E47 Quantum Error Correction — spectral core, mint lock rings. Mini AI Labs visual system.

<aside> ◼

VISUAL SYSTEM · MINI AI LABS

Near-black laboratory. Cyan live · bronze Λ-ghost · mint lock. No type on stills.

Record: CITY-LABS-VISUAL-SYSTEM-20260915.

</aside>

Minimum-qubit certificate intake · 2026-09-07

Drive source — E47 MINIMUM-QUBIT QUANTUM CIRCUIT CERTIFICATE

The embedded NumPy/SymPy reconstruction is newly reproducible. Independent rerun under Python 3.13.5, NumPy 2.3.5, SymPy 1.14.0, complex128 reproduces the information-theoretic minimum n_Q=7, CG unitarity max error 2.2204e-16, ||CU-Udiag(C)||max=3.5527e-15, rank(P47)=47, ||P²-P||max=1.6653e-16, ||KP||max=2.1092e-14, ||R†R-I||max=4.4409e-16, and the contiguous coupled-basis E47 address ranges 10..34 and 90..111.

Canonical certification decision · 2026-09-07: human authority selected standalone citizenship/canonical certificate status. The artifact is now enrolled as citizen E47-7Q-001 with certificate credential E47-7Q-CERT-20260907, routed to the Quantum Information borough, and bound to the existing Machine Certificates ledger. The canonical source is Drive revision 25 of the embedded certificate, modified 2026-09-04T18:49:33.275Z; this supplies a versioned source identity even though Drive does not mark the revision keepForever.

Certified execution scope: Python 3.13.5, NumPy 2.3.5, SymPy 1.14.0, complex128, max-entry norm. The rerun reproduces CG unitarity 2.220446049250313e-16, ||CU-Udiag(C)||max=3.552713678800501e-15, rank(P47)=47, ||P²-P||max=1.665334536937735e-16, ||KP||max=2.109176776213206e-14, ||R†R-I||max=4.440892098500626e-16, and projector-polynomial error 1.854072451124011e-14. Declared tolerances are TOL=1e-10, KP<1e-9, and rank tolerance 1e-8.

Boundary preserved: optional Qiskit synthesis remains outside the executed certificate scope because qiskit is absent from the audit runtime. This is not a failed NumPy/SymPy reconstruction. No hardware execution, experimental protection advantage, or universal quantum-error-correction claim is inferred. The earlier unassigned-status language on this page is preserved historically by this superseding decision record.

⚛️ 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.