Explain the theorem metaForcedArithmeticInvariance from IndisputableMonolith.Foundation.UniversalForcingSelfReference.

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confidence: high in recognition cached

The definition metaForcedArithmeticInvariance reifies the Universal Forcing Meta-Theorem inside the meta-realization on MetaCarrier (the type of LogicRealization.{0,0} instances).

It states: for any R, S : MetaCarrier, there exists a canonical equivalence R.Orbit ≃ S.Orbit, obtained by direct application of universal_forcing_via_NNO R S.

This supplies the forced_arithmetic_invariance field of MetaRealizationCert.

Reflexivity holds by metaForcedArithmeticInvariance_self: metaForcedArithmeticInvariance R R = Equiv.refl R.Orbit, proved via recursor uniqueness on the NNO structure of R.Orbit.

The construction is used in framework_is_reflexively_closed to establish that the meta-cost satisfies the three Aristotelian conditions and the meta-theorem supplies the invariance law, closing the framework structurally.

cited recognition theorems

UniversalForcingSelfReference.metaForcedArithmeticInvariance Direct definition reifying universal forcing as the meta-comparison law on orbits.
UniversalForcingSelfReference.metaForcedArithmeticInvariance_self Establishes reflexivity of the equivalence via NNO recursor uniqueness.
UniversalForcingSelfReference.framework_is_reflexively_closed Integrates the invariance into the reflexive-closure statement of the framework.

recognition modules consulted

The Recognition library is at github.com/jonwashburn/shape-of-logic. The model is restricted to the supplied Lean source and instructed not to invent theorem names. Treat output as a starting point, not a verified proof.