{
  "layers": [
    "Root import",
    "Shared foundation",
    "Finite Shannon layer",
    "Semantic bridge layer",
    "Non-stable anchors"
  ],
  "local_edge_count": 94,
  "module_count": 46,
  "modules": [
    {
      "external_imports": [],
      "layer": "Root import",
      "local_imports": [
        "LeanInfoTheory.InformationMeasures",
        "LeanInfoTheory.Probability.Finite"
      ],
      "name": "LeanInfoTheory",
      "path": "LeanInfoTheory.lean",
      "root_reachable": true,
      "summary": "Lightweight public root import for finite PMF and Shannon APIs."
    },
    {
      "external_imports": [
        "Mathlib.Data.ENNReal.BigOperators",
        "Mathlib.Data.ENNReal.Real",
        "Mathlib.Probability.ProbabilityMassFunction.Basic",
        "Mathlib.Probability.ProbabilityMassFunction.Constructions"
      ],
      "layer": "Shared foundation",
      "local_imports": [],
      "name": "LeanInfoTheory.Probability.Finite",
      "path": "LeanInfoTheory/Probability/Finite.lean",
      "root_reachable": true,
      "summary": "Finite PMF real-mass, finite-bind, support, and pointwise PMF.map bridge lemmas."
    },
    {
      "external_imports": [],
      "layer": "Shared foundation",
      "local_imports": [
        "LeanInfoTheory.Probability.Finite"
      ],
      "name": "LeanInfoTheory.Probability.FiniteChannel",
      "path": "LeanInfoTheory/Probability/FiniteChannel.lean",
      "root_reachable": false,
      "summary": "Type-generic PMF channel constructions and their elementary laws."
    },
    {
      "external_imports": [],
      "layer": "Shared foundation",
      "local_imports": [
        "LeanInfoTheory.Probability.Finite"
      ],
      "name": "LeanInfoTheory.Probability.FiniteMixture",
      "path": "LeanInfoTheory/Probability/FiniteMixture.lean",
      "root_reachable": false,
      "summary": "Binary PMF mixtures with NNReal weights and exact endpoint laws; general finite selectors use PMF.bind."
    },
    {
      "external_imports": [],
      "layer": "Finite Shannon layer",
      "local_imports": [
        "LeanInfoTheory.Shannon.Entropy",
        "LeanInfoTheory.Shannon.InfoMeasures"
      ],
      "name": "LeanInfoTheory.InformationMeasures",
      "path": "LeanInfoTheory/InformationMeasures.lean",
      "root_reachable": true,
      "summary": "Convenience re-export for the finite information-measure API."
    },
    {
      "external_imports": [],
      "layer": "Finite Shannon layer",
      "local_imports": [
        "LeanInfoTheory",
        "LeanInfoTheory.Shannon.Fano",
        "LeanInfoTheory.Shannon.SemanticBridge",
        "LeanInfoTheory.Shannon.Units"
      ],
      "name": "LeanInfoTheory.Shannon",
      "path": "LeanInfoTheory/Shannon.lean",
      "root_reachable": false,
      "summary": "Import-only umbrella for the complete supported finite information-theory stack."
    },
    {
      "external_imports": [
        "Mathlib.Analysis.SpecialFunctions.BinaryEntropy"
      ],
      "layer": "Finite Shannon layer",
      "local_imports": [
        "LeanInfoTheory.Shannon.Entropy"
      ],
      "name": "LeanInfoTheory.Shannon.BinaryEntropy",
      "path": "LeanInfoTheory/Shannon/BinaryEntropy.lean",
      "root_reachable": false,
      "summary": "Boolean-PMF entropy bridge to mathlib's Real.binEntropy."
