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Foundation.QuantumLedger /
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170 noncomputable def expectedCost {n : ℕ} (ψ : QuantumState n) : ℝ :=
proof body
Definition body.
171 Finset.univ.sum fun i => probability ψ i * totalCost (ψ.configurations i)
172
173 /-- **BORN RULE INTERPRETATION**: The probability of a configuration is
174 inversely related to its J-cost (cost-weighted selection).
175
176 In full RS, this is derived from the variational principle:
177 The observed configuration minimizes expected J-cost subject to constraints.
178
179 Here we state the connection: lower J-cost configurations have higher probability
180 in the cost-optimal distribution (analogous to Boltzmann: P ∝ exp(-βE)). -/
used by (1)
From the project-wide theorem graph. These declarations reference this one in their body.
depends on (24)
Lean names referenced from this declaration's body.
of
in IndisputableMonolith.Astrophysics.NucleosynthesisTiers
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totalCost
in IndisputableMonolith.Constants.LambdaRecDerivation
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of
in IndisputableMonolith.Foundation.DAlembert.LedgerFactorization
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cost
in IndisputableMonolith.Foundation.MultiplicativeRecognizerL4
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cost
in IndisputableMonolith.Foundation.ObserverForcing
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is
in IndisputableMonolith.Foundation.OptionAEmpiricalProgram
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of
in IndisputableMonolith.Foundation.PhiForcingDerived
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from
in IndisputableMonolith.Foundation.PrimitiveDistinction
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totalCost
in IndisputableMonolith.Foundation.QRFT.SMLagrangianSkeleton
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probability
in IndisputableMonolith.Foundation.QuantumLedger
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QuantumState
in IndisputableMonolith.Foundation.QuantumLedger
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totalCost
in IndisputableMonolith.Foundation.QuantumLedger
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is
in IndisputableMonolith.Foundation.SimplicialLedger.EdgeLengthFromPsi
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E
in IndisputableMonolith.Foundation.SpectralEmergence
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of
in IndisputableMonolith.Foundation.SpectralEmergence
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is
in IndisputableMonolith.GameTheory.MechanismDesignFromSigma
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QuantumState
in IndisputableMonolith.Information.NoCloning
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of
in IndisputableMonolith.Information.PhysicsComplexityStructure
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is
in IndisputableMonolith.Mathematics.RamanujanBridge.MockThetaPhantom
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QuantumState
in IndisputableMonolith.QFT.PauliExclusion
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probability
in IndisputableMonolith.QFT.SMatrixUnitarity
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QuantumState
in IndisputableMonolith.QFT.Unitarity
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QuantumState
in IndisputableMonolith.Quantum.Measurement.WavefunctionCollapse
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probability
in IndisputableMonolith.Thermodynamics.BoltzmannDistribution
decl_use