository is to *digitise* some mathematical definitions, theorem statements\nand theorem proofs. Digitisation, or formalisation, is a process where the source material,\ntypically a mathematical textbook or a pdf file or website or video, is transformed into definitions\nin a target system consisting of a computer implementation of a logical theory (such as set theory\nor type theory).\n\n## The source\n\nThe definitions, theorems and proofs in this repository are taken from the book [Gibbs Measures and\nPhase Transitions](https://doi.org/10.1515/9783110250329) by Hans-Otto Georgii.\n\nThe goal is to prove existence and uniqueness of Gibbs measures.\n\n## The target\n\nThe formal system which we are using as a target system is Lean's dependent type theory. Lean is a\nproject being developed by the [Lean FRO](https://lean-lang.org/fro).\n\n## Content\n\nThis project currently contains a definition of Gibbs measures, but no construction yet.\n\n### Code organisation\n\nThe Lean code is contained in the directory `GibbsMeasure/`. The subdirectories are:\n* `Mathlib`: Material missing from existing Mathlib developments\n* `Prereqs`: New developments to be integrated to Mathlib\n\n## What next?\n\nOn top of the new developments, there are many basic lemmas needed for this project that are\ncurrently missing from Mathlib.\n\nSee the [upstreaming dashboard](https://james18lpc.github.io/GibbsMeasure/upstreaming) for more information.\n\n## Getting the project\n\nTo build the Lean files of this project, you need to have a working version of Lean.\nSee [the installation instructions](https://lean-lang.org/install/).\nAlternatively, click on the button below to open an Ona workspace containing the project.\n\n[![Open in Gitpod](https://gitpod.io/button/open-in-gitpod.svg)](https://gitpod.io/#https://github.com/james18lpc/GibbsMeasure)\n\nIn either case, run `lake exe cache get` and then `lake build` to build the project.\n\n## Contributing\n\n**This project is open to contribution.**\n\n## Source reference\n\n[G]: https://doi.org/10.1515/9783110250329\n",1782661962672]