Common-Mode Angular Registration in Hypertriton Coalescence: A Nonlinear Nucleon Estimator and Provenance-Preserving QMU Reanalysis

This paper presents a nonlinear and provenance-preserving reanalysis of the hypertriton polarization framework developed by Liu et al. for noncentral heavy-ion collisions. The source study proposed reconstructing proton polarization from the measurable polarizations of the Λ hyperon and the hypertriton, with hypertriton polarization denoted by PH. Starting directly from the reported spin-density weights, the complete nonlinear coalescence relation is derived as PH =2Pₙ + 2Pₚ - P_Λ - 3PₙPₚP_Λ/3 - 2P_Λ(Pₙ + Pₚ) + PₙPₚ. The principal structural result is exact common-mode preservation. Within the adopted J^π = 1/2⁺ spin-density coalescence map, Pₙ = Pₚ = P_Λ = PA H = PA. A polarization shared by the neutron, proton, and Λ is therefore transmitted to the hypertriton without attenuation or nonlinear distortion. This is an exact conditional identity of the stated coalescence map. Its experimental applicability depends on whether the constituent polarization, phase-space, and hypertriton projection assumptions describe physical hypertriton formation. The commonly used linear relation 3PH + P_Λ/4 is shown to reconstruct the average nucleon polarization PN = Pₙ + Pₚ/2, rather than uniquely reconstructing proton polarization. It becomes a proton estimator only after imposing the additional condition Pₙ = Pₚ. Under nucleon equality, the exact nonlinear inverse satisfies (PH + 3P_Λ)PN²-4(1 + PHP_Λ)PN+(3PH + P_Λ)=0. The stable physical solution is PN =3PH + P_Λ2(1 + PHP_Λ)+√4(1 + PHP_Λ)²-(PH + 3P_Λ)(3PH + P_Λ). Its linear limit is PNˡⁱⁿ=3PH + P_Λ/4, and the leading nonlinear correction is PNⁿˡ - PNˡⁱⁿ=3(PH-P_Λ)²(3PH+P_Λ)/64+O(P⁵). Figures 2 and 3 of the source paper were extracted into a provenance-preserving numerical ledger. The reconstruction records source figure, panel, raster calibration, sampled pixel coordinates, visible band limits, confidence level, and occlusion status. Hidden portions of overlapping uncertainty bands were not inferred. Independently reconstructed quantities were used where direct raster values were obscured. Across nine sampled collision energies, the maximum nonlinear correction is approximately 9.066×10⁻⁶ percentage points, corresponding to approximately $3.789$ parts per million of the reconstructed polarization. The published linear estimator is therefore numerically sufficient throughout the displayed polarization regime. Within the Aether Physics Model, the exact common mode is interpreted as shared angular registration transmitted through composite formation. The analysis preserves the universal quantum length λₓ = λC and the invariant mass-to-magnetic-charge relation mₓeₓₘₐₓ²=mchg. Particle-dependent polarization differences are therefore assigned to charge organization, compatibility geometry, constituent-state differences, and transport history rather than to particle-specific quantum lengths or varying mass-to-magnetic-charge ratios. The unresolved proton-neutron difference mode Δₙₚ=Pₙ-Pₚ cannot be determined from the hypertriton relation alone because the proton and neutron enter with equal coefficients. Separating them requires a second composite-polarization observable with unequal proton and neutron projection weights. The accompanying reproducibility materials include the LaTeX manuscript source, numerical spreadsheet, machine-readable JSON and CSV ledgers, calibration records, source-figure extractions, sampling overlays, validation report, and reconstruction documentation.