    },
    {
      "external_imports": [
        "Mathlib.Analysis.SpecialFunctions.Log.NegMulLog",
        "Mathlib.Probability.ProbabilityMassFunction.Constructions"
      ],
      "layer": "Finite Shannon layer",
      "local_imports": [
        "LeanInfoTheory.Probability.Finite"
      ],
      "name": "LeanInfoTheory.Shannon.Entropy",
      "path": "LeanInfoTheory/Shannon/Entropy.lean",
      "root_reachable": true,
      "summary": "Finite Shannon entropy, entropy of finite-valued random variables, and first entropy invariance theorems."
    },
    {
      "external_imports": [
        "Mathlib.Analysis.Convex.Jensen",
        "Mathlib.Probability.Distributions.Uniform"
      ],
      "layer": "Finite Shannon layer",
      "local_imports": [
        "LeanInfoTheory.Shannon.Entropy"
      ],
      "name": "LeanInfoTheory.Shannon.EntropyBounds",
      "path": "LeanInfoTheory/Shannon/EntropyBounds.lean",
      "root_reachable": false,
      "summary": "Sharp alphabet/support entropy bounds and their uniform-law equality cases."
    },
    {
      "external_imports": [
        "Mathlib.Analysis.Convex.Jensen"
      ],
      "layer": "Finite Shannon layer",
      "local_imports": [
        "LeanInfoTheory.Probability.FiniteMixture",
        "LeanInfoTheory.Shannon.Entropy"
      ],
      "name": "LeanInfoTheory.Shannon.EntropyConcavity",
      "path": "LeanInfoTheory/Shannon/EntropyConcavity.lean",
      "root_reachable": false,
      "summary": "Finite-selector entropy concavity and its binary interior-weight equality characterization, proved directly by Jensen."
    },
    {
      "external_imports": [],
      "layer": "Finite Shannon layer",
      "local_imports": [
        "LeanInfoTheory.Shannon.BinaryEntropy",
        "LeanInfoTheory.Shannon.EntropyBounds",
        "LeanInfoTheory.Shannon.SemanticBridge.Theorems"
      ],
      "name": "LeanInfoTheory.Shannon.Fano",
      "path": "LeanInfoTheory/Shannon/Fano.lean",
      "root_reachable": false,
      "summary": "Deterministic decoding error, exact and weak finite Fano inequalities, and converse-facing corollaries."
    },
    {
      "external_imports": [
        "Mathlib.Data.Finset.Pi",
        "Mathlib.Data.Fintype.Pi"
      ],
      "layer": "Finite Shannon layer",
      "local_imports": [
        "LeanInfoTheory.Shannon.InfoMeasures"
      ],
      "name": "LeanInfoTheory.Shannon.FiniteFamily",
      "path": "LeanInfoTheory/Shannon/FiniteFamily.lean",
      "root_reachable": false,
      "summary": "Dependent finite-family laws, finite marginals, family entropy/MI/CMI algebra, pair/triple bridges, and binary/ordered entropy, MI, and conditional-MI chain rules."
    },
    {
      "external_imports": [],
      "layer": "Finite Shannon layer",
      "local_imports": [
        "LeanInfoTheory.Shannon.Entropy"
      ],
      "name": "LeanInfoTheory.Shannon.InfoMeasures",
      "path": "LeanInfoTheory/Shannon/InfoMeasures.lean",
      "root_reachable": true,
      "summary": "Marginals, conditional entropy, mutual information, conditional mutual information, orientation lemmas, and the auxiliary-variable information decomposition."
    },
    {
      "external_imports": [
        "Mathlib.Analysis.Convex.Jensen",
        "Mathlib.Analysis.SpecialFunctions.Log.ENNRealLog",
        "Mathlib.Analysis.SpecialFunctions.Log.NegMulLog",
        "Mathlib.Data.EReal.Operations"
      ],
      "layer": "Finite Shannon layer",
      "local_imports": [],
      "name": "LeanInfoTheory.Shannon.LogSum",
      "path": "LeanInfoTheory/Shannon/LogSum.lean",
      "root_reachable": false,
      "summary": "Zero-safe finite EReal log-sum inequality and equality with guarded Real corollaries."
