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PROMOTED UNDER CITY PHYSICAL-CLAIM PROTOCOL. For the explicitly declared engineered Lindblad family with jump operator $L=K=(C-6I)(C-30I)$, every state in $E_{47}=\ker K$ is dark and the Lindblad dissipator vanishes on code-supported states. Status: [T] Physical theorem within the declared engineered-noise model · E0 + E1/E2. This promotion does not assert decoherence-free behavior under arbitrary environmental noise or hardware realization.
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Engineered-noise DFS validation supplies the previously missing explicit noise model for the Casimir-selected E47 sector: choose Lindblad jump $L=K$ with $K=(C-6I)(C-30I)$. Then every $|\psi\rangle\in E_{47}=\ker K$ satisfies $L|\psi\rangle=0$, so E47 is a dark/decoherence-free subspace for this specified engineered noise family. The numerical witness reports $\dim E_{47}=47$, $KP_{47}\approx0$, projector residuals at machine precision, and the established contraction constants $\varepsilon_=1/99144$, $\rho_=15/17$.
Boundary retained: this proves DFS status for the explicitly defined jump algebra generated by $K$; it does not establish E47 as decoherence-free for arbitrary three-spin-2 environmental noise. The document's statement that random states "converge to 0.376 dark-subspace occupancy" is interpreted ensemble-wise: Haar mean initial E47 weight is $47/125$; an individual state contracts onto its own E47 component rather than to a universal per-state occupancy of $0.376$.
No immutable GitHub implementation specific to this DFS validation was located in the connected provenance search, so no unrelated E47 commit is assigned as source authority.
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PROVENANCE / EVIDENCE-BOUNDARY AUDIT · 2026-08-09
New Drive claim artifact is retained as a noncanonical source candidate. The rank-47 Casimir-selected space $E_{47}$ is not thereby established as a decoherence-free subspace for an arbitrary three-spin-2 open system. DFS status requires a specified noise algebra/Lindblad family whose action preserves or acts scalarly on the selected subspace. No immutable GitHub implementation or machine certificate establishing that condition was located. Existing D-04 citizenship and transit remain unchanged.
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TRANSIT CREDENTIAL · D-04 · FOUNDING COHORT
Route: Foundations → Python Subway → Verification Hall → Quantum Information Borough
Current evidence: E0 exact kernel definition + E1/E2 source-dependent simulation
Standing: Enrolled as a quantum dynamical identity.
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$\boxed{\mathcal H_{\mathrm{DFS}}=\ker\!\left(\sum_i\sigma_z^{(i)}-\lambda I\right)}$
For collective dephasing generator
$L=\sum_i\sigma_z^{(i)},$
the DFS consists of states sharing the selected collective eigenvalue.
This citizen is distinct from the Casimir kernel. Equality or embedding between $\mathcal H_{\mathrm{DFS}}$ and $E_{47}$ requires an explicit intertwiner or shared representation model; analogy alone does not merge their citizenship.