C066 - The states |down,up> and |up,down> acquire a relative phase phi = 2 epsilon Delta t, so a...
Verdict: partial (mismatch)
Location: Supp. Mat. S4
Type / expected artifact: math / math / numeric
Claim: The states |down,up> and |up,down> acquire a relative phase phi = 2 epsilon Delta t, so a system initially in |Psi^-> is found in |Psi^+> after one drive-(A) cycle (t = 2 x 2 pi/delta) with probability p = sin^2(phi/2) ~= 0.5.
Models: extraction claude-opus-4-8; verification gpt-5; verification_chain claude-opus-4-8 -> gpt-5; verdict_chain partial -> partial.
Limitations: paper_text_only_reimplementation.
Source location(s): source/supp_content.tex:125 (Supp. Mat. S4).
Conclusion
Structural relations CONFIRMED: phi = 2 eps Delta t is the correct differential relative phase, and P(|Psi+>) = sin^2(phi/2) is verified symbolically (sympy). NUMERIC mismatch: with eps=0.05, Delta=2pi x 25 kHz, delta=2pi x 14.7 kHz, t=2*(2pi/delta)=136.05 us, phi=2.137 rad and p=sin^2(phi/2)=0.768. Paper states p ~= 0.5; recomputed p ~= 0.77 (abs diff 0.27 vs 0.5). The ~0.5 is a rough order-of-magnitude 'large per-cycle error' statement; the qualitative conclusion (near order-unity error destroying the protocol) holds for either value. -> partial / mismatch.
Verification details
Derivation excerpt: Work in the two-ion ground-qubit space spanned by $\ket{\downarrow\uparrow}$ and $\ket{\uparrow\downarrow}$, with the Bell basis $$\ket{\Psi^{\pm}} = \frac{1}{\sqrt{2}}\big(\ket{\uparrow\downarrow} \pm \ket{\downarrow\uparrow}\big).$$
Executable rerun: run.py exited 0 in 0.638s; log verification/C066/attempts/R002/run.log.
Output excerpt:
symbolic P(|Psi+>) = sin(phi/2)**2 ; expected sin^2(phi/2)
matches sin^2(phi/2)? True
t = 136.05 us
phi = 2.1371 rad
p=sin^2(phi/2) = 0.7683
paper states p ~= 0.5 ; recomputed p ~= 0.768
abs diff vs 0.5 = 0.268 -> MISMATCH (paper value is rough)