N,N-dimethyltryptamine (DMT) is an endogenous tryptamine neurotransmitter whose extracellular concentrations rival serotonin, whose release increases during cardiac arrest, and whose sigma-1 receptor (Sig-1R) activation provides potent neuroprotection against hypoxia. Despite decades of research, no first-principles framework explains why the brain synthesizes a molecule that produces near-death experience phenomenology, nor connects its neuroprotective and consciousness-altering functions within a single mechanism. We integrate DMT pharmacology into the machine-verified Recognition Science (RS) framework using 17 new Lean 4 modules. This paper explicitly distinguishes between the mathematically forced core of the framework and the phenomenological models built upon it. The logical structure follows a rigorous chain: Forced Structure: The Recognition Composition Law (RCL) forces the existence of the φ-ladder, the J-cost function, and the universal theta field (Θ). Modeling Interpretation: We map specific biological components to this forced structure: DMT is identified with the φ¹ ladder rung, yielding a "golden balance" (coupling multiplier × control factor = 1); Sigma-1 receptor activation is modeled as lowering the cellular J-cost barrier; and NDE phenomenology is injectively mapped to theta-field geometry. Testable Consequences: This model generates specific, falsifiable predictions: (a) DMT will preferentially amplify EEG power at 5φ ≈ 8.09 Hz; (b) Faraday shielding will attenuate inter-subject theta coherence; (c) tryptamine analogs (e.g., 4-HO-DMT) will exhibit coupling/control ratios at discrete φ-ladder half-rungs. The Lean 4 formalization verifies the strict logical consistency of our biological model with the underlying physics, demonstrating that neuroprotection and NDE phenomenology are mathematically identical operations on the tether channel.