Predicting Interstate Conflict 72 Days in Advance: A Topological Approach to Weaponized Interdependence

Topological Conflict Prediction Davis Framework Predicting Interstate Conflict 72 Days in Advance: A Topological Approach to Weaponized Interdependence Bee Rosa Davis bee da[email protected]wn.edu December 2025 Working Paper — Submitted for Review Abstract We present a framework that predicts interstate conflict with F1 = 0.73 and mean lead time of 72 days—outperforming existing approaches by 12 points on F1 and 60 days on lead time. The Russia-Ukraine dyad triggered a Level 4 (Singularity) alert on December 14, 2021, 72 days before the February 2022 invasion. Our approach models bilateral relationships as points on a configuration manifold Mgeo, deriving a scalar Helicity measure H=V×A (economic flux ×diplomatic alignment) and a mass gap ∆ that quantifies structural fragility. The central theorem—the Integration-Alignment Divergence—states that conflict becomes structurally inevitable when diplomatic alignment inverts (A<0) while economic flux persists (ZV>1), operationalizing “weaponized interdependence” (Farrell & Newman, 2019). Validated on 47 militarized interstate disputes (1990–2022; see Supplementary Table S1), the model achieves AUC = 0.84 (95% CI: 0.79–0.89). The mass gap provides earlier structural warning: for Russia-Ukraine, ∆ <0 signaled stress in 2013—one year before Crimea—while Z-score-only detection showed “Stable.” Contents 1 Introduction 3 1.1 TheCoreInsight .................................... 3 1.2 Contributions...................................... 3 2 Literature Review and Theoretical Positioning 3 2.1 The Commercial Peace Debate . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.2 Weaponized Interdependence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.3 ConflictForecasting .................................. 4 2.4 Phase Transitions and Tipping Points . . . . . . . . . . . . . . . . . . . . . . . . 4 3 Theory: The Geopolitical Manifold 5 3.1 ManifoldStructure................................... 5 4 Davis Framework Foundations 5 4.1 TheDavisLaw ..................................... 5 4.2 The Navier-Stokes Connection . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 4.3 The Mass Gap and Singularity Prevention . . . . . . . . . . . . . . . . . . . . . . 6 4.4 The Geometric Trichotomy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 5 The Helicity Framework 7 5.1 TheMasterEquation.................................. 7 5.2 TheFluxTerm..................................... 7 5.3 TheAlignmentTerm.................................. 7 Page 1 Topological Conflict Prediction Davis Framework 5.4 The Integration-Alignment Divergence . . . . . . . . . . . . . . . . . . . . . . . . 8 5.5 Conservation and Stability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 6 Detection Logic: Alert Levels 8 6.1 Z-ScoreNormalization................................. 8 6.2 Practical Mass Gap Computation . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 6.3 AlertLevelDefinitions................................. 8 7 Data and Methods 9 7.1 Sample.......................................... 9 7.2 DataSources ...................................... 9 7.3 MissingData ...................................... 9 7.4 OutcomeDefinition................................... 10 7.5 EvaluationMetrics................................... 10 8 Results 10 8.1 Phase Space Visualization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 8.2 PrimaryValidation................................... 10 8.3 ConfusionMatrix.................................... 11 8.4 ROCCurve....................................... 11 8.5 LeadTimeDistribution ................................ 12 8.6 Mass Gap Enhancement: Comparative Metrics . . . . . . . . . . . . . . . . . . . 12 8.7 BaselineComparisons ................................. 13 8.8 Case Study: Russia-Ukraine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 8.9 Case Study: US-Japan 1941 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 9 Robustness 15 9.1 ParameterSensitivity ................................. 15 9.2 TemporalRobustness ................................. 15 9.3 DataSourceSensitivity ................................ 15 9.4 Out-of-SampleTesting................................. 15 10 Discussion 15 10.1 Theoretical Implications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 10.2PolicyImplications................................... 15 10.3Limitations ....................................... 16 11 Conclusion 16 Appendix A: Technical Details 17 Appendix B: Supplementary Table S1 19 References 20 Page 2 Topological Conflict Prediction Davis Framework 1 Introduction The prediction of interstate conflict remains one of the grand challenges of political science. Despite decades of research on the correlates of war, quantitative forecasting has proven elusive: the best-performing models achieve AUC scores of 0.70–0.75 (Hegre et al., 2013; Cederman & Weidmann, 2017), and most rely on proximal indicators (military mobilization, diplomatic crises) that provide minimal lead time for policy intervention. We propose a fundamentally different approach grounded in differential geometry and topological dynamics. Rather than modeling conflict as an event to be predicted, we model the structural conditions that make conflict possible—and identify the specific configuration in which it becomes effectively inevitable. 