Practical text-recognition pipelines for historical documents typically decompose layout analysis into line detection followed by a separate reading-order step, with the latter most often handled by a hand-coded geometric heuristic that struggles with marginalia, multiple columns, tables, and source-specific editorial conventions. This article introduces Orli (Ordered Regression of Lines), an end-to-end model that casts both sub-tasks as a single image-to-sequence problem: from a page image, Orli autoregressively generates text-line baselines directly in reading order. Baselines are represented in a chord-frame parameterization that anchors a line's position, orientation, and extent while encoding local geometry through perpendicular offsets; an iterative refinement head and a local visual refiner produce the final curve. Trained on a heterogeneous corpus of 196,691 pages spanning ten writing systems, Orli marginally exceeds the previously reported state of the art for cBAD line detection without dataset-specific training, reaches near perfect coverage and ordering on multiple reading-order benchmarks zero-shot, and adapts to more specialized out-of-domain layouts with limited fine-tuning. The method's source code and model weights are available under an open license at https://github.com/mittagessen/orli.