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formal statement (Lean)
83def thetaContributions : List String := [
proof body
Definition body.
84 "Bare QCD theta",
85 "Quark mass phase: arg det M_q",
86 "Total: θ_eff = θ_QCD + arg det M_q"
87]
88
89/-! ## The Axion Solution -/
90
91/-- The Peccei-Quinn (PQ) solution:
92
93 Introduce a new U(1)_PQ symmetry.
94 When broken, a Goldstone boson (axion) appears.
95 The axion field dynamically relaxes θ → 0.
96
97 Axion mass: m_a ~ f_π m_π / f_a
98 where f_a is the PQ breaking scale. -/
depends on (12)
Lean names referenced from this declaration's body.
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U
in IndisputableMonolith.Constants.RSNativeUnits
decl_use
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Axion
in IndisputableMonolith.Cosmology.DarkMatter
decl_use
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scale
in IndisputableMonolith.Cosmology.LargeScaleStructureFromRS
decl_use
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Quark
in IndisputableMonolith.CrossDomain.CubeFaceUniversality
decl_use
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phase
in IndisputableMonolith.Foundation.EightTick
decl_use
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is
in IndisputableMonolith.Foundation.OptionAEmpiricalProgram
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is
in IndisputableMonolith.Foundation.SimplicialLedger.EdgeLengthFromPsi
decl_use
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is
in IndisputableMonolith.GameTheory.MechanismDesignFromSigma
decl_use
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is
in IndisputableMonolith.Mathematics.RamanujanBridge.MockThetaPhantom
decl_use
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theta
in IndisputableMonolith.NumberTheory.RiemannHypothesis.BRFPlumbing
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phase
in IndisputableMonolith.NumberTheory.RiemannHypothesis.Wedge
decl_use
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U
in IndisputableMonolith.Recognition
decl_use