recognition /
Gravity /
Gravity.AcousticPhaseLevitation /
explainer
lemma
proved
term proof
modified_coherence_defect_simplify
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formal statement (Lean)
106 lemma modified_coherence_defect_simplify
107 (field : ProcessingField) (ext : ExternalPhaseField)
108 (obj : ExtendedObject) (a : ℝ) :
109 modified_coherence_defect field ext obj a =
110 abs (2 * obj.extent * (deriv field.phi obj.h_cm + deriv ext.psi obj.h_cm + a)) := by
proof body
Term-mode proof.
111 rw [modified_coherence_defect_expand]
112 congr 1
113 ring
114
115 /-! ## 3. The Levitation Theorem -/
116
117 /-- THEOREM: Modified Falling Condition.
118
119 With an external phase field, the unique acceleration restoring coherence is
120 a = -(∇Φ_grav + ∇Φ_ext), NOT just -∇Φ_grav.
121
122 The external field SHIFTS the equilibrium acceleration. -/
used by (3)
From the project-wide theorem graph. These declarations reference this one in their body.
depends on (12)
Lean names referenced from this declaration's body.
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in IndisputableMonolith.Foundation.SimplicialLedger.EdgeLengthFromPsi
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is
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ExternalPhaseField
in IndisputableMonolith.Gravity.AcousticPhaseLevitation
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modified_coherence_defect
in IndisputableMonolith.Gravity.AcousticPhaseLevitation
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modified_coherence_defect_expand
in IndisputableMonolith.Gravity.AcousticPhaseLevitation
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ExtendedObject
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ProcessingField
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is
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phase
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equilibrium
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