    },
    {
      "external_imports": [
        "Mathlib.Analysis.SpecialFunctions.Log.Base"
      ],
      "layer": "Finite Shannon layer",
      "local_imports": [
        "LeanInfoTheory.Shannon.InfoMeasures"
      ],
      "name": "LeanInfoTheory.Shannon.Units",
      "path": "LeanInfoTheory/Shannon/Units.lean",
      "root_reachable": false,
      "summary": "Opt-in scalar conversion from canonical nats to arbitrary valid logarithm bases and bits."
    },
    {
      "external_imports": [],
      "layer": "Semantic bridge layer",
      "local_imports": [
        "LeanInfoTheory.Shannon.SemanticBridge.Conditional",
        "LeanInfoTheory.Shannon.SemanticBridge.ConditionalKL",
        "LeanInfoTheory.Shannon.SemanticBridge.Convexity",
        "LeanInfoTheory.Shannon.SemanticBridge.DataProcessing",
        "LeanInfoTheory.Shannon.SemanticBridge.Entropy",
        "LeanInfoTheory.Shannon.SemanticBridge.FiniteFamily",
        "LeanInfoTheory.Shannon.SemanticBridge.FiniteFamilyIndependence",
        "LeanInfoTheory.Shannon.SemanticBridge.FiniteSums",
        "LeanInfoTheory.Shannon.SemanticBridge.Independence",
        "LeanInfoTheory.Shannon.SemanticBridge.KL",
        "LeanInfoTheory.Shannon.SemanticBridge.Markov",
        "LeanInfoTheory.Shannon.SemanticBridge.Product",
        "LeanInfoTheory.Shannon.SemanticBridge.Sufficiency",
        "LeanInfoTheory.Shannon.SemanticBridge.Sufficiency.KL",
        "LeanInfoTheory.Shannon.SemanticBridge.Theorems"
      ],
      "name": "LeanInfoTheory.Shannon.SemanticBridge",
      "path": "LeanInfoTheory/Shannon/SemanticBridge.lean",
      "root_reachable": false,
      "summary": "Import-only aggregate for finite semantic, KL, convexity, conditional-KL, independence, Markov, sufficiency, data-processing, recovery, and finite-family bridges."
    },
    {
      "external_imports": [
        "Mathlib.Probability.ProbabilityMassFunction.Constructions"
      ],
      "layer": "Semantic bridge layer",
      "local_imports": [
        "LeanInfoTheory.Shannon.InfoMeasures"
      ],
      "name": "LeanInfoTheory.Shannon.SemanticBridge.Conditional",
      "path": "LeanInfoTheory/Shannon/SemanticBridge/Conditional.lean",
      "root_reachable": false,
      "summary": "Finite conditional-law API and expected conditional entropy / conditional mutual-information formulas."
    },
    {
      "external_imports": [],
      "layer": "Semantic bridge layer",
      "local_imports": [
        "LeanInfoTheory.Shannon.SemanticBridge.DataProcessing",
        "LeanInfoTheory.Shannon.SemanticBridge.KL"
      ],
      "name": "LeanInfoTheory.Shannon.SemanticBridge.ConditionalKL",
      "path": "LeanInfoTheory/Shannon/SemanticBridge/ConditionalKL.lean",
      "root_reachable": false,
      "summary": "Common-base channel conditional KL, finite weighted semantics, joint KL chain rule, and support-guarded Real forms."
    },
    {
      "external_imports": [],
      "layer": "Semantic bridge layer",
      "local_imports": [
        "LeanInfoTheory.Probability.FiniteChannel",
        "LeanInfoTheory.Probability.FiniteMixture",
        "LeanInfoTheory.Shannon.EntropyConcavity",
        "LeanInfoTheory.Shannon.LogSum",
        "LeanInfoTheory.Shannon.SemanticBridge.KL",
        "LeanInfoTheory.Shannon.SemanticBridge.Product"
      ],
      "name": "LeanInfoTheory.Shannon.SemanticBridge.Convexity",
      "path": "LeanInfoTheory/Shannon/SemanticBridge/Convexity.lean",
      "root_reachable": false,
      "summary": "Finite-selector KL joint convexity, binary KL equality, and mutual-information input-law concavity and channel convexity."
