HLV-SF-SECONF-002: Post-Freeze Analytic P1/P2 Results for Native and Non-Vanishing Structural Obstruction in the HLV Strong-Force Programme

This archive records the post-freeze analytic P1/P2 evaluation of the prospectively frozen protocol HLV-SF-SECONF-002. The corresponding pre-evaluation protocol was frozen and publicly archived before this analysis as: Krüger, M. (2026). HLV-SF-SECONF-002: Pre-Evaluation Freeze for a Native Structural-Obstruction and Admissible-Path Test in the HLV Strong-Force Programme [Dataset]. Zenodo. https://doi.org/10.5281/zenodo.22017573 The purpose of the present analysis is to determine whether the winding-based structural route proposed for the HLV strong-force programme provides a genuine native obstruction to continuous deformation from a closed/source-free winding sector to a separated-channel target. Two prospectively distinguished configuration spaces are evaluated. In the conditional non-vanishing branch A_nz, each relevant complex channel field satisfies |psi_a| > 0. The normalized phase field therefore defines a continuous map u_a = psi_a / |psi_a| : |G| -> S^1. P1 is proved analytically: under continuous homotopies that remain in the non-vanishing configuration space, the associated H^1(|G|; Z) class and cycle winding integers are invariant. This is a standard topological property of non-vanishing complex fields and is not HLV-specific. The native branch A_native instead retains the source-field condition rho_a >= 0 and therefore permits amplitude zeros. Under the frozen ambient-space definition C(|G|, C^3), this configuration space is convex and contractible. A winding configuration can be continuously contracted through the zero field and subsequently expanded into a configuration carrying a different winding vector. Accordingly, P2 refutes a native structural obstruction based solely on preservation of the winding vector or on the derived quantity chi_gamma = n_1 n_2 n_3. The resulting structural verdict for the tested mechanism is: NO_NATIVE_STRUCTURAL_OBSTRUCTION The corresponding conditional result is: CONDITIONAL_NONVANISHING_OBSTRUCTION_ONLY and the specificity verdict is: STRUCTURAL_CAPACITY_GENERIC_NOT_HLV_SPECIFIC. The quantity chi_gamma is found to be a derived function of the channel winding integers rather than an independent topological obstruction. It therefore does not restore native structural protection when amplitude zeros are admissible. No large numerical path search is required for the P1/P2 conclusion. In particular, failure of a finite numerical optimizer to locate a path could not provide a stronger no-path result than the analytic topology considered here. A qualification remains explicit: if a future HLV formulation independently derives an additional nonlinear admissibility or source-free constraint that excludes the zero-mediated homotopy without being introduced for the purpose of protecting confinement, that new constrained space would require a separate prospectively frozen analysis. The present result does not refute every conceivable HLV confinement mechanism. It specifically rejects the tested winding/topology route as a native structural confinement mechanism under the frozen field-space definitions. It also does not establish or refute QCD color confinement, SU(3) gauge dynamics, a Yang-Mills mass gap, physical string tension, glueball spectroscopy, X(2370), Y(2240), or the validity of HLV as a fundamental physical theory. Within the current HLV strong-force programme, the appropriate consequence is therefore that the previous SE-CONF energetic/stability status remains E-ONLY; it is not upgraded to native structural confinement by the tested winding mechanism.