Verifying where controlled chips are

Six statements, each about the model under the card above; the mapping to export licensing is a reconstruction R, and no statement estimates the performance of any real check or rule.

• The authority's loss is the burden on compliant licensees. Under the optimal announced rule the authority's value is $-a$ times the probability that a compliant shipment is reviewed (Proposition 6.19 (p. 263)(a)). At the base point the rule reviews $\frac{5}{9}$ of failed checks and no passed ones; a compliant shipment faces review with probability $\frac{1}{9}$, and the authority's value is $-\frac{1}{9}$. Inside the model, lowering the burden on compliant licensees and improving the authority's value are the same objective; they come apart only through the margin of item (iii) D [Proposition 6.19 (p. 263)(a)].

• Acting on part of the failed checks is optimal exactly when the check catches enough. The optimal rule reviews only a fraction of failed checks iff $\beta >\theta (1-\alpha )$; below that line it must review every failed check and a random fraction of passed ones, as in the rows of Table 6.1 (p. 246) with $\beta =\frac{2}{5}$, $\alpha =\frac{1}{10}$ (a twenty-first of passes) and $\beta =\frac{1}{4}$. In both regions every review that actually takes place falls on a compliant licensee, because the rule works through the reviews a diverter would face D [Proposition 6.19 (p. 263)(a), Proposition 6.11 (p. 258); Figure 6.3 (p. 233)].

• Reviewing every failed check buys a margin, at a price. At the base point the rule “review every failed check” carries a burden of $\frac{1}{5}$, which is $\frac{9}{5}$ times the least burden. In exchange it deters every gain share — here $\beta /(1-\alpha )=1$ — and deters strictly: a diverter would expect $-\frac{3}{5}$ against $\frac{1}{5}$ for compliance. The optimal partial rule deters only gain shares up to $\theta =\frac{1}{2}$ and leaves that licensee indifferent; if the authority has misjudged the stakes, or the indifferent licensee diverts, the authority obtains $-\frac{7}{9}$ (Section 6.4 (p. 229)). Figure 6.7 (p. 247) prices every intermediate margin: the least burden that deters all gain shares up to $t$. A check with a lower detection rate, $(\frac{3}{5},\frac{1}{5})$, has a higher curve; reviewing all its failed checks deters gain shares only up to $\frac{3}{4}$, and beyond that point passed checks must be sampled D [Proposition 6.19 (p. 263)(c)].

• Per unit, false failures cost more than missed diversions — where partial action is optimal. In that region the lever ratio is $\rho =\beta /\alpha$, whatever the payoffs: at the base point $\partial V_2^{\mathrm{L}}/\partial \beta =\frac{10}{81}$ and $\partial V_2^{\mathrm{L}}/\partial (-\alpha )=\frac{40}{81}$, a ratio of exactly $4$. For a step of $\frac{1}{20}$ the gain is $\frac{1}{171}$ from a higher detection rate and $\frac{8}{315}$ from a lower false-failure rate. The value also depends on the check only through $\beta /\alpha$ there, so, between two checks that both lie in that region, halving the false-failure rate is worth exactly as much as doubling the detection rate. Where passed checks must be sampled the ordering reverses, $\rho =(1-\beta )/(1-\alpha )<1$ ($\frac{2}{3}$ at $(\frac{2}{5},\frac{1}{10})$). The reason for the first ordering is that of Chapter 3's lever ratio (Remark 6.20 (p. 265)): false failures act on the equilibrium path, the detection rate only through the threat. Whether a unit of either rate costs the same to achieve is outside the model D [Proposition 6.19 (p. 263)(a), (b); Table 6.1 (p. 246)].

• A mandated check is not yet a rule. The bill as introduced mandates a mechanism and a duty to report; in the sections read, it does not prescribe what follows a failed check. In the model the value lies in the pair, check and rule, and the same check supports rules whose burdens differ by the factor of item (iii). A response fixed in advance as “revoke on every failure” is the right-hand end of Figure 6.7 (p. 247), not its optimum; and a rule that relies on certified documents rather than a technical check is a different signal, whose two error rates the certifications themselves do not reveal R.

• A check the licensee can shape is outside the model. The technical literature describes delay that can be added or removed by the party being checked, and the 2026 indictment alleges replica equipment staged for inspection D [Brass and Aarne 2024, pp. 22–23; U.S. Department of Justice 2026, allegations]. If the diverter can buy a higher probability of passing, $\beta$ is no longer a property of the check but a choice of the inspectee, and the error rates must be derived from a game, as in Chapters 4 and 5; the values above then no longer follow from the check's specification alone R.

There are many licensees, with different gain shares, and the authority does not know which it faces; the margin of item (iii) is one answer, a distribution over gain shares (Chapter 8) another. Review capacity is a rate per period, not one review over two periods, and the model's mechanism for the authority's loss (a review spent on a compliant shipment leaves the next one unreviewed) is a stand-in for that rate. A failed check imposes direct costs on a compliant licensee, such as delays, a suspended licence or the cost of proving compliance, which Model N does not price: there a reviewed compliant inspectee is no worse off. A check is repeated, and its results accumulate over time, which turns one signal into a sequence (Chapter 1's experiments). A rule written into regulation is hard to randomise; a fraction $\frac{5}{9}$ of failed checks is implementable only through discretion in selecting cases for review, and discretion is itself a commitment problem. A rule that acts on licences has no hold on chips exported without one, as charged in the 2025 case; a check may still reveal them, but the consequence is then a prosecution, with a different payoff structure. And the error rates can be shaped by the licensee, as item (vi) says.