    },
    {
      "external_imports": [
        "Mathlib.InformationTheory.KullbackLeibler.ChainRule",
        "Mathlib.Probability.Kernel.CompProdEqIff"
      ],
      "layer": "Semantic bridge layer",
      "local_imports": [
        "LeanInfoTheory.Shannon.SemanticBridge.Markov",
        "LeanInfoTheory.Shannon.SemanticBridge.Sufficiency"
      ],
      "name": "LeanInfoTheory.Shannon.SemanticBridge.DataProcessing",
      "path": "LeanInfoTheory/Shannon/SemanticBridge/DataProcessing.lean",
      "root_reachable": false,
      "summary": "Finite channel posteriors, supported sufficiency, KL data processing and equality, and entropy-growth consequences."
    },
    {
      "external_imports": [
        "Mathlib.Probability.ProbabilityMassFunction.Integrals"
      ],
      "layer": "Semantic bridge layer",
      "local_imports": [
        "LeanInfoTheory.Shannon.Entropy"
      ],
      "name": "LeanInfoTheory.Shannon.SemanticBridge.Entropy",
      "path": "LeanInfoTheory/Shannon/SemanticBridge/Entropy.lean",
      "root_reachable": false,
      "summary": "Expected-self-information semantics for finite entropy."
    },
    {
      "external_imports": [],
      "layer": "Semantic bridge layer",
      "local_imports": [
        "LeanInfoTheory.Shannon.FiniteFamily",
        "LeanInfoTheory.Shannon.SemanticBridge.Theorems"
      ],
      "name": "LeanInfoTheory.Shannon.SemanticBridge.FiniteFamily",
      "path": "LeanInfoTheory/Shannon/SemanticBridge/FiniteFamily.lean",
      "root_reachable": false,
      "summary": "Finite-family Shannon inequalities, including submodularity and n-way subadditivity."
    },
    {
      "external_imports": [],
      "layer": "Semantic bridge layer",
      "local_imports": [
        "LeanInfoTheory.Shannon.SemanticBridge.FiniteFamily",
        "LeanInfoTheory.Shannon.SemanticBridge.Independence"
      ],
      "name": "LeanInfoTheory.Shannon.SemanticBridge.FiniteFamilyIndependence",
      "path": "LeanInfoTheory/Shannon/SemanticBridge/FiniteFamilyIndependence.lean",
      "root_reachable": false,
      "summary": "Dependent-family mutual independence, restriction and pair laws, and n-way entropy-additivity equality characterizations."
    },
    {
      "external_imports": [],
      "layer": "Semantic bridge layer",
      "local_imports": [
        "LeanInfoTheory.Shannon.InfoMeasures"
      ],
      "name": "LeanInfoTheory.Shannon.SemanticBridge.FiniteSums",
      "path": "LeanInfoTheory/Shannon/SemanticBridge/FiniteSums.lean",
      "root_reachable": false,
      "summary": "Finite real-sum rewrites and mutual-information log-ratio formulas."
    },
    {
      "external_imports": [
        "Mathlib.Probability.Independence.Basic"
      ],
      "layer": "Semantic bridge layer",
      "local_imports": [
        "LeanInfoTheory.Shannon.SemanticBridge.Theorems"
      ],
      "name": "LeanInfoTheory.Shannon.SemanticBridge.Independence",
      "path": "LeanInfoTheory/Shannon/SemanticBridge/Independence.lean",
      "root_reachable": false,
      "summary": "PMF-first ordinary/conditional independence, arbitrary-type deterministic postprocessing, zero MI/CMI, and entropy equality cases."
