AI-Friendly LaTeX: Using LaTeX Code as a Knowledge Source for Retrieval-Augmented Generation

Large language models are increasingly capable at closed-world mathematical reasoning, but research assistance also requires source-grounded use of the literature. When a proof reaches a non-trivial step, a useful assistant should determine whether the needed tool (e.g., a lemma) already exists, identify a suitable scholarly source, and verify that its assumptions align with the current proof context. To rigorously evaluate such capabilities, we introduce Re$^2$Math, a benchmark for tool-grounded retrieval from partial mathematical proofs. Each instance is built from a candidate instrumental citation in the proof of a main theorem, with hierarchical context and an optional leakage-controlled anchor hint. We also make the task source-grounded yet citation-agnostic in that any admissible theorem sufficient for the proof transition is accepted. Evaluation uses a release-frozen retrieval artifact, ensuring reproducibility, while the benchmark itself supports automatic, continual expansion with newly constructed instances. On the current benchmark test set, the best fixed-judge ToolAcc reaches 7.0%, despite substantially higher rates of source grounding, indicating that current systems often retrieve valid statements but fail to establish their applicability to the local proof step. By decoupling citation recall, grounding, and proof-gap sufficiency, Re$^2$Math transforms literature-grounded mathematical tool use into a controlled diagnostic task.

Sharing mathematical content in online forums remains a significant friction point for students and educators: writing raw LATEX is error-prone, standalone optical character recognition tools require platform switching, and current forum software offers no integrated path from a photograph of a formula to a rendered post. We present a unified system that eliminates this friction by embedding an image to LATEX conversion pipeline directly inside a forum posting interface. A user uploads or captures an image of a mathematical expression; the system routes it through the Mathpix OCR API, detects whether the returned output is LATEX or plain text containing inline math, applies the appropriate delimiter normalisation, and renders a live preview in either LATEX or Markdown mode before the post is committed to the database. The architecture is organized in three loosely coupled layers: image processing, rendering, and storage, and supports both desktop and mobile clients. A provisional US patent application has been filed covering the core methods. We describe the full system design, each component in detail, the data schema, and the key technical innovations, and we position the work against existing standalone tools and forum platforms to demonstrate the practical gap it closes. Beyond immediate usability, we argue that a deployed platform of this kind constitutes a continuously growing, community-validated dataset of mathematical problems and step-by-step solutions, a resource that can be used to train and benchmark AI systems for accurate mathematical reasoning

Scientific and technical writing depends on markup sources that must compile: LaTeX, Typst, and Markdown pipelines fail on missing delimiters, mismatched environments, broken imports, or package conflicts. Existing document-repair evaluations inject faults with ad-hoc edits that lack an empirical fault model. We present TeXFix-Bench, a multi-format benchmark for LLM-based full-source document repair grounded in a mined fault taxonomy. A Grounded-Theory study of localized hard-crash LaTeX faults from TeX Stack Exchange, GitHub commits, and package documentation (168 verified faults, dual open coding at $κ$=0.34) yields an 18-category taxonomy instantiated as DocMut: 48 AST-aware operators across three formats. A three-model cross-benchmark shows DocMut faults are 5.6-9.2 pp harder to repair than pattern-based mutations on the same seeds, and a real-error case study (88 mined human crashes, 67.0% repair success) brackets both synthetic sets from below. We construct 10,437 instances from 743 openly licensed seeds and evaluate seven LLMs under a fixed zero-shot protocol with provider-pinned routing, collecting 48,651 attempts at about USD 200 total inference cost. A complete 6,613-instance x 7-model balanced matrix confirms all rankings. A pinned engine gate yields a 27.5-point intention-to-treat compile spread (56.7-84.2%). Typst is markedly harder than LaTeX and Markdown. A restoration oracle over 28,129 compiling repairs shows that 13.6-18.5% of compiling repairs materially alter document text, and restoration rank diverges from compile rank: the model with the lowest compile rate restores content best among its successes. Compile success alone overstates repair quality. We release the taxonomy, DocMut, and all campaign artifacts.