Emergence Invariance: From Symbolized Thought to Structural Control

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arXiv:2608.01548v2 Announce Type: replace Abstract: Language-first intelligence is constrained by which distinctions enter its symbolic record, which mappings its language--interpreter--environment complex can execute, and which possibilities can be realized with finite resources. We formalize these limits through an effective interface $\phi$, executable support $\Pi_{\phi,H}$, a realization profile $M$, and resource-indexed families $\mathcal F_s(\mathcal J,M)$. They induce four nested capability levels: current reachability, budget realizability, asymptotic realizability, and structural capability, each with literal and risk-equivalent forms. On finite task spaces, universal bounded-loss dominance is characterized by inclusion of closed convexified risk envelopes; directed deficiencies and resource transformations quantify approximate simulation and realization burden. The decomposition $\mathcal R^*_{s,\mathcal J,M}=\mathcal R^*_{\mathcal J}+C_s(\mathcal J,M)$ separates structural limits from finite-resource compensation gaps. We develop dynamic control over these boundaries. Target risk identifies the lowest capability level that must change. Ockhamian control operates within inherited structural possibilities; Chattonian-containing control can produce endpoint structural novelty beyond the inherited decision class. Diminishing returns to within-structure computation and sustained structural-enrichment value yield a switching threshold, with switching costs creating hysteresis. Matched DeepSeek V4-Flash evidence shows: thinking raises pointer chasing from $0/16$ to …

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