    },
    {
      "external_imports": [
        "Mathlib.InformationTheory.KullbackLeibler.Basic",
        "Mathlib.Probability.Distributions.Uniform",
        "Mathlib.Probability.ProbabilityMassFunction.Integrals"
      ],
      "layer": "Semantic bridge layer",
      "local_imports": [
        "LeanInfoTheory.Shannon.SemanticBridge.Conditional",
        "LeanInfoTheory.Shannon.SemanticBridge.FiniteSums",
        "LeanInfoTheory.Shannon.SemanticBridge.Product"
      ],
      "name": "LeanInfoTheory.Shannon.SemanticBridge.KL",
      "path": "LeanInfoTheory/Shannon/SemanticBridge/KL.lean",
      "root_reachable": false,
      "summary": "PMF support/KL finiteness and equality, uniform-reference identities, and MI/CMI KL bridges."
    },
    {
      "external_imports": [],
      "layer": "Semantic bridge layer",
      "local_imports": [
        "LeanInfoTheory.Probability.FiniteChannel",
        "LeanInfoTheory.Shannon.SemanticBridge.Independence"
      ],
      "name": "LeanInfoTheory.Shannon.SemanticBridge.Markov",
      "path": "LeanInfoTheory/Shannon/SemanticBridge/Markov.lean",
      "root_reachable": false,
      "summary": "Finite Markov characterizations, channel factorization, information loss, and mutual-information data processing."
    },
    {
      "external_imports": [
        "Mathlib.MeasureTheory.Measure.Prod",
        "Mathlib.Probability.ProbabilityMassFunction.Constructions"
      ],
      "layer": "Semantic bridge layer",
      "local_imports": [
        "LeanInfoTheory.Shannon.InfoMeasures"
      ],
      "name": "LeanInfoTheory.Shannon.SemanticBridge.Product",
      "path": "LeanInfoTheory/Shannon/SemanticBridge/Product.lean",
      "root_reachable": false,
      "summary": "Independent-product PMFs, product-measure semantics, support formulas, and absolute-continuity facts."
    },
    {
      "external_imports": [],
      "layer": "Semantic bridge layer",
      "local_imports": [
        "LeanInfoTheory.Shannon.SemanticBridge.Markov"
      ],
      "name": "LeanInfoTheory.Shannon.SemanticBridge.Sufficiency",
      "path": "LeanInfoTheory/Shannon/SemanticBridge/Sufficiency.lean",
      "root_reachable": false,
      "summary": "Fixed-prior and model-family sufficiency, common recovery, and full-support/all-prior characterizations."
    },
    {
      "external_imports": [],
      "layer": "Semantic bridge layer",
      "local_imports": [
        "LeanInfoTheory.Shannon.SemanticBridge.DataProcessing"
      ],
      "name": "LeanInfoTheory.Shannon.SemanticBridge.Sufficiency.KL",
      "path": "LeanInfoTheory/Shannon/SemanticBridge/Sufficiency/KL.lean",
      "root_reachable": false,
      "summary": "Pairwise KL preservation and guarded equality characterizations through common exact recovery."
    },
    {
      "external_imports": [],
      "layer": "Semantic bridge layer",
      "local_imports": [
        "LeanInfoTheory.Shannon.SemanticBridge.KL"
      ],
      "name": "LeanInfoTheory.Shannon.SemanticBridge.Theorems",
      "path": "LeanInfoTheory/Shannon/SemanticBridge/Theorems.lean",
      "root_reachable": false,
      "summary": "User-facing semantic nonnegativity, chain rules, deterministic processing, and information inequalities."
    },
    {
      "external_imports": [],
      "layer": "Non-stable anchors",
      "local_imports": [],
      "name": "LeanInfoTheory.Basic",
      "path": "LeanInfoTheory/Basic.lean",
      "root_reachable": false,
      "summary": "Non-stable development anchor for project metadata and roadmap vocabulary."
