recognition /
Quantum /
Quantum.AreaQuantization /
explainer
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formal statement (Lean)
73 theorem area_quantization (h : H_AreaQuantization H A ψ) (H : Type*) [RSHilbertSpace H] (A : AreaOperator H) (ψ : H) :
74 is_ledger_eigenstate H ψ → ∃ n : ℕ, ⟪ψ, A.op ψ⟫_ℂ = (n : ℂ) * (Complex.ofReal (ell0^2)) := by
proof body
Term-mode proof.
75 intro he
76 exact h he
77
78 /-- **THEOREM: Minimal Area Eigenvalue**
79 The minimal non-zero eigenvalue of the area operator is exactly \ell_0^2. -/
used by (1)
From the project-wide theorem graph. These declarations reference this one in their body.
depends on (20)
Lean names referenced from this declaration's body.
H
in IndisputableMonolith.Algebra.CostAlgebra
decl_use
of
in IndisputableMonolith.Astrophysics.NucleosynthesisTiers
decl_use
ell0
in IndisputableMonolith.Constants
decl_use
ell0
in IndisputableMonolith.Constants.Derivation
decl_use
H
in IndisputableMonolith.Cost.FunctionalEquation
decl_use
of
in IndisputableMonolith.Foundation.DAlembert.LedgerFactorization
decl_use
A
in IndisputableMonolith.Foundation.IntegrationGap
decl_use
is
in IndisputableMonolith.Foundation.OptionAEmpiricalProgram
decl_use
of
in IndisputableMonolith.Foundation.PhiForcingDerived
decl_use
is
in IndisputableMonolith.Foundation.SimplicialLedger.EdgeLengthFromPsi
decl_use
of
in IndisputableMonolith.Foundation.SpectralEmergence
decl_use
is
in IndisputableMonolith.GameTheory.MechanismDesignFromSigma
decl_use
of
in IndisputableMonolith.Information.PhysicsComplexityStructure
decl_use
A
in IndisputableMonolith.Masses.Anchor
decl_use
is
in IndisputableMonolith.Mathematics.RamanujanBridge.MockThetaPhantom
decl_use
A
in IndisputableMonolith.Modal.Actualization
decl_use
AreaOperator
in IndisputableMonolith.Quantum.AreaQuantization
decl_use
H_AreaQuantization
in IndisputableMonolith.Quantum.AreaQuantization
decl_use
is_ledger_eigenstate
in IndisputableMonolith.Quantum.AreaQuantization
decl_use
RSHilbertSpace
in IndisputableMonolith.Quantum.HilbertSpace
decl_use