 184    ∀ R : MetaCarrier,
 185      forced_arithmetic_invariance R R = Equiv.refl R.Orbit
 186
 187noncomputable def metaRealizationCert : MetaRealizationCert where
 188  carrier_type := LogicRealization.{0, 0}
 189  carrier_eq_realization_type := rfl
 190  cost_total := metaCost_total
 191  identity := metaCost_self
 192  non_contradiction := metaCost_symm
 193  totality := metaCost_total
 194  cost_zero_iff_eq := metaCost_eq_zero_iff
 195  forced_arithmetic_invariance := metaForcedArithmeticInvariance
 196  arithmetic_invariance_self := metaForcedArithmeticInvariance_self
 197
 198theorem metaRealizationCert_inhabited : Nonempty MetaRealizationCert :=
 199  ⟨metaRealizationCert⟩
 200
 201/-! ## The Reflexive-Closure Theorem -/
 202
 203/-- **The framework is reflexively closed.**
 204
 205The Universal Forcing Meta-Theorem itself instantiates the Law-of-Logic
 206structural shape: the meta-cost satisfies the three definitional
 207Aristotelian conditions, and the meta-theorem itself supplies the
 208forced-arithmetic-invariance condition. The framework that proves
 209"every Law-of-Logic realization has the same forced arithmetic" is
 210itself a Law-of-Logic-shaped structure on the type of realizations.
 211
 212The forced-arithmetic-invariance condition is wrapped in `Nonempty`
 213because the equivalence is `Type 1`-valued, while the conjunction here
 214is propositional. The Nonempty wrapper is harmless: the equivalence
 215exists for every pair, so its `Nonempty` is trivially inhabited. -/
 216theorem framework_is_reflexively_closed :
 217    -- Identity, non-contradiction, totality of meta-cost are automatic:

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