    },
    {
      "external_imports": [],
      "layer": "Non-stable anchors",
      "local_imports": [
        "LeanInfoTheory.Examples.CommonCause",
        "LeanInfoTheory.Examples.ConditionalKL",
        "LeanInfoTheory.Examples.Convexity",
        "LeanInfoTheory.Examples.Fano",
        "LeanInfoTheory.Examples.FiniteFamily",
        "LeanInfoTheory.Examples.IndependenceProcessing",
        "LeanInfoTheory.Examples.InformationDecomposition",
        "LeanInfoTheory.Examples.KLTop",
        "LeanInfoTheory.Examples.StochasticChannels",
        "LeanInfoTheory.Examples.SufficientStatistics",
        "LeanInfoTheory.Examples.SupportSensitive",
        "LeanInfoTheory.Examples.Units"
      ],
      "name": "LeanInfoTheory.Examples",
      "path": "LeanInfoTheory/Examples.lean",
      "root_reachable": false,
      "summary": "Non-stable aggregate for maintained conditional-KL, convexity, finite-family, independence-processing, information-decomposition, support-sensitive, Markov, channel, sufficiency, Fano, and units regression consumers."
    },
    {
      "external_imports": [],
      "layer": "Non-stable anchors",
      "local_imports": [
        "LeanInfoTheory.Shannon.SemanticBridge.Markov"
      ],
      "name": "LeanInfoTheory.Examples.CommonCause",
      "path": "LeanInfoTheory/Examples/CommonCause.lean",
      "root_reachable": false,
      "summary": "Noisy binary common-cause example for conditional independence and Markov factorization."
    },
    {
      "external_imports": [],
      "layer": "Non-stable anchors",
      "local_imports": [
        "LeanInfoTheory.Shannon.SemanticBridge.ConditionalKL"
      ],
      "name": "LeanInfoTheory.Examples.ConditionalKL",
      "path": "LeanInfoTheory/Examples/ConditionalKL.lean",
      "root_reachable": false,
      "summary": "Private maintained regressions for common-base conditional KL across null, active, finite, infinite, and guarded Real cases."
    },
    {
      "external_imports": [],
      "layer": "Non-stable anchors",
      "local_imports": [
        "LeanInfoTheory.Probability.FiniteMixture",
        "LeanInfoTheory.Shannon.EntropyConcavity",
        "LeanInfoTheory.Shannon.LogSum",
        "LeanInfoTheory.Shannon.SemanticBridge.Convexity"
      ],
      "name": "LeanInfoTheory.Examples.Convexity",
      "path": "LeanInfoTheory/Examples/Convexity.lean",
      "root_reachable": false,
      "summary": "Private maintained regressions for finite log-sum, mixtures, entropy concavity, KL convexity, and mutual-information input-law concavity and channel convexity."
    },
    {
      "external_imports": [],
      "layer": "Non-stable anchors",
      "local_imports": [
        "LeanInfoTheory.Shannon.Fano"
      ],
      "name": "LeanInfoTheory.Examples.Fano",
      "path": "LeanInfoTheory/Examples/Fano.lean",
      "root_reachable": false,
      "summary": "Perfect-decoder, singleton-source, and nonzero-error examples for the finite Fano API."
    },
    {
      "external_imports": [],
      "layer": "Non-stable anchors",
      "local_imports": [
        "LeanInfoTheory.Shannon.EntropyBounds",
        "LeanInfoTheory.Shannon.SemanticBridge.FiniteFamilyIndependence"
      ],
      "name": "LeanInfoTheory.Examples.FiniteFamily",
      "path": "LeanInfoTheory/Examples/FiniteFamily.lean",
      "root_reachable": false,
      "summary": "Homogeneous and dependent-alphabet finite-family examples covering conditional-MI chains, product laws, and pairwise-but-not-mutual independence."
    },
    {
      "external_imports": [],
      "layer": "Non-stable anchors",
      "local_imports": [
        "LeanInfoTheory.Shannon.SemanticBridge.Independence"
      ],
      "name": "LeanInfoTheory.Examples.IndependenceProcessing",
      "path": "LeanInfoTheory/Examples/IndependenceProcessing.lean",
      "root_reachable": false,
      "summary": "Private arbitrary-PMF consumers for non-injective and constant independence postprocessing, infinite types, symmetry, and finite zero mutual information."
