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126 lines
4.3 KiB
Text
126 lines
4.3 KiB
Text
import Semantics.FixedPoint
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import Semantics.OrthogonalAmmr
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import Semantics.LandauerCompression
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namespace Semantics.EnvironmentMechanics
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open Semantics
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open Semantics.OrthogonalAmmr
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open Semantics.LandauerCompression
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/--
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Environment-level witness for bounded interaction structure retained after
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compression. This is the proof-layer object that links a committed O-AMMR
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summary to later mechanics claims.
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-/
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structure EnvironmentWitness where
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summary : AmmrSummary
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retainedOrder : Nat
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interactionBudget : Q16_16
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couplingBound : Q16_16
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residualBudget : Q16_16
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deriving Repr, Inhabited, DecidableEq
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/--
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How many retained basis directions can support the claimed interaction order.
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-/
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def retainedDirections (w : EnvironmentWitness) : Nat :=
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Nat.min w.summary.shape.basisDim w.retainedOrder
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/--
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The witness carries enough retained directions to support the claimed order.
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-/
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def orderCovered (w : EnvironmentWitness) : Bool :=
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w.retainedOrder ≤ w.summary.shape.basisDim
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/--
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The explicit long-range coupling contribution stays inside the interaction
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budget.
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-/
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def boundedCoupling (w : EnvironmentWitness) : Bool :=
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Q16_16.le w.couplingBound w.interactionBudget
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/--
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Residual interaction mass excluded from the retained basis also stays inside the
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same budget.
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-/
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def boundedResidual (w : EnvironmentWitness) : Bool :=
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Q16_16.le w.residualBudget w.interactionBudget
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/--
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Typed admissibility predicate for compressed summaries used in mechanics claims.
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-/
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def longRangeAdmissible (w : EnvironmentWitness) : Bool :=
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dimensionConsistent w.summary &&
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energyConsistent w.summary &&
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orderCovered w &&
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boundedCoupling w &&
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boundedResidual w
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/--
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Bridge from a compression witness into an environment witness over the post-state.
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-/
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def witnessOfCompression
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(compression : CompressionWitness)
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(retainedOrder : Nat)
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(interactionBudget couplingBound residualBudget : Q16_16) :
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EnvironmentWitness :=
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{ summary := compression.postSummary
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, retainedOrder := retainedOrder
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, interactionBudget := interactionBudget
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, couplingBound := couplingBound
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, residualBudget := residualBudget }
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/--
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If each constituent bound holds, the environment witness is admissible.
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-/
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theorem admissibleOfBounds (w : EnvironmentWitness)
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(hDim : dimensionConsistent w.summary = true)
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(hEnergy : energyConsistent w.summary = true)
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(hOrder : orderCovered w = true)
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(hCoupling : boundedCoupling w = true)
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(hResidual : boundedResidual w = true) :
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longRangeAdmissible w = true := by
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simp [longRangeAdmissible, hDim, hEnergy, hOrder, hCoupling, hResidual]
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/--
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Compression-level bridge theorem: if the post-summary is admissible under the
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provided budgets, the derived environment witness is admissible by definition.
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-/
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theorem witnessOfCompressionAdmissible
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(compression : CompressionWitness)
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(retainedOrder : Nat)
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(interactionBudget couplingBound residualBudget : Q16_16)
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(hDim : dimensionConsistent compression.postSummary = true)
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(hEnergy : energyConsistent compression.postSummary = true)
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(hOrder : retainedOrder ≤ compression.postSummary.shape.basisDim)
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(hCoupling : Q16_16.le couplingBound interactionBudget = true)
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(hResidual : Q16_16.le residualBudget interactionBudget = true) :
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longRangeAdmissible
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(witnessOfCompression compression retainedOrder
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interactionBudget couplingBound residualBudget) = true := by
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apply admissibleOfBounds
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· simpa [witnessOfCompression]
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· simpa [witnessOfCompression]
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· simpa [witnessOfCompression, orderCovered] using hOrder
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· simpa [witnessOfCompression, boundedCoupling] using hCoupling
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· simpa [witnessOfCompression, boundedResidual] using hResidual
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def sampleEnvironmentWitness : EnvironmentWitness :=
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{ summary := samplePostSummary
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, retainedOrder := 1
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, interactionBudget := Q16_16.ofInt 2
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, couplingBound := Q16_16.one
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, residualBudget := Q16_16.one }
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def sampleCompressionEnvironmentWitness : EnvironmentWitness :=
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witnessOfCompression sampleWitness 1 (Q16_16.ofInt 2) Q16_16.one Q16_16.one
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#eval retainedDirections sampleEnvironmentWitness
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#eval orderCovered sampleEnvironmentWitness
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#eval boundedCoupling sampleEnvironmentWitness
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#eval boundedResidual sampleEnvironmentWitness
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#eval longRangeAdmissible sampleEnvironmentWitness
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#eval longRangeAdmissible sampleCompressionEnvironmentWitness
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end Semantics.EnvironmentMechanics
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