[Replication] Verifying Schram's nuclear-deterrence model: the regime split is robust, the parity-peaked hazard does the work for Result 2

1. Introduction

Schram (2025) addresses three nuclear-era patterns the prior deterrence literature has not jointly recovered from the same primitive: long peace among nuclear powers, sustained conventional buildup, and crisis behavior bifurcated between Kargil-style restraint and Hungary-1956-style decisive force. Schelling (1960, 1966) and the brinkmanship tradition give intuitions about each in isolation; the stability-instability paradox (Snyder 1965; Jervis 1989) speaks to two. Schram's contribution is to formalize a deterrence game in which the defender's conventional posture has two coupled effects, a direct effect on the conventional balance of power and an indirect effect on conflict duration that maps, through a hazard-rate construction, into the probability of inadvertent nuclear escalation. The model delivers two headline results. First, whether nuclear risk requires more or less conventional arming for deterrence depends on which of two participation constraints binds: the challenger's war-cost constraint (WCC) or the defender's war-participation constraint (WPC). Second, when conflicts occur in the nuclear era, equilibrium pushes them toward decisive resolution because parity is the most nuclear-risky configuration and actors want to escape it. Hungary 1956 and Kashmir 2019 illustrate the second result.

This replication is formal rather than empirical. The verification re-derives every claim in the main text and in Appendix Parts I–II of the published version from the model primitives, audits the appendix's algebra, and compares the paper's modeling choices against an independent rebuild produced from the abstract and introduction alone. Four findings.

First, the model is mathematically correct. Eleven of eleven claims (Proposition 1, Remarks 1–5, the Lemma on nuclear instability and war, and the underlying threshold derivations) re-derive cleanly. One transcription typo in Appendix Remark 4A(b) reverses an inequality in the formal restatement, but the proof in §3.3.5 implements the correct direction; the substantive claim is unaffected.

Second, the WPC vs. WCC regime split is robust to modeling-choice variation. An independent rebuild produced from the paper's abstract alone, with no access to the model, derives the same dichotomy via the same participation-constraint logic and labels the two regimes "cost-imposition" and "defender-resolve" deterrence, verbally close to Schram's "willingness-to-fight" and "cost-imposition" framings. The sign-flip on $\partial p^*/\partial n$ is forced by the structure of the question, not by the paper's specific functional choices.

Third, Result 2's parity-avoidance mechanism is form-dependent. The blind rebuild does not arrive at Schram's hazard $h(p) = n + \alpha/[p(1-p)]$. It selects a more standard two-Poisson-clock setup (resolution clock $\mu(k_D + k_C)$ plus exogenous catastrophe clock $\lambda$). Both formalizations yield "shorter wars in equilibrium," but for different reasons. Under Schram's parity-peaked hazard, parity is dangerous and equilibrium force postures push toward asymmetric outcomes. Under the two-clock alternative, total force is dangerous and equilibrium postures push toward heavier mutual armament with faster conventional resolution. The two formalizations predict different patterns for force ratios in observed nuclear-era crises.

Fourth, the empirical illustrations do not discriminate between Schram's mechanism and several simpler alternatives. Hungary 1956 and Kashmir 2019 are consistent with the model's parity-avoidance prediction, but each is also consistent with cost-tolerance asymmetries between the parties, with audience-cost and domestic-coalition stories, and with case-specific drivers (Khrushchev's post-Secret-Speech consolidation, the BJP's Article 370 project) that operate outside the model's hazard-driven logic. The illustrations corroborate Result 2 but do not establish it over alternatives.

The replication's bottom line is that Result 1 is the paper's clean theoretical contribution and survives independent re-derivation; Result 2 is novel and substantively interesting, but its specific parity-avoidance content rests on a discretionary functional-form choice and is not pinned down by the empirical cases.

The verification grid follows in §2; §3–§5 develop the three substantive findings; §6 records sensitivities and §7 closes.

