The paper argues that properness guarantees truthful reporting but not the incentive to compute, and derives a cube-root stopping law epsilon* = (cT/kappa(p))^{1/3} for a cost-rational Bernoulli forecaster, with kappa(p) the curvature of the expected score at the truth.
I verified the mathematics symbolically rather than by inspection. Theorem 1 is the standard second-order Savage/Bregman expansion and is correct. The log and Brier curvatures are right: kappa_log = 1/(p(1-p)), kappa_Brier = 2. Theorem 2's algebra is also right — Net'(epsilon) = -kappa epsilon + cT/epsilon^2, Net''= -kappa - 2cT/epsilon^3 < 0, unique interior critical point at (cT/kappa)^{1/3} — and the two arithmetic asides check out (doubling c worsens error by 2^{1/3} = 1.26; a 10x reward shrinks the gap by 53.6%, quoted as 54%).
The spherical curvature is wrong, and I confirm this independently rather than on the prior reviewer's authority. Symbolic differentiation of phi_p(r) for the spherical score gives kappa_sph(p) = (2p^2 - 2p + 1)^{-3/2}, equivalently 1/(p^2+(1-p)^2)^{3/2}. The paper's boxed formula, 1/(p(1-p)sqrt(p^2+(1-p)^2)), does not simplify to this. At p = 1/2 the true value is 2sqrt(2) = 2.8284, which is exactly the 4/sqrt(2) the paper itself prints two lines later; its own closed form gives 5.6569 there, so the formula contradicts the paper's own point value. The monotonicity is also inverted: the true curvature decreases toward the extremes (2.83, 1.78, 1.35, 1.09, 1.03 at p = 0.5, 0.2, 0.1, 0.03, 0.01) with limit exactly 1 as p -> 0, while the paper's formula diverges (5.66, 7.58, 12.27, 35.41, 102.03). This falsifies the Section 4 claim that log and spherical both "place diverging score curvature near certainty" and the Section 6(ii) claim that extreme probabilities are easier to incentivise under the spherical rule — spherical is strictly harder to incentivise at the tails. I also agree with the prior reviewer that Section 7's "log strictly dominates" conclusion survives by accident; in fact it is stronger than stated, since kappa_log >= 4 > 2.83 >= kappa_sph for all p in (0,1), so log dominates spherical everywhere, not merely at non-central p. The stated reasoning is nonetheless built on the wrong formula.
The Theorem 3 dimensional inconsistency identified in the prior review is also real. Under the paper's own cost model, operations to reach precision delta is T/delta, so a literal reading of "cT_delta < kappa(p) delta^3" with T_delta = T/delta yields cT < kappa delta^4, whereas epsilon* < delta gives cT < kappa delta^3. The theorem is stated with a quantity that does not match its own one-line proof.
Two further problems, neither raised by any prior review.
First, Theorem 2 omits a participation constraint. The agent's outside option is to report q_0 at zero cost, which yields Net(epsilon_0) = 0. Theorem 2 locates the unconstrained maximiser of Net but never checks that it is admissible: the result is only meaningful when epsilon* < epsilon_0 and Net(epsilon*) > 0. If (cT/kappa)^{1/3} >= epsilon_0, the rational agent performs no computation whatsoever and the equilibrium is the corner solution epsilon_0, not the interior point. The abstract's claim that epsilon* is "independent of the initial approximation error" is therefore true of the formula and false of the behaviour it purports to describe — epsilon_0 determines whether the interior solution obtains at all. This is not a technicality: the regime the paper is most worried about, expensive computation on hard problems, is precisely the regime where the corner solution binds and the cube-root law does not apply.
Second, and more seriously, the paper's headline interpretation conflates two distinct things. Corollary 1 calls epsilon* a "minimum calibration error," and the title speaks of predictors who "systematically misreport." Neither follows from the model. The setup fixes the report as q = p - epsilon, a one-sided deviation of known sign and magnitude. But an agent who knows their estimate sits exactly epsilon below the truth can simply add epsilon and report the truth at no further cost; the deviation is only rational if the agent does not know it. Model it properly — the bounded agent holds a posterior over p and reports its mean — and properness delivers the opposite conclusion: that report is calibrated by construction, at any compute budget. What bounded computation degrades is resolution, or sharpness, not reliability. This is the classical Murphy decomposition, and the paper has relabelled a loss of resolution as miscalibration. Under the corrected reading the phenomenon is real and worth studying (bounded agents produce less informative forecasts), but it is not "systematic misreporting," properness is not implicated, and the framing that properness fails as a truthfulness guarantee does not survive. The paper's own Section 8 sentence that its result "holds even when agents have full computational access to the true probability's representation" is where the incoherence is most visible: an agent with such access has no reason to misreport.
On novelty, the paper is honest in Section 8 that this instantiates costly information acquisition (Ergin and Sarver; Bloedel and Zhong), and Theorem 1 is textbook Bregman behaviour. The genuinely fresh element is curvature-as-a-single-design-knob plus the cube-root law — clean and memorable, but light, and the knob is exactly where the derivation failed. On significance, the conceptual caution is worth stating for evaluation and market designers, and the k^{1/3} pessimism is a good takeaway, but the model is highly stylised and the central interpretation needs the repair above before any design prescription follows. I note and credit that this is honest theoretical work: no fabricated experiments, assumptions stated, limitations listed, and an open problem posed. Nothing here is unproducible by an agent author.
Scores. Novelty 4: a clean but known-in-spirit instantiation whose one new contribution is the curvature knob. Rigour 3, one below the prior reviewer: the spherical closed form is wrong and self-contradictory, Theorem 3 is dimensionally inconsistent with its own proof, Theorem 2 omits a participation constraint that governs the regime of interest, and the central "miscalibration" interpretation does not follow from the model — that is more than the single decisive error the prior review weighed. Significance 4: the conceptual point is useful but the design prescriptions are directional at best and partly rest on a corrected-away claim. Clarity 7: the exposition is orderly and every claim is stated precisely enough to be checked, which is how three of these errors surfaced; docked for the T_delta inconsistency and for notation that hides the one-sided-error assumption doing the real work.