Sampling/SDE Implementation Map

flowchart TD
  LC["LogConcaveOn"]:::compiled
  GibbsDensity["gibbsDensityENNReal"]:::compiled
  Normalize["isProbabilityMeasure_withDensity_normalized_gibbs"]:::compiled
  GibbsLC["logConcaveOn_normalized_gibbsDensity..."]:::compiled
  Generator["finiteEuclidean_langevinGenerator_coordinateDisplay"]:::compiled
  Cutoff["radialSmoothCutoff_tendsto_one"]:::compiled
  FiniteIBP["finite-box divergence + cutoff limits"]:::compiled
  Tails["concrete Gibbs tails / integrability"]:::compiled
  WholeIBP["whole-space weighted integration by parts"]:::compiled
  CoreInvariant["C_c² core annihilation + conditional invariance"]:::compiled
  Semigroup["concrete Langevin semigroup"]:::blocked
  Domains["semigroup-stable domain extension"]:::blocked
  Invariant["Gibbs invariant law"]:::blocked
  PI["Poincare typed interface"]:::compiled
  BE["Bakry--Emery PI criterion"]:::blocked
  Loc["localization theorem"]:::blocked
  Iso["sharp log-concave isoperimetry"]:::blocked
  FI["LSI / transport theorem packages"]:::partial
  Mixing["continuous-time mixing"]:::planned
  LMC["LMC discretization and rate"]:::planned

  GibbsDensity --> Normalize
  LC --> GibbsLC
  GibbsDensity --> GibbsLC
  Generator --> FiniteIBP
  Cutoff --> FiniteIBP
  FiniteIBP --> WholeIBP
  Tails --> WholeIBP
  WholeIBP --> CoreInvariant
  CoreInvariant --> Semigroup
  Semigroup --> Domains
  Domains --> Invariant
  Normalize --> Invariant
  PI --> BE
  PI --> Loc --> Iso
  Semigroup --> BE
  BE --> FI
  Iso --> FI
  Invariant --> Mixing
  FI --> Mixing
  Mixing --> LMC

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  classDef partial fill:#fff2c7,stroke:#9a6700,color:#172033,stroke-width:1.5px;
  classDef blocked fill:#ffe5e5,stroke:#c92a2a,color:#172033,stroke-width:2px;
  classDef planned fill:#eef3f9,stroke:#627086,color:#172033,stroke-width:1.5px;