Algorithmic Submersion Part I: Thermodynamics and Mid-Level Dynamics

Algorithmic Submersion—the transition of cognitive models from explicit, high-energy inference to implicit, low-energy physical constraints—is the thermodynamic engine of learning, habit formation, and biological instinct. While Part II established its cross-domain architectural convergence, this paper develops its rigorous thermodynamic formalism under the strict ontological boundaries of EET Core Rules v4. 2. We define the Submersion Depth d 0, 1 as an ontologically derived variable d = 1/ (1+), quantifying the degree to which a model has been etched into the substrate. Its dynamics are governed by a modified Ben-Shi equation. We introduce the Submersion Constant, a mapping-layer parameter that quantifies the efficiency of the submersion process for a given substrate. The central result is the Inverse Law of Flexibility: b = ₒₔ₁ ₄₅₅, ₄₅₅ = Ė₌₀₈₍/C (Q) is the effective maintenance cost per unit complexity, and ₒₔ₁ is a domain-specific temporal constant. This law states that the more energy-efficient a submerged model becomes (lower ₄₅₅), the exponentially higher its topological barrier Eb against revision—a fundamental thermodynamic trade-off between efficiency and flexibility. We derive the Emergence Criterion: blockage occurs when the mismatch power exceeds a threshold, triggering explicit inquiry. Emergence is a soft interrupt (reversible, local), while Cognitive Meltdown is a hard crash (irreversible, global) triggered by accumulated response pool A (t) Eb. The full lifecycle—inquiry encapsulation buffering submersion blockage inquiry—forms a closed dynamical loop governed by the Mid-Level Dynamics of EET. Three falsifiable predictions with explicit statistical design are provided: (1) saturation of skill acquisition speed with submersion depth; (2) power-law decay of revision probability; (3) overfitting as ``over-submersion'' in AI models. This paper completes the Algorithmic Submersion series, bridging the phenomenological architecture of Part II with the first-principles thermodynamics of Energy-Efficiency Theory.: Algorithmic submersion; submersion constant; inverse law of flexibility; Ben-Shi dynamics; mid-level dynamics; energy autonomy; thermodynamic trade-off.