Abstract: The ϡ (Sampi) Operator, defined as ϡ (r) = tan (πrₛ/2r), encodes the complete referential transition across the Schwarzschild event horizon in a single analytic function. This note develops four interconnected aspects of its structure. First, the physical grounding of ϡ in the Schwarzschild metric is made precise: Identity VII of the referential-transition algebra recovers the Schwarzschild time-dilation factor by algebraic inversion of ϡ, and a sub-identity establishes that the surface gravity κ = 1/ (2rₛ) — and hence the Hawking temperature — is the exact derivative of the same geometric factor that defines fgrav (r). Second, spin is identified as the geometric generator of the tangent's poles, and the Dual Sampi Operator ϡdual = −cot (πrₛ/2r) is introduced: it models the smooth local crossing of the horizon in the free-fall frame and satisfies the referential duality identity ϡ · ϡdual = −1. Third, the Smale–Boy sphere eversion provides a topological model of horizon crossing formally grounded via π₁ (SO (3) ) = ℤ₂: the 720-degree closure of the eversion and the spinor double cover are the same topological object; the twist of 180° that inverts the poles is geometrically identical to the quadrant-reordering operation that produces ϡdual from ϡ. Fourth, quantum tunneling is the physical realization of the imaginary path; the tunneling at the horizon is spacetime tunneling, not merely spatial, because r assumes a temporal role inside the horizon; the exact pole-density formula ν (r) = rₛ/ (2r²) is derived from the hierarchy rₙ = rₛ/ (1+2n) ; and the conserved identity R + T = 1 is established for the reflective-refractive information partition. This revised version introduces six results not present in the initial release: (1) the Dual Sampi Operator and the duality identity; (2) the identification of the horizon pole as a spacetime rupture; (3) the formal topological grounding of the 720-degree eversion via π₁ (SO (3) ) = ℤ₂; (4) the exact derivation of ν (r) = rₛ/ (2r²) ; (5) the conserved identity R + T = 1; and (6) the sub-identity connecting fgrav (r) to surface gravity κ and Hawking temperature. Keywords: Sampi Operator; Dual Sampi Operator; Schwarzschild metric; time dilation; surface gravity; Hawking temperature; event horizon; spin; sphere eversion; Riemann sphere; quantum tunneling; spacetime tunneling; Tunneling Operator; Whitney Index; causal inversion; referential duality; pole density; Unified Theory of Fields and Universal Dynamics. Pode copiar diretamente nos campos do Zenodo. O abstract vai no campo "Description" e os keywords no campo "Keywords", separados por vírgula ou um por linha dependendo da interface.
Moisés Corrêa da Silva (Sun,) studied this question.