PhysicsLogic / Kadanoff 1966

Coarse Graining and Model Closure

Inspect what exact elimination preserves, what a model ansatz adds, and which information is lost.

Definitions and assumptions

Scope and physical limitations

This is an independent finite Ising-star and one-dimensional decimation test of the elimination, closure, and reexpression distinctions used in renormalization. It is not Kadanoff's critical lattice, an interacting fluid, or a refutation of controlled RG truncations.

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Examples and distinctions

Constructed examples of this model; each answer includes the Lean statement.

Exact root statement

(reduction.NonvacuousRetainedPredictionAt fun configuration =>
    coordinate configuration 0 * coordinate configuration 1) ∧
  ∫ (configuration : Outer), coordinate configuration 0 * coordinate configuration 1 ∂reduction.retainedLaw = 1 / 9 ∧
    ¬reduction.ClosedInModelFamilyAt pairwiseLawFamily
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Notes and questions

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Definitions, structures, and assumptions

Structures, classes, and inductive alternatives

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Definitions and domain choices

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Checked statements: parameters, hypotheses, and interpretation

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Constructors, projections, and other meaning dependencies

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External mathematical declarations

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