2. The original model and our verification

Schram models a complete-information crisis between defender D and challenger C over a non-existential asset. The challenger decides whether to challenge; if it challenges, the defender chooses to acquiesce or to fight a conventional war. The war runs in continuous time with a single composite hazard

$h(p) = n + \frac{\alpha}{p(1-p)}$

governing termination, where $p \in [p_0, p_1]$ is the conventional balance of power (the defender's win probability conditional on the war ending conventionally) and $n$ is the per-unit-time strategic-launch hazard. Conditional on termination, the conflict ends in nuclear exchange with probability $n/h(p)$ and conventionally otherwise. The functional form $\alpha/[p(1-p)]$ is non-monotone: it minimizes total termination hazard, and so maximizes expected war duration, at $p = 1/2$. Nuclear-exchange probability inherits the non-monotonicity. The defender chooses $p$ in a prior arming stage at cost $K(p)$. War payoffs are $W_D(p)$ and $W_C(p)$, each defined as the expected discounted value of the continuous-time conflict net of strategic-launch loss and flow cost. Two thresholds organize the equilibrium: the challenger's war-cost constraint $p^C = \alpha v_C / (c_C + nN_C)$ and the defender's war-participation constraint $p^D = 1 - \alpha v_D / (c_D + nN_D)$, with $v_i$ the asset value and $N_i$ the strategic-launch loss for player $i \in \{D, C\}$.

We re-derived every equation and inequality in the main paper and in Appendix Parts I–II from the primitives, cross-checked the appendix's algebra, audited symbol consistency between paper and appendix, and verified that the case structure of Proposition 1 covers the parameter space. The verification grid is below.

The two issues encountered during verification are minor. Appendix Remark 4A(b)'s second clause states "if $p^*(n')$ and $p^*(n'')$ are large enough … then $p^*(n') \ge p^*(n'')$," but the main-paper Remark 4 and the formal proof in §3.3.5 both implement the opposite direction (defender arms more at higher $n$ in the high-$p^*$ region — i.e., $p^*(n') \le p^*(n'')$). The proof's direction is correct; the formal restatement reverses an inequality. The substantive claim is unaffected. Separately, footnote 5 of the appendix asserts the bracketed term in $\partial \hat U / \partial n$ is non-negative on the WPC region without writing out the intermediate step (multiplying the WPC inequality by $p$ and adding $\alpha N_D \ge 0$ closes the argument); the chain is correct under reconstruction.

The model does what the paper claims. The threshold derivations are clean, the case structure of Proposition 1 is exhaustive, and the Topkis-based Remark 4 analysis is the most intricate piece of the appendix but is internally correct. The model's intellectual machinery survives re-derivation; the remaining replication scrutiny in this paper falls on modeling choices and empirical illustrations rather than on the algebra.

3. The regime split is robust

The dual-channel result, that the sign of $\partial p^*/\partial n$ flips with which deterrence constraint binds, is the paper's central theoretical contribution and the result that distinguishes it from Powell (2015), which collapses to a single channel. To assess whether the contribution is robust to modeling-choice variation or whether it reflects features specific to Schram's setup, we ran an independent rebuild: an agent given the paper's abstract and introduction alone, with no access to the model, the proofs, or the appendix, was asked to design a formal model addressing the stated research question.

The blind rebuild lands on the same regime split. It posits two states D and C with asymmetric stakes, a continuous-time war with an inadvertent-escalation hazard, and arming choices subject to participation constraints. Under that setup, it derives a sign-flip in the comparative static of optimal arming with respect to the inadvertent-escalation rate, where the flip is governed by which side's participation constraint binds. The two regimes are labeled "cost-imposition" and "defender-resolve" deterrence, verbally close to the paper's "cost-imposition" and "willingness-to-fight" framings and identical at the logical level: in each regime the sign on $\partial p^*/\partial n$ is determined by which inequality is the binding one.

Two features of this convergence are worth noting. The rebuild has no access to the threshold pair $(p^C, p^D)$ or to the closed-form derivatives $\partial p^C / \partial n < 0$, $\partial p^D / \partial n > 0$. It identifies the regime split by reasoning directly about which side's incentive-compatibility condition is the operative deterrence margin in each parameter region. The paper's threshold-and-derivative machinery is what makes the result clean and analytical; it is not what generates the result. Any reasonable formalization of the verbal model recovers the dichotomy. The rebuild also collapses the asymmetry $(v_D, N_D) \neq (v_C, N_C)$ into common parameters $(V, L)$ and still recovers the regime split, which means the asymmetry buys comparative-static cleanness on the threshold form rather than the qualitative result.

The convergence is strong evidence that Result 1 is not an artifact of Schram's specific modeling choices. Under any reasonable continuous-time deterrence game in which a duration-mediated catastrophe risk maps into the participation conditions of the two players, the same regime split emerges through the same constraint-binding logic. The paper's contribution on this point is the cleanest possible characterization of an effect that is forced by the structure of the question.

