The Protected Reversal Capsule: Local-Capsule Decomposition, Capacity-Triggered Role Exchange, and Robust Hybrid Stability in Six-Throat Directed Geometry

Abstract

Paper XIX develops the protected local realization of directed reversal in Six-Throat Directed Geometry. It introduces the Local-Capsule Decomposition Principle, separating capsule polarity, internal mechanical realization, persistent node identity, and functional node role. The two stellar nodes remain fixed in identity while their emissive and absorptive roles exchange at a finite-capacity surface, with the protected planetary mechanical state remaining continuous across the zero event.The local transition clock is derived from capsule throughput and absorptive capacity rather than from an imposed orbital period. A node-resolved energy ledger gives an energy-continuous hybrid reset, while the retained planetary mantle is represented by an eight-node dimensionless mass–damping–stiffness protection network. Removal of the mass-weighted common mode defines a seven-degree-of-freedom capsule-frame relative witness and a 14-dimensional first-order reduced mechanical system.For the frozen canonical source-exact manifest, the dominant state pole is −0.235510204896 ± 0.212605783667 i and the mechanical Floquet radius is 0.389831447340. Because the exact reduced mechanical equations are affine-linear with a Hurwitz state matrix, the unique periodic response is globally exponentially attracting within the exact 14-dimensional reduced capsule model. The node-energy/throughput sector contributes only the neutral cycle-phase tangent, so after fixed-phase Poincaré reduction the augmented transverse monodromy is exactly the mechanical monodromy.The energy-normalized monodromy has a certified stability radius r_E = 0.496949800090. A discrete Lyapunov construction gives V_{n+1} ≤ 0.475160089169 V_n, and any later nonlinear completion with remainder ||R(z)|| ≤ β_P ||z||² has a certified attraction basin whenever β_P r < 0.265550842763.These results are internal mathematical stability statements for the specified dimensionless protected-capsule model and its explicitly stated completion class. They are not presented as observational detection of a real Solar-System reversal, and the frozen dimensionless couplings are not claimed to be universal measured constants.