⚛️ Physical-model promotion · 2026-08-31

<aside> ✅

PROMOTED UNDER CITY PHYSICAL-CLAIM PROTOCOL. The following are physical quantum-information theorems for the declared finite model: $\rho\mapsto P_{47}\rho P_{47}$ is a CP-TNI selective quantum operation; $\mathcal D_{47}(\rho)=P_{47}\rho P_{47}+(I-P_{47})\rho(I-P_{47})$ is CPTP and preserves the sector decomposition; and for the declared kernel-aligned Lindblad jump $L=K$, $E_{47}$ is decoherence-free/dark. These statements are promoted at E0/E1 scope. Not promoted: universal QEC against arbitrary errors, a hardware code realization, or an experimentally measured protection advantage, because those are different propositions with additional error-model or empirical obligations.

</aside>

Latest E47 channel normalization · Revision C seed

Unified exact-validation monograph · JSON certificate · Python witness

Credential QF-RC-E47-20260728 independently reaffirms the existing E47-QOP-C01…C10 correction family:

• $\mathcal M_P(\rho)=P\rho P$ is CP-TNI on the full space and TP on code-supported inputs;
• minimal Kraus/Choi rank is 1, while $\operatorname{rank}P=47$;
• $\dim\operatorname{Fix}(\mathcal M_P)=47^2=2209$;
• $\mathcal M_t(\rho)=e^{-tK^2}\rho e^{-tK^2}$ is CP-TNI and full-space TP only at $t=0$;
• the smallest positive eigenvalue of $K^2$ is 11664;
• $\mathcal D_P(\rho)=P\rho P+Q\rho Q$ is CPTP with fixed algebra dimension 8293.

This is a credential strengthening operation, not a new citizenship cohort.

Quantum-operation correction and QEC boundary · 2026-07-28

Canonical correction archive

The projector branch $\rho\mapsto P_{47}\rho P_{47}$ is a valid selective quantum operation, not a full-space CPTP channel. Its success probability is $\operatorname{tr}(P_{47}\rho)$, and its normalized postselected update is conditional and nonlinear.

The valid two-outcome nonselective channel is

$$ \mathcal D_{47}(\rho)=P_{47}\rho P_{47}+(I-P_{47})\rho(I-P_{47}). $$

This channel is CPTP and preserves the sector decomposition, but it does not by itself establish Knill–Laflamme recovery, a noiseless subsystem for an arbitrary error algebra, or attractive pumping into $E_{47}$.

New credentials: E47-QOP-C01…C10.

Still required for QEC promotion: declared error channel, KL/OQEC condition, logical subsystem, recovery map, leakage metric, and independent execution in the pinned QuTiP environment.