Pseudo-Gauge Stabilizers and Fibration Structure of the Cooper--Frye Map at Freeze-Out

Abstract

We study the pseudo-gauge transformation (PGT) freedom at freeze-out in relativistic spin hydrodynamics. The Cooper--Frye map is shown to factor through the quotient of freeze-out data by a universal stabilizer, yielding a stratified fibration over the space of thermodynamic Lagrange multipliers. This classifies observables into base and fiber types, bounds the number of independent PGT-sensitive observables by the family-restricted fiber dimension, and implies cross-observable consistency relations. Applied to heavy-ion polarization data, the fibration structure provides a structural interpretation of the tension between $Λ$ polarization and $ϕ$-meson spin alignment as evidence that the vorticity-dominated response sector may need to be enlarged with local field-correlation data. We show that Weyl-anomaly-induced currents studied recently are classified as base observables and recover the known Belinfante--canonical obstruction $Ω_{ab}\neq\varpi_{ab}$ from the stabilizer condition.