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formal statement (Lean)
147def orderParameterExamples : List (String × String) := [
proof body
Definition body.
148 ("Ferromagnet", "Magnetization M"),
149 ("Liquid-gas", "Density difference ρ_l - ρ_g"),
150 ("Superconductor", "Gap Δ"),
151 ("Superfluid", "Condensate fraction"),
152 ("Crystal", "Periodic density")
153]
154
155/-! ## Spontaneous Symmetry Breaking -/
156
157/-- Symmetry breaking: High-T symmetric, low-T asymmetric.
158
159 The J-cost is symmetric in order parameter.
160 But the minimum chosen breaks symmetry.
161
162 Examples:
163 - Magnet: Up/down symmetry → all spins align (one direction)
164 - Crystal: Translation symmetry → periodic structure -/
depends on (20)
Lean names referenced from this declaration's body.
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all
in IndisputableMonolith.Aesthetics.NarrativeGeodesic
decl_use
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all
in IndisputableMonolith.Anthropology.KinshipGraphCohomology
decl_use
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all
in IndisputableMonolith.Engineering.AsteroidOreSpectroscopy
decl_use
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T
in IndisputableMonolith.Foundation.Breath1024
decl_use
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one
in IndisputableMonolith.Foundation.IntegersFromLogic
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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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one
in IndisputableMonolith.Foundation.RationalsFromLogic
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is
in IndisputableMonolith.Foundation.SimplicialLedger.EdgeLengthFromPsi
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is
in IndisputableMonolith.GameTheory.MechanismDesignFromSigma
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T
in IndisputableMonolith.Gap45.SyncMinimization
decl_use
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Superconductor
in IndisputableMonolith.Gravity.CoherenceGain
decl_use
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is
in IndisputableMonolith.Mathematics.RamanujanBridge.MockThetaPhantom
decl_use
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all
in IndisputableMonolith.Musicology.ModalPreferenceFromPhi
decl_use
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density
in IndisputableMonolith.Physics.NeutronStarCrustalRegimesFromRS
decl_use
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one
in IndisputableMonolith.QFT.SpinStatistics
decl_use
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M
in IndisputableMonolith.Recognition
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M
in IndisputableMonolith.Recognition.Cycle3
decl_use
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one
in IndisputableMonolith.RecogSpec.Core
decl_use