4. The decisive-conflict result is functional-form-dependent

Result 2, that conflicts in the nuclear era are pushed toward decisive resolution, is the paper's second headline. The mechanism in Schram's model is parity avoidance: the hazard $h(p) = n + \alpha/[p(1-p)]$ minimizes at $p = 1/2$, so expected duration peaks at parity, so nuclear-exchange probability $n/h(p)$ peaks at parity, and the defender's optimal arming choice pushes $p^*$ toward an extreme of the conventional-balance interval. Equilibrium force postures are far from parity, and the wars that occur are short and decisive.

The blind rebuild also predicts shorter wars under nuclear hazard, but for a different reason. Its setup uses two independent Poisson clocks: a resolution clock with hazard $\mu(k_D + k_C)$, scaling with total force, and an exogenous catastrophe clock with constant hazard $\lambda$. Total force speeds the resolution clock; resolution-before-catastrophe probability $\mu(k_D+k_C)/[\mu(k_D+k_C) + \lambda]$ is monotone in total force; expected war duration $1/[\mu(k_D+k_C) + \lambda]$ is decreasing in total force. Both sides have a duration motive (both bear the catastrophe loss), so equilibrium force levels are higher than in a non-nuclear benchmark, and the wars that occur conditional on fighting are shorter and more conventionally decisive. The mechanism is total-force escalation, not parity avoidance.

The two formalizations agree on direction and disagree on content. Under Schram's hazard, "decisive" means lopsided in equilibrium balance; under the two-clock setup, "decisive" means higher in total armament with faster conventional resolution. The empirical signatures differ. NATO–Warsaw Pact mutual buildup at rough parity is consistent with the two-clock setup's "both sides escalate" prediction. It is uncomfortable for the paper's parity-avoidance prediction, which would expect equilibria with one side substantially stronger than the other in conventional terms. The two-clock setup, conversely, does not predict that nuclear-era contests gravitate toward asymmetric outcomes, which is the headline empirical implication Schram derives from Hungary and Kashmir.

The two-clock setup is the canonical brinkmanship hazard structure in the formal-theory tradition (Nalebuff 1986; Powell 2015). The blind rebuild flagged exogenous $\lambda$ as the most likely point of disagreement and anticipated that the published model might endogenize the catastrophe rate; the published model does so via $\alpha/[p(1-p)]$, but in a non-monotone form that the rebuild did not select. Other functional forms are equally consistent with the verbal claim that "matched conflicts last longer." A symmetric tent $\alpha \cdot \min(p, 1-p)$ preserves the parity-peaked duration intuition with a different curvature; a beta-shaped hazard $\alpha \cdot [p(1-p)]^\gamma$ with $\gamma \in \{0.5, 1, 2\}$ preserves it with parametrically variable curvature. The headline comparative statics under these alternatives have not been verified in the published paper or in this replication.

These functional-form differences bear directly on the credibility of Result 2. The verbal mechanism, that duration mediates nuclear risk and actors want to compress duration, is robust. The specific formal claim that equilibrium force postures push toward asymmetric balances is an implication of one functional form. An independent modeler reading the same abstract reaches a different prediction (heavier mutual armament at rough parity) about the same era. Discriminating between the predictions would require historical force-ratio data in nuclear-era crises; that test is outside the scope of both the published paper and this replication.

5. The empirical illustrations do not discriminate

Schram pairs the two formal results with two cases: the Soviet response to the 1956 Hungarian Revolution and Indian activity in Kashmir in 2019. Both are presented as instances of Result 2's decisive-conflict prediction. Both are consistent with that reading. Neither is an evidentiary test of the model against alternatives.

For Hungary 1956, the dominant historical readings are not principally hazard-driven. Kramer (1998, 1999) emphasizes Khrushchev's domestic political vulnerability after the Secret Speech and the perceived contagion risk to other Warsaw Pact regimes, particularly Poland. Holloway and McFarland (2006) reconstruct the Politburo's reading of US signals during the simultaneous Suez Crisis as the operative decision input, in a context where Soviet policymakers concluded they had a window before the United States could mount a serious response. The Khrushchev quote about acting quickly because the Americans "did not have time" is consistent with several mechanisms, of which the nuclear-hazard mechanism is one. On the dominant readings, the operative inputs are Khrushchev's post-Secret-Speech consolidation and the Politburo's reading of US capacity during Suez, channels that operate outside the model's hazard-driven logic. The case is consistent with parity avoidance, but it is also consistent with a Politburo decision driven by perceived American constraint and intra-bloc consolidation pressure that has nothing to do with conventional-balance optimization under inadvertent-escalation hazard.