    },
    {
      "external_imports": [],
      "layer": "Non-stable anchors",
      "local_imports": [
        "LeanInfoTheory.Shannon.InfoMeasures"
      ],
      "name": "LeanInfoTheory.Examples.InformationDecomposition",
      "path": "LeanInfoTheory/Examples/InformationDecomposition.lean",
      "root_reachable": false,
      "summary": "Private lightweight consumers for the auxiliary-variable MI decomposition, algebraic zero terms, singleton variables, and sparse joint laws."
    },
    {
      "external_imports": [],
      "layer": "Non-stable anchors",
      "local_imports": [
        "LeanInfoTheory.Shannon.SemanticBridge.KL"
      ],
      "name": "LeanInfoTheory.Examples.KLTop",
      "path": "LeanInfoTheory/Examples/KLTop.lean",
      "root_reachable": false,
      "summary": "Disjoint-support PMF example exposing the infinite-KL toReal zero trap."
    },
    {
      "external_imports": [],
      "layer": "Non-stable anchors",
      "local_imports": [
        "LeanInfoTheory.Shannon.EntropyBounds",
        "LeanInfoTheory.Shannon.SemanticBridge.DataProcessing"
      ],
      "name": "LeanInfoTheory.Examples.StochasticChannels",
      "path": "LeanInfoTheory/Examples/StochasticChannels.lean",
      "root_reachable": false,
      "summary": "Finite stochastic-channel examples for KL contraction, cascade support, and entropy growth."
    },
    {
      "external_imports": [],
      "layer": "Non-stable anchors",
      "local_imports": [
        "LeanInfoTheory.Shannon.SemanticBridge.Sufficiency.KL"
      ],
      "name": "LeanInfoTheory.Examples.SufficientStatistics",
      "path": "LeanInfoTheory/Examples/SufficientStatistics.lean",
      "root_reachable": false,
      "summary": "Finite sufficient-statistics examples covering noninjective sufficiency, constant-statistic failure, and recovery/posterior/KL boundaries."
    },
    {
      "external_imports": [],
      "layer": "Non-stable anchors",
      "local_imports": [
        "LeanInfoTheory.Shannon.EntropyBounds",
        "LeanInfoTheory.Shannon.SemanticBridge.Theorems"
      ],
      "name": "LeanInfoTheory.Examples.SupportSensitive",
      "path": "LeanInfoTheory/Examples/SupportSensitive.lean",
      "root_reachable": false,
      "summary": "Support-aware entropy, conditional-fiber, functional-dependence, and recovery examples."
    },
    {
      "external_imports": [],
      "layer": "Non-stable anchors",
      "local_imports": [
        "LeanInfoTheory.Shannon.SemanticBridge.KL",
        "LeanInfoTheory.Shannon.Units"
      ],
      "name": "LeanInfoTheory.Examples.Units",
      "path": "LeanInfoTheory/Examples/Units.lean",
      "root_reachable": false,
      "summary": "Private maintained regressions for arbitrary-base, bits, entropy, MI, CMI, and guarded real-KL conversion."
    },
    {
      "external_imports": [
        "Mathlib.Analysis.SpecialFunctions.BinaryEntropy",
        "Mathlib.InformationTheory.Coding.KraftMcMillan",
        "Mathlib.InformationTheory.KullbackLeibler.Basic",
        "Mathlib.InformationTheory.KullbackLeibler.ChainRule",
        "Mathlib.Probability.ProbabilityMassFunction.Constructions"
      ],
      "layer": "Non-stable anchors",
      "local_imports": [],
      "name": "LeanInfoTheory.MathlibFragments",
      "path": "LeanInfoTheory/MathlibFragments.lean",
      "root_reachable": false,
      "summary": "Non-stable reference checklist of heavier mathlib information-theory and coding anchors."
    }
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}