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Coordinate Actions on the Golden Cubic Tower

Abstract

Cubic coordinate actions from Galois cardinality and actual tower generation.

Theorem 1.1 (Coordinate automorphisms from Galois degree).

Lean statement: D5/S3/Factorization/Galois/GoldenCubicBlockCoordinateActions.cubic_coordinate_automorphism

Proof. Machine-checked in Lean as D5/S3/Factorization/Galois/GoldenCubicBlockCoordinateActions.cubic_coordinate_automorphism (✓ std3). ∎

Source. Repository-derived.

Commentary.

In a cubic radical tower generated by nonzero roots, Galois cardinality realizes each selected coordinate rotation while fixing the other roots.

Theorem 1.2 (Galois structure and generators of the complex tower).

Lean statement: D5/S3/Factorization/Galois/GoldenCubicBlockCoordinateActions.actual_complex_tower_galois_and_generators

Proof. Machine-checked in Lean as D5/S3/Factorization/Galois/GoldenCubicBlockCoordinateActions.actual_complex_tower_galois_and_generators (✓ std3). ∎

Source. Repository-derived.

Commentary.

The actual complex cubic tower is a Galois composite of the cubic splitting fields and is generated by its selected positive roots.

References