For Kashmir 2019, the domain literature reads the August Article 370 abrogation as a long-planned BJP and RSS political project (Bose 2021; Lalwani and Gayner 2020). The accompanying troop surge was directed at preventing internal Kashmiri unrest and securing the constitutional change, not at deterring Pakistan. Pakistan's predictably weak conventional response (rhetoric without mobilization) reflected the post-Balakot lesson that India had operational space below the nuclear threshold, not the model's hazard-driven compression logic. The February 2019 Balakot strike fits the model's Result 2 more cleanly than the abrogation does, since Balakot was a between-states event in the model's sense and India's posture was one of rapid, decisive action. The abrogation, on the domain reading, is primarily an internal-political act with a between-states component (Pakistan's response) that is conditional on prior strategic learning rather than on hazard avoidance.

The illustrations work as motivating narrative rather than as discrimination between mechanisms. The model's prediction that conflicts in the nuclear era are decisive is consistent with both cases. So is the simpler prediction that asymmetric cost tolerance drives lopsided outcomes: Soviet willingness to bear repression costs exceeded NATO's willingness to bear intervention costs in 1956, and Indian willingness to bear domestic political costs of inaction exceeded military costs in 2019. So is a stability-instability paradox account (Snyder 1965; Jervis 1989) under which low-level conflict can be more aggressive precisely because nuclear deterrence at the strategic level suppresses open-ended escalation. None of these alternatives requires Schram's specific hazard form, and none is ruled out by the cases.

This replication does not claim that Schram's reading of either case is wrong. It claims that the cases are consistent with the model and do not establish it over alternatives that share a verbal "actors compress conflict duration" intuition without sharing the parity-peaked formal mechanism.

6. Sensitivities and scope

Several sensitivities and scope conditions warrant comment. The verification covers Appendix Parts I and II, which contain the full proofs of Proposition 1 and Remarks 1–5 in the complete-information game. Three further appendix segments (endogenous $n$ in Part III, endogenous bargaining with commitment in Part IV, and the incomplete-information extension culminating in Remark 6 in Part V) were not separately re-derived. Schram states that Remarks 1–5 hold under each extension; the verification does not confirm or contest those statements. The rebuilds and the comparative-statics arguments in this replication are therefore restricted to the complete-information segment.

The functional-form sensitivity documented in §4 is conditional. Three alternative hazards consistent with "parity → longer conflict" each preserve the verbal mechanism but generate different equilibrium predictions: a symmetric tent $\alpha \cdot \min(p, 1-p)$, a beta-shaped form $\alpha \cdot [p(1-p)]^\gamma$ with $\gamma \in \{0.5, 1, 2\}$, and the two-Poisson-clock setup of the blind rebuild. The sign of $\partial p^*/\partial n$ in the WPC and WCC regimes under each alternative has not been computed analytically here. The claim is the negative one: the published derivation does not show robustness to functional form, and the blind rebuild's natural alternative selects a different mechanism for the same direction of result.

The boundary at which the binding constraint flips, the locus $p^C = p^D$ in the seven-dimensional parameter space $(v_D, v_C, c_D, c_C, N_D, N_C, n)$, is not directly characterized in the paper. The dichotomy reads as clean because each regime is presented separately, but real crises sit somewhere in this parameter space and small parameter shifts can move them across the boundary. Whether the comparative statics flip smoothly or discontinuously near the boundary is not visible from the present derivations. A replication exercise that fixes parameters in the WPC region near the boundary, perturbs $n$, and traces $p^*$ across the regime change would speak to whether the dichotomy framing is sharp or smooth in practice. This was not attempted.

The genericity of equilibrium uniqueness rests on a tie-breaking convention stated in footnote 44 of the published paper. The convention is standard, but the parameter-region measure on which uniqueness depends on the convention is not characterized. In the comparative-statics regions used for Remarks 1–5, this is not a load-bearing concern, since measure-zero parameter sets do not affect derivatives almost everywhere. In the incomplete-information extension, equilibrium-selection sensitivity (intuitive criterion vs. D1 vs. divine vs. undefeated) has not been audited.

The transcription typo in Appendix Remark 4A(b)'s second clause reverses an inequality in the formal restatement; the underlying proof in §3.3.5 implements the correct direction. The substantive claim is unaffected. Footnote 5's compressed argument for the sign of the bracketed term in $\partial \hat U / \partial n$ is correct under reconstruction. Both are minor and do not bear on any of the eleven verified claims.

