Open, collaborative research is a powerful paradigm that can immensely strengthen the scientific process by integrating broad and diverse expertise. However, traditional research and multi-author writing processes break down at scale. We present new software named Manubot, available at https://manubot.org, to address the challenges of open scholarly writing. Manubot adopts the contribution workflow used by many large-scale open source software projects to enable collaborative authoring of scholarly manuscripts. With Manubot, manuscripts are written in Markdown and stored in a Git repository to precisely track changes over time. By hosting manuscript repositories publicly, such as on GitHub, multiple authors can simultaneously propose and review changes. A cloud service automatically evaluates proposed changes to catch errors. Publication with Manubot is continuous: When a manuscript's source changes, the rendered outputs are rebuilt and republished to a web page. Manubot automates bibliographic tasks by implementing citation by identifier, where users cite persistent identifiers (e.g. DOIs, PubMed IDs, ISBNs, URLs), whose metadata is then retrieved and converted to a user-specified style. Manubot modernizes publishing to align with the ideals of open science by making it transparent, reproducible, immediate, versioned, collaborative, and free of charge.