Chapter 79: The Identity-Faithful Reception Criterion

The preceding two chapters established that diagonal resonance (I.D89) creates identity slippage (I.D90) and shadow identities (I.D91) in any foundation whose structural rules permit unbounded contraction, extensional equality, and diagonal self-reference. The ontic identity invariance theorem (I.T46) showed that τ is immune: distinct normal forms correspond to distinct objects, and no partial decoherence is possible (I.C03). the relevant theorem (I.T47) demonstrated that identity slippage prevents the stabilization of a unique ω.

This chapter draws the implications. We define identity-faithful reception (the relevant definition, I.D92): the requirement that a VM system preserve the ontic distinctness of τ-objects. We define structural instability (the relevant definition, I.D93): the condition in which diagonal resonance prevents a foundation from hosting an identity-faithful interpretation. The Structural Instability Theorem (the relevant theorem, I.T48) shows that diagonal-resonant foundations cannot host identity-faithful reception of τ.

The chapter closes with two scope declarations. The first (Remark [rem:absolute-meaning], I.R26) traces the implications for absolute meaning and the proliferation of infinities. The second (Remark [rem:honest-scope-identity], I.R27) states precisely what this chapter claims and what it costs.