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Canonical zeta Cayley Krein inverse

Abstract

Mirror symmetry constructs the bounded two-sided inverse of the zero Cayley operator and identifies it with J U-star J.

Theorem 1.1 (The zero Cayley operator is unconditionally invertible).

Lean statement: D5/S3/Midline/Cayley/CanonicalZetaCayleyKreinInverse.zeroCayleyOperator_isUnit_unconditional

Proof. Machine-checked in Lean as D5/S3/Midline/Cayley/CanonicalZetaCayleyKreinInverse.zeroCayleyOperator_isUnit_unconditional (✓ std3). ∎

Source. Repository-derived.

Commentary.

The reciprocal multiplier is bounded by transporting the original bounded coefficients through mirror permutation and conjugation.

Theorem 1.2 (The explicit inverse equals J U-star J).

Lean statement: D5/S3/Midline/Cayley/CanonicalZetaCayleyKreinInverse.zeroCayleyKreinInverse_eq_explicit

Proof. Machine-checked in Lean as D5/S3/Midline/Cayley/CanonicalZetaCayleyKreinInverse.zeroCayleyKreinInverse_eq_explicit (✓ std3). ∎

Source. Repository-derived.

Commentary.

The same proof yields the companion conservation identity U J U-star = J without ordinary unitarity.

References