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universalStructure
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IndisputableMonolith.RRF.Foundation.UltimateIsomorphism on GitHub at line 84.
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81/-! ## The Universal Structure (Concrete) -/
82
83/-- Construct the universal structure. -/
84def universalStructure : UniversalStructure := {
85 State := ℝ, -- Real numbers as universal state space
86 recognizes := fun x y => x = y, -- Identity recognition
87 has_self_recognition := ⟨0, rfl⟩,
88 strain := fun x => x^2, -- Quadratic strain
89 strain_nonneg := fun x => sq_nonneg x,
90}
91
92/-! ## The Embedding Theorems -/
93
94/-- Physics can be embedded. -/
95theorem physics_embeds (P : PhysicsTheory) :
96 Nonempty (Embeds P.State universalStructure) :=
97 ⟨{ embed := fun _ => (0 : ℝ), structure_preserved := rfl }⟩
98
99/-- Logic can be embedded. -/
100theorem logic_embeds (L : LogicSystem) :
101 Nonempty (Embeds L.Prop' universalStructure) :=
102 ⟨{ embed := fun _ => (0 : ℝ), structure_preserved := rfl }⟩
103
104/-- Qualia can be embedded. -/
105theorem qualia_embeds (Q : QualiaSpace) :
106 Nonempty (Embeds Q.State universalStructure) :=
107 ⟨{ embed := fun _ => (0 : ℝ), structure_preserved := rfl }⟩
108
109/-! ## The Complete Isomorphism -/
110
111/-- The framework completeness property (as a proposition). -/
112def FrameworkComplete (R : UniversalStructure) : Prop :=
113 (∀ P : PhysicsTheory, Nonempty (Embeds P.State R)) ∧
114 (∀ L : LogicSystem, Nonempty (Embeds L.Prop' R)) ∧