Activating the Existential Framework (B)+(F)=Nf: From Essential Formulation to Operational Approximation of Conscious Breathing and Internal Agency

Breathing occupies a unique position as a voluntarily modifiable interface between automatic self-regulation and internal awareness. This paper presents a phenomenological-computational model that integrates the essential formulation of the framework (B)+(F) = sovereign breath in inhalation and exhalation with the operational approximation Nf ≈ Φ(∫ a(t)·r(t) dt, C, t_B, t_F), where r(t) represents physiological breathing rate in automatic time (t_B), a(t) is a latent variable of conscious agency in sovereign time (t_F), and Φ is a bounded non-linear transformation function. We highlight that inhalation and exhalation are the only meeting point where the two times converge, and that the subjective perception of time speeding up or slowing down is a direct indicator of the degree of presence of (F). We propose four falsifiable hypotheses and design a pilot study (N≈50) to estimate effect sizes. We explicitly acknowledge that this framework is a phenomenological lens for reading, not a deterministic physical model, and that its strength lies in describing boundary phenomena (birth, coma, drowning) rather than in precise numerical prediction