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68 lines
2.4 KiB
Text
68 lines
2.4 KiB
Text
namespace Semantics.ENE
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-- Universality
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--
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-- Captures substrate-independent dynamical behavior and scaling laws.
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-- A structure is admissible only if it preserves its universality-class
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-- identity under projection, collapse, and evolution.
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/-- A universality class captures substrate-independent dynamical behavior. -/
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inductive UniversalityClass
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| kpz -- KPZ universal scaling (interface growth / roughness)
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| directedPercolation -- Directed percolation universality
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| ising -- Ising critical behavior
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| mott -- Mott transition
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| genericDiffusion -- Simple diffusive behavior
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| custom (name : String)
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deriving Repr, BEq
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/-- A scaling invariant is a quantity that remains unchanged under renormalization. -/
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structure ScalingInvariant where
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name : String
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exponent : Float
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description : String
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deriving Repr, BEq
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/-- A universal law governs dynamics across substrates. -/
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structure UniversalLaw where
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name : String
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invariant : ScalingInvariant
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univClass : UniversalityClass
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statement : String
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deriving Repr, BEq
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/-- Classified dynamics bind a concrete process to a universality class. -/
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structure ClassifiedDynamics where
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processName : String
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universalityClass : UniversalityClass
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law : UniversalLaw
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preservedUnderProjection : Bool
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preservedUnderCollapse : Bool
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preservedUnderEvolution : Bool
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deriving Repr, BEq
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/-- A projection preserves universality only if the dynamics classification is maintained. -/
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def projectionPreservesUniversality (cd : ClassifiedDynamics) : Prop :=
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cd.preservedUnderProjection = true
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/-- A scalar collapse preserves universality only if the class survives scalarization. -/
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def collapsePreservesUniversality (cd : ClassifiedDynamics) : Prop :=
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cd.preservedUnderCollapse = true
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/-- Evolution preserves universality only if the class remains unchanged. -/
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def evolutionPreservesUniversality (cd : ClassifiedDynamics) : Prop :=
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cd.preservedUnderEvolution = true
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/-- No admissible structure may lose its universality-class identity
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under projection, collapse, or evolution. -/
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theorem no_universality_loss
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(cd : ClassifiedDynamics)
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(h1 : projectionPreservesUniversality cd)
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(h2 : collapsePreservesUniversality cd)
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(h3 : evolutionPreservesUniversality cd) :
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cd.preservedUnderProjection = true ∧
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cd.preservedUnderCollapse = true ∧
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cd.preservedUnderEvolution = true := by
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exact ⟨h1, h2, h3⟩
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end Semantics.ENE
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