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NEW MATHEMATICAL CITIZEN · E0 EXACT

This identity records the representation-invariant transport of the spectral kernel under unitary equivalence.

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Canonical identity

For a unitary $U:\mathcal H\to\mathcal H'$, define

$C'=UCU^\dagger,\qquad K'=UKU^\dagger,\qquad P'=UPU^\dagger.$

Then

$\boxed{\ker K'=U(\ker K)}$

and

$\boxed{\dim\ker K'=\dim\ker K=47.}$

If the open-system data are transported by

$H'=UHU^\dagger,\qquad L_\mu'=UL_\mu U^\dagger,$

then the transformed Lindblad generator is unitarily conjugate to the original generator and preserves the same abstract invariant-sector structure.

Logical boundary

This proves substrate-neutrality of the operator architecture under unitary realization. It does not prove that arbitrary gravitational, biological, or cognitive systems instantiate that architecture.

Evidence class

• E0: exact unitary-equivalence theorem.
• E1: not required for the theorem.
• Interpretive boundary: physical identification requires an explicit encoder or intertwiner from the proposed substrate into the canonical carrier.

Transit credential

Credential: CIT-U20-E0-UNITARY-TRANSPORT

Route: Representation Theory → Foundations → Verification Hall → Citizenship Bureau