Exact Linearity of the Contracted Pure-Axial Torsionful α-Surface Transport

Key Points

• To demonstrate the exact linearity of the contracted pure-axial torsionful α-surface obstruction in the algebraic holomorphic sector.
• Proved the linearity of the obstruction in algebraic frameworks.
• Analyzed the vanishing of the quadratic pure-axial Weyl-type obstruction after triple projection.
• Established the form of the transport equation based on normalization parameters.
• Demonstrated that the quadratic pure-axial Weyl-type obstruction vanishes post triple-π projection.
• Identified that the transport equation relies on a singular normalization parameter connecting forms.
• Confirmed linearity in the holomorphic sector for the contracted obstruction.