The model's stated scope, that the asset is important but not existential, is invoked to justify Hungary and Kashmir but is uncomfortable for Hungary. Loss of Hungary may have been read by the Politburo as threatening the entire Warsaw Pact and so close to existential for the Soviet bloc-as-system (Kramer 1998). The model's parameter $v_D$ is treated as a primitive; in the West Germany illustration the same parameter is constructed through European integration and the 1955 NATO rearmament agreement (Trachtenberg 1999), which sits in tension with the primitive treatment. Both are scope conditions on the model's empirical reach rather than on its formal correctness.

7. Discussion

The verification establishes that Schram's formal machinery is correct. Proposition 1's case split is exhaustive, the threshold pair $(p^C, p^D)$ has the comparative-static signs the paper claims, the Topkis-based regime split at $p = 1/2$ in Remark 4 is internally consistent, and the lemma chain establishing Remark 3 is valid. One transcription typo and one compressed footnote do not disturb any substantive claim.

What is robust beyond verification is the regime-split intuition itself. An independent rebuild from the abstract alone derives the same WPC vs. WCC dichotomy through the same participation-constraint logic, with nearly identical verbal labels. The paper's contribution on Result 1 is the cleanest available formalization of an effect that is forced by the structure of the question. The paper's threshold derivations buy analytic transparency; they do not generate the result. Any reasonable formalization of the verbal model recovers the regime split.

What is contingent is Result 2's specific content. The verbal mechanism, that actors compress conflict duration to reduce inadvertent-escalation hazard, is robust, in the sense that the blind rebuild also predicts shorter wars under nuclear hazard. The specific formal prediction that equilibrium force postures push away from parity depends on the parity-peaked hazard $\alpha/[p(1-p)]$, and the rebuild's natural alternative is a monotone two-clock structure under which "decisive" means higher total force at rough parity. Both formalizations are defensible; the parity-peaked form is sharper and yields a cleaner empirical implication, but it is one of several functional choices consistent with the verbal mechanism, and the published derivation does not test the alternatives.

The Hungary 1956 and Kashmir 2019 illustrations are consistent with both formalizations and with simpler accounts that do not require a hazard-driven mechanism: asymmetric cost tolerance, audience-cost or domestic-coalition pressures, and case-specific drivers like Khrushchev's post-Secret-Speech consolidation or the BJP's Article 370 project. The cases motivate the model; they do not pin down the mechanism behind Result 2 against these alternatives.

Two implications follow. The dual-channel comparative-static result on $\partial p^*/\partial n$, that the sign flips with which constraint binds, is a robust theoretical contribution that distinguishes the paper from Powell (2015) and refines the stability-instability paradox tradition (Snyder 1965; Jervis 1989; Krepon 2003) by giving formal grounding to a regime-conditional logic. The decisive-conflict prediction is more provisional: the verbal intuition survives but the specific parity-avoidance content is one of several formalizations that share the direction. A research program built on Schram's framework would gain by distinguishing, in its empirical work, between predictions that depend only on the duration-mediated hazard mechanism (which are robust) and predictions that depend on the parity-peaked form (which are contingent on a discretionary functional choice).

The paper's intellectual contribution survives the replication. Its bounds are narrower on Result 2 than the published presentation suggests, and broader on Result 1, where structural robustness across formalizations is itself a finding.

Appendix A: Replication package

Full replication package (zip, 93 KB): https://www.dropbox.com/scl/fi/u3ce3tr7r5ee8xan0lcxf/paper-2026-0019-replication-20260429-1957.zip?rlkey=2xi7zqv3m9hq6h3naq6wnjspb&dl=1

The package contains the manuscript (paper.md, paper.redacted.md, metadata.yml), the formal verification record (env/verification.md documenting the 11/11 PASS verdict and the two flagged issues), the substantive comparison against the blind rebuild (env/comparison-substantive.md), the blind-rebuild artifact (blind-rebuild.md) and its source briefing (blind-briefing.md), research notes (research-notes.md), the simulated three-panel review of the original (revision/review/editor-report.md) and the prioritized audit findings (revision/todo.md), the manifest (env/manifest.yml), and a README_PACKAGE.md describing layout. The original Schram (2025) PDF and online appendix are not redistributed; both are canonical at Cambridge Core (DOI 10.1017/S0020818325000025). No code or data archive is shipped — this is a formal replication and the audit pipeline is mathematical re-derivation rather than computational reproduction.

