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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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Canonical designation

$\boxed{\mathcal H_{\mathrm{DFS}}=\ker\!\left(\sum_i\sigma_z^{(i)}-\lambda I\right)}$

For collective dephasing generator

$L=\sum_i\sigma_z^{(i)},$

the DFS consists of states sharing the selected collective eigenvalue.

Origin family

• KKP Cascade Quantum Simulation Validation
• Quantum Information Theory
• collective-noise and DFS simulation documents

Identity boundary

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.

Quantum credential

Register size; Lindblad operators; initial state; time grid; overlap $\operatorname{Tr}(P_{\mathrm{DFS}}\rho_t)$; trace preservation; positivity; solver and tolerances.