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Canonical zeta Cayley J-unitarity

Abstract

The diagonal zero Cayley operator preserves the indefinite inner product induced by same-height reflection.

Theorem 1.1 (Mirror Cayley coefficients are inverse conjugates).

Lean statement: D5/S3/Midline/Cayley/CanonicalZetaCayleyJUnitary.cayleyCoefficient_mirrorIndex

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

Source. Repository-derived.

Commentary.

This is the coefficient-level consequence of the existing Cayley mirror-coordinate theorem.

Theorem 1.2 (The zero Cayley operator is J-unitary).

Lean statement: D5/S3/Midline/Cayley/CanonicalZetaCayleyJUnitary.zeroCayleyOperator_j_unitary

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

Source. Repository-derived.

Commentary.

Coordinatewise inverse-conjugate coefficients preserve the mirror Krein form, and summation yields the operator identity.

References