recognition /
Quantum /
Quantum.AreaQuantization /
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formal statement (Lean)
67 def H_AreaQuantization (H : Type*) [RSHilbertSpace H] (A : AreaOperator H) (ψ : H) : Prop :=
proof body
Definition body.
68 is_ledger_eigenstate H ψ → ∃ n : ℕ, ⟪ψ, A.op ψ⟫_ℂ = (n : ℂ) * (Complex.ofReal (ell0^2))
69
70 /-- **THEOREM (GROUNDED)**: Area Quantization
71 The eigenvalues of the area operator are restricted to integer multiples of \ell_0^2.
72 This follows from the discrete nature of recognition bits on the ledger. -/
used by (2)
From the project-wide theorem graph. These declarations reference this one in their body.
depends on (16)
Lean names referenced from this declaration's body.
H
in IndisputableMonolith.Algebra.CostAlgebra
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of
in IndisputableMonolith.Astrophysics.NucleosynthesisTiers
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ell0
in IndisputableMonolith.Constants
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ell0
in IndisputableMonolith.Constants.Derivation
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H
in IndisputableMonolith.Cost.FunctionalEquation
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of
in IndisputableMonolith.Foundation.DAlembert.LedgerFactorization
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A
in IndisputableMonolith.Foundation.IntegrationGap
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of
in IndisputableMonolith.Foundation.PhiForcingDerived
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from
in IndisputableMonolith.Foundation.PrimitiveDistinction
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of
in IndisputableMonolith.Foundation.SpectralEmergence
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of
in IndisputableMonolith.Information.PhysicsComplexityStructure
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A
in IndisputableMonolith.Masses.Anchor
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A
in IndisputableMonolith.Modal.Actualization
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AreaOperator
in IndisputableMonolith.Quantum.AreaQuantization
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is_ledger_eigenstate
in IndisputableMonolith.Quantum.AreaQuantization
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RSHilbertSpace
in IndisputableMonolith.Quantum.HilbertSpace
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