Constellations

Transform mathematical papers into interactive visualizations that illuminate the logical structure underpinning the research.

Each paper is rendered as a constellation:

• theorems, lemmas, definitions, and remarks are the stars
• logical dependencies are the edges between them

Status: research prototype / experimental

Demo

• Landing page: http://localhost:3000/
• Example constellation: http://localhost:3000/1705.03104/

Features

• Interactive graph (D3): pan/zoom and drag nodes
• Dynamic node sizing based on connectivity
• Typed dependency edges (normalized for readability)
• Focus mode: select a node to isolate its neighborhood
• Info panel: read an artifact’s preview and prerequisites
• Legend filters: toggle node types to declutter
• Proof Path Explorer: expand/collapse prerequisite depth
• Review mode (prototype): guided review of theorems

Quickstart

Prerequisites

• Node.js (LTS recommended)

Install

npm install

Run

npm run dev

Then open http://localhost:3000/.

Project layout

• index.html – landing page
• 1705.03104/ – an example constellation (static page + embedded data)
• assets/style.css – shared site styling
• assets/modules/ – graph rendering, interactions, UI, and proof/review logic

How the visualizations are made (high level)

The interactive constellations are generated from an analysis pipeline (developed as part of ongoing research) that:

1. identifies logical artifacts (theorems, lemmas, definitions, …)
2. extracts/normalizes definitions and prerequisites for richer tooltips
3. infers citations and dependency types from context, then normalizes edges for visualization

Because this is a research system, extractions and inferred relationships may be incomplete or imperfect.

Data format (in this repo)

The included example constellation page (1705.03104/index.html) defines window.graphData:

• nodes: { id, type, display_name, content_preview, prerequisites_preview, ... }
• edges: { source, target, dependency_type, context, ... }

License

MIT © Turnstile Labs — see LICENSE.