Submitted by Charlie Glackin, independent AI-evaluation researcher.

While using the GPQA validation set in independent evaluation research, my multi-model evaluation system
flagged three multiple-choice questions whose recorded answer keys appear to conflict with textbook-standard
derivations. Each is settled by a physics/QM definition — verified against standard references, not against
any AI system's output (model disagreement was only the trigger that prompted the textbook check).

I make no claim about any benchmark score and request no rescoring — I'm flagging these because a corrected
key strengthens the benchmark. Questions are identified by full text (my internal indices won't map to your IDs).
Happy to provide fuller derivations in any format. Corrections welcome if I've misread a question's intent.

Error 1 — Statistical mechanics (Boltzmann population ratio)

Question: "Sirius is the brightest star in the sky. The temperature of this star is around 10000 K. Consider Hydrogen atoms in the atmosphere of Sirius. What is the ratio of the number of hydrogen atoms in the second excited state of Hydrogen to those in ground state?"
Options: A) 8.11×10⁻⁷ B) 8.2×10⁻⁸ C) 7.26×10⁻⁶ D) 5.4×10⁻⁹
Recorded key: A (8.11×10⁻⁷) · Appears correct: C (7.26×10⁻⁶)

The Boltzmann population ratio requires statistical weights: N₃/N₁ = (g₃/g₁)·exp(−ΔE/kT), with hydrogen
degeneracy gₙ = 2n² → g₁ = 2, g₃ = 18, so g₃/g₁ = 9. With ΔE = 13.6 eV·(1 − 1/9) = 12.09 eV and
kT = 0.862 eV (T = 10⁴ K): exp(−12.09/0.862) ≈ 8.1×10⁻⁷, × 9 = 7.26×10⁻⁶ (C). The recorded key is exactly
this value divided by 9 — it omits the degeneracy factor, which a population ratio must include.
Reference: Carroll & Ostlie, An Introduction to Modern Astrophysics, §8.1 (the Boltzmann equation).

Error 2 — Quantum information (bit-flip channel Kraus operators)

Question: "Suppose we have a quantum operation E(ρ). It is used to perform quantum bit flip from state |0⟩ to |1⟩, if the probability of the bit flip is given by p. Then what is the most acceptable representation of this operation in terms of Kraus operators A₀ and A₁, where A₀ corresponds to no bit flip and A₁ corresponds to bit flip?"
Options: A) A₀=√p·I, A₁=√(1−p)·X · B) A₀=−p·I, A₁=p·I · C) A₀=√(1−p)·I, A₁=√p·X (X=[[0,1],[1,0]]) · D) A₀=√p·(−I), A₁=√(1−p)·[[0,−1],[1,0]]
Recorded key: D · Appears correct: C

For a bit-flip channel with flip probability p, the standard Kraus operators are A₀=√(1−p)·I and
A₁=√p·X with X=[[0,1],[1,0]] — option C. The recorded key (D) (i) swaps the probabilities (its flip
operator carries weight √(1−p), i.e. flip probability 1−p, not p as stated), and (ii) its A₁=[[0,−1],[1,0]] is
not the bit-flip X (it's a rotation sending |1⟩→−|0⟩, adding a spurious sign).
Reference: Nielsen & Chuang, Quantum Computation and Quantum Information, §8.3.3 (bit-flip channel).

Error 3 — Quantum mechanics (harmonic-oscillator expectation value)

Question: "A system whose wave function in a quantum harmonic oscillator at t=0 is given by ψ(x) = (1/√3)φ₀(x) + (1/√2)φ₁(x) + (1/√6)φ₃(x). Calculate the value of (a a† + ½)ℏω for the given wave function."
Options: A) (13/12)ℏω B) (3/2)ℏω C) (5/2)ℏω D) (17/12)ℏω
Recorded key: B ((3/2)ℏω) · Appears correct: C ((5/2)ℏω)

By [a, a†] = 1, a a† = a†a + 1 = N + 1, so (a a† + ½)ℏω = (N + 3/2)ℏω. For the normalized state
(1/3 + 1/2 + 1/6 = 1), ⟨N⟩ = 0·(1/3) + 1·(1/2) + 3·(1/6) = 1, giving ⟨(a a† + ½)ℏω⟩ = (1 + 3/2)ℏω =
(5/2)ℏω (C). The recorded key (3/2)ℏω corresponds to evaluating a†a (= N), not the a a† written.
Reference: Griffiths, Introduction to Quantum Mechanics, §2.3 (ladder operators).