Formalization progress
Source audit and Lean progress
Theorem audit, mathematical dependencies, and Lean completion are tracked separately.
9exact theorem audits
21primary theorem audits pending
4literature-open cases
34mathematical cases
Dependency-first formalization route
Common Chewi Chapter 1 interfaces
- Finish the Chapter 1.1 Ito/SDE/Markov-process route already owned by the existing Chapter 1 branches.
- Reuse the Chapter 1.2-1.3 semigroup, carre-du-champ, transport, and Wasserstein roots from the existing foundation lane.
- Add a regularity-aware relative-Fisher interface and KL/Fisher dissipation.
- Close Chewi Theorem 1.4.5 and its Fisher-Wasserstein first-order consequence.
Proximal-sampler analytic spine
- Chewi Theorem 8.3.1 simultaneous f-divergence flow.
- Forward/backward heat-flow specializations and W2 contraction/time reversal.
- Chewi Theorem 8.4.1 ideal proximal sampler under log-concavity.
- Chewi Theorems 8.5.1/8.5.2 and Corollary 8.6.3.
Classical LMC / ULD / MALA roots
- Chewi 4.2.7, 4.3.6, 4.3.11.
- Chewi 5.3.17, 6.1.2, 6.3.2.
- Chewi 7.3.5 and 7.6.5.
Frontier proximal/FORS implementation
- Chen-Chewi-Daskalakis-Rakhlin Theorem G.1, with inherited RGO-error tracking made explicit.
Exact ULD / FORS
- Girsanov path density and FORS estimator.
- Single-step Renyi error and error composition.
- Chen-Chewi-Rakhlin-Zhang Theorem 3.2.
Non-log-concave Fisher frontier
- Chewi Theorem 11.2.1 and Fisher convexity/averaging.
- High-accuracy RGO reduction (Theorem 6.1 in the FORS paper).
- Chen-Chewi-Rakhlin-Zhang Theorem 6.2.
- Chewi 11.4.3/11.4.4 lower bounds after an oracle-complexity interface exists.
Stochastic and finite-sum oracle results
- Formalize the stochastic-gradient/finite-sum oracle model first.
- Then Chewi 10.1.2/10.1.3 and the COLT 2026 upper/lower bounds.
Weak-smooth and mirror geometry
- Formalize Bregman/mirror geometry and reuse the Chapter 1 Ito formula.
- Then Chewi 10.3.28 and the weak-smooth frontier cases.
Convex-body membership-oracle branch
- Build convex-body and membership-query interfaces.
- Then Kook-Zhang and Kook-Vempala warm-start/annealing results.
Case audit index
Convex body + membership oracle
- Proximal / In-and-Out with restartNormalized SampleWiki statement
- General sampling lower boundOpen problem
- Rényi-preserving annealingNormalized SampleWiki statement
- Constrained proximal samplerNormalized SampleWiki statement
Log-smooth + PI or LSI
- Implemented proximal samplerNormalized SampleWiki statement
- Matching PI/LSI oracle lower boundOpen problem
- LMCExact source theorem
- LMC Rényi interpolationNormalized SampleWiki statement
- ULMC warm-start constructionNormalized SampleWiki statement
Weakly smooth log-concave
- FORS + proximal samplerExact source theorem
- Matching Hölder-model lower boundOpen problem
- Averaged LMCExact source theorem
- Nonsmooth mirror-LangevinNormalized SampleWiki statement
Log-concave + log-smooth
- Implemented proximal samplerNormalized SampleWiki statement
- Matching first-order lower boundOpen problem
- FORS-implemented proximal samplerExact source theorem
- Averaged LMCExact source theorem
- Ideal proximal chainExact source theorem
Smooth non-log-concave + Fisher accuracy
- Exact ULD / FORSExact source theorem
- General first-order Fisher lower boundNormalized SampleWiki statement
- Averaged LMCExact source theorem
- One-dimensional first-order Fisher lower boundNormalized SampleWiki statement
- Large-initial-gap query complexityNormalized SampleWiki statement
Stochastic and finite-sum oracles
- High-accuracy stochastic-gradient samplerNormalized SampleWiki statement
- Bounded-variance stochastic-gradient lower boundNormalized SampleWiki statement
- Variance-reduced high-accuracy samplerNormalized SampleWiki statement
- Finite-sum RM-ULMCNormalized SampleWiki statement
- Finite-sum zeroth-order lower boundNormalized SampleWiki statement
Strongly log-concave + log-smooth
- Exact ULD / FORSExact source theorem
- General first-order oracle lower boundNormalized SampleWiki statement
- MALANormalized SampleWiki statement
- Randomized-midpoint ULMCNormalized SampleWiki statement
- Block-Krylov Gaussian samplerNormalized SampleWiki statement
- MALA lower boundNormalized SampleWiki statement