01
Introduction
Source map, theorem nodes, upstream matches, and exact Lean correspondence will be attached here.
Riemannian Optimization Library · Boumal
An Introduction to Optimization on Smooth Manifolds
A chapter-by-chapter graph for smooth-manifold geometry, Riemannian algorithms, and Euclidean-to-manifold transfer.
Research resources: guides, formal libraries and papers
Formalization contract
Map first, reuse first, prove only real gaps.
Search Mathlib and Samplinglib geometry interfaces before opening new proofs; make every convention bridge explicit.
reuseadaptmissingout of scope
Book contents
Chapter scaffolds
02
Simple examples
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03
Embedded geometry: first order
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04
First-order optimization algorithms
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05
Embedded geometry: second order
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06
Second-order optimization algorithms
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07
Embedded submanifolds: examples
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08
General manifolds
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09
Quotient manifolds
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10
Additional tools
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11
Geodesic convexity
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Pinned external proof memory
OpenAI Math extension shelf
7 audited upstream routes are placed beside this library's real chapters or named Samplinglib extensions. External verification is shown separately from ASTIS compilation.