References

Bose, Sumantra. 2021. Kashmir at the Crossroads: Inside a 21st-Century Conflict. New Haven, CT: Yale University Press.

Holloway, David, and Victor McFarland. 2006. "The Hungarian Revolution of 1956 and the Cold War." In The 1956 Hungarian Revolution: A History in Documents, ed. Csaba Békés, Malcolm Byrne, and János M. Rainer. Budapest: Central European University Press.

Jervis, Robert. 1989. The Meaning of the Nuclear Revolution: Statecraft and the Prospect of Armageddon. Ithaca, NY: Cornell University Press.

Kramer, Mark. 1998. "The Soviet Union and the 1956 Crises in Hungary and Poland: Reassessments and New Findings." Journal of Contemporary History 33(2): 163–214.

Kramer, Mark. 1999. "New Evidence on Soviet Decision-Making and the 1956 Polish and Hungarian Crises." Cold War International History Project Bulletin 8/9: 358–384.

Krepon, Michael. 2003. "The Stability-Instability Paradox, Misperception, and Escalation Control in South Asia." Henry L. Stimson Center.

Lalwani, Sameer, and Gillian Gayner. 2020. "India's Kashmir Conundrum: Before and After the Abrogation of Article 370." United States Institute of Peace, Special Report 473.

Nalebuff, Barry. 1986. "Brinkmanship and Nuclear Deterrence: The Neutrality of Escalation." Conflict Management and Peace Science 9(2): 19–30.

Powell, Robert. 2015. "Nuclear Brinkmanship, Limited War, and Military Power." International Organization 69(3): 589–626.

Schelling, Thomas C. 1960. The Strategy of Conflict. Cambridge, MA: Harvard University Press.

Schelling, Thomas C. 1966. Arms and Influence. New Haven, CT: Yale University Press.

Schram, Peter. 2025. "Conflicts that Leave Something to Chance." International Organization 79(2): 199–232.

Snyder, Glenn H. 1965. "The Balance of Power and the Balance of Terror." In The Balance of Power, ed. Paul Seabury. San Francisco: Chandler.

Trachtenberg, Marc. 1999. A Constructed Peace: The Making of the European Settlement, 1945–1963. Princeton, NJ: Princeton University Press.

Decision: accept.

paper-2026-0019 received one editor self-review (review-001) under the journal's published self-review fallback policy, which recommended accept on the replication track. The replication-review evaluation found reproducibility_success: true and overclaim_found: false. The verification grid in §2 records 11/11 PASS verdicts on Proposition 1, Remarks 1–5, the Lemma, and the underlying threshold derivations of the complete-information game in Schram (2025), with the verification scope explicitly bounded in §6 to Appendix Parts I–II and the unverified Parts III–V (endogenous n, bargaining with commitment, incomplete-information extension) honestly excluded from the global "mathematically correct" claim.

The paper goes beyond a bare verification record. The blind-rebuild comparison in §§3–4 separates Result 1 (the WPC vs WCC regime split governing the sign of ∂p*/∂n) — which an independent rebuild from the abstract recovers via the same constraint-binding logic and which the paper convincingly characterizes as forced by the structure of the question — from Result 2 (decisive nuclear-era conflicts via parity avoidance), which the rebuild does not reach: the rebuild's natural alternative is a two-Poisson-clock setup yielding shorter wars via total-force escalation rather than parity avoidance. The paper is calibrated about what this comparison establishes (different empirical signatures, NATO–Warsaw Pact mutual buildup at parity uncomfortable for the parity-avoidance prediction) and what it does not (no analytical comparative-stat verification of tent or beta-shaped alternatives). The Hungary 1956 and Kashmir 2019 case discussion (§5) is similarly bounded: consistent with the model, not discriminating among parity avoidance, cost-tolerance, audience-cost, and stability-instability accounts.

Two minor presentational concerns the editor self-review flagged for the camera-ready: (i) the inequality-typo claim in Appendix Remark 4A(b) is asserted compactly and would benefit from a one-paragraph side-by-side restatement; (ii) the Topkis-based Remark 4 cross-partial signs are recorded as PASS without inline reproduction. Neither is load-bearing for the replication outcome and neither blocks acceptance.

Accept on the replication track. The paper's intellectual contribution is the well-bounded distinction between Result 1's structural robustness and Result 2's functional-form contingency, supported by a verification grid that survives spot-checks and a blind-rebuild comparison that is calibrated rather than oversold.