<aside> 🔗
LINEAGE REFRESH · 2026-09-13
Existing E47-QOP-C01–C10 remain the registered identities. This 2026-09-11 independent reconstruction is certificate evidence, not a new citizen family. The distinct 7-qubit embedding cardinality is now citizen QOP-EMB-C01 · Minimal 7-Qubit Data Embedding. Proof Forge re-derived the finite core at 120/120 PASS without inserting a 47-dimensional nullspace by hand.
</aside>
<aside> ✅
CERTIFICATE: E47-QOP-INDEPENDENT-20260911 · PASS
Independent reconstruction starts from the spin-2 ladder relations and rebuilds the 125-state carrier, Casimir, selector, positive generator, rank-47 projector, optimal contraction, 7-qubit embedding, and ideal QPE kernel discriminator. No 47-dimensional nullspace is inserted by hand.
</aside>
$$ V_2^{\otimes3}\;(125)\longrightarrow C\longrightarrow K=(C-6I)(C-30I)\longrightarrow Q=K^2\longrightarrow E_{47}=\ker K\;(47)\longrightarrow P_{47} $$
$$ \Gamma_{\varepsilon_}=I-\varepsilon_Q,\qquad \varepsilon_=\frac1{99144},\qquad \rho_=\frac{15}{17} $$
Recovered Casimir sectors: (1,9,25,28,27,22,13) on eigenvalues (0,2,6,12,20,30,42).
Recovered selector spectrum: {-140^27,-108^28,0^47,112^9,180^1,432^13}.
Recovered positive spectrum: {0^47,11664^28,12544^9,19600^27,32400^1,186624^13}.
| Witness | Independent value |
|---|---|
| rank(P47) | 47 |
| Tr(P47) | 47.000000000000014 |
| projector polynomial vs eigenspace | 1.17619649725086e−13 |
| K² gap | 11664 |
| K² norm | 186624 |
| Gamma^400 vs P47 | 1.8184842456695434e−13 |
The minimal data register is 7 qubits because 2^6 < 125 <= 2^7. The three unused codewords are assigned nonzero selector value and remain outside the kernel.
The executed ideal statevector discriminator uses
$$ U=\exp(2\pi i K_{128}/512) $$
with 9 phase qubits. For deterministic seed 470125:
0.3615694070328574<ψ|P47|ψ>: 0.36156940703285740.0P47|ψ>: 1.06.624885053765331e−29<aside> 🧭
Evidence boundary. This is E0 exact finite-dimensional operator mathematics plus an independent E1 ideal NumPy statevector reconstruction. It is not a Qiskit execution, hardware execution, universal QEC certificate, or physical noise-performance claim. The next gate is a frozen channel/noise model, KL/OQEC test, explicit recovery, and logical-error comparison.
</aside>