1.1 The Core Insight The key insight comes from an analogy to fluid dynamics. In the Navier-Stokes equations, helicity is a topological invariant that measures the “knottedness” of flow: H=ZΩ v ·(∇×v)d3x(1) When helicity is conserved, singularities (blow-up) cannot form in finite time. When helicity depletes while kinetic energy persists, catastrophic collapse becomes possible. We apply this principle to international relations: bilateral relationships have a “helicity” measuring the alignment between economic flows and diplomatic trust. When this alignment inverts—when states become enemies while remaining economically integrated—the system enters a trap from which war is the only exit. 1.2 Contributions This paper makes four contributions: 1. Theoretical: We provide a mathematical operationalization of “weaponized interdependence” (Farrell & Newman, 2019) that resolves the longstanding debate between commercial peace and commercial conflict theories. 2. Methodological: We introduce the Helicity metric H=V×A and a graduated 5-level alert system with explicit detection thresholds. 3. Empirical: We validate the framework on 47 MIDs (1990–2022), demonstrating superior performance to existing forecasting approaches. 4. Applied: We provide actionable early warning indicators with mean lead times exceeding 8 weeks. 2 Literature Review and Theoretical Positioning Our framework engages with three major literatures: the commercial peace debate, weaponized interdependence, and conflict forecasting. 2.1 The Commercial Peace Debate The relationship between economic interdependence and conflict has been contested for over a century. Liberal theory, formalized by Oneal & Russett (1999), holds that trade creates opportunity costs for war: states with strong commercial ties have too much to lose from Page 3 Topological Conflict Prediction Davis Framework conflict. Empirically, the “Kantian peace” finding—that democracy, trade, and international organizations reduce conflict—has been replicated across specifications (Russett & Oneal, 2001). However, Barbieri (1996) challenged this consensus, showing that under certain conditions trade can increase conflict. Asymmetric dependencies, she argued, create leverage and resentment. Gartzke (2007) refined this by distinguishing trade from financial integration: the “capitalist peace” operates through capital mobility, not goods exchange. States with integrated capital markets cannot afford the currency collapses and capital flight that accompany war. Our framework resolves this debate by identifying the configuration that determines whether interdependence deters or enables conflict. The key is not the level of trade, but the alignment between economic flows and diplomatic trust. High trade with high trust is stabilizing (the liberal prediction). High trade with low trust is destabilizing (the Barbieri prediction). The mathematical structure makes explicit when each regime applies. 2.2 Weaponized Interdependence Farrell & Newman (2019) introduced the concept of “weaponized interdependence” to describe how network centrality can be converted into coercive power. States at the center of global networks (financial, informational, logistical) can impose costs on adversaries by threatening exclusion. Drezner (2021) extended this analysis, documenting how the US has weaponized SWIFT access, semiconductor supply chains, and cloud computing infrastructure. Our helicity framework provides a dyadic operationalization of weaponized interdependence. The “trap” (Level 3: Divergence) is precisely the condition Farrell and Newman describe: high flux with negative alignment. States are locked into economic relationships they cannot exit without catastrophic costs, but those relationships have become vectors of coercion rather than cooperation. The “snap” (war) occurs when the geometric inertia (contracts, supply chains, sunk costs) can no longer contain the topological rupture (diplomatic collapse). 2.3 Conflict Forecasting Quantitative conflict prediction has advanced significantly since Ward et al. (2010) critiqued the field’s reliance on p-values over predictive accuracy. The ViEWS system (Hegre et al., 2013) uses ensemble machine learning on structural and event data to forecast armed conflict at the country-month level. ICEWS and GDELT provide real-time event coding that enables short-term prediction. Our approach differs in three ways: 1. Structural vs. Event-Based: We predict from slow-moving structural variables (trade, treaties, voting patterns) rather than news events. This sacrifices short-term accuracy for longer lead times. 2. Dyadic vs. Monadic: We predict bilateral conflict between specific state pairs, not country-level instability. 3. Threshold-Based vs. Probabilistic: Our alert levels provide interpretable decision thresholds rather than continuous probabilities. 2.4 Phase Transitions and Tipping Points Finally, our framework draws on the literature on critical transitions in complex systems. Scheffer et al. (2009) identified generic early-warning signals (increased variance, autocorrelation, skewness) that precede tipping points across ecological, climate, and social systems. Lenton et al. (2008) applied this framework to climate subsystems. Page 4 Topological Conflict Prediction Davis Framework The Integration-Alignment Divergence is a specific type of tipping point: the system enters a metastable state (Level 3) from which only two exits are possible—diplomatic restoration of alignment, or violent collapse to zero flux. The helicity gradient provides the early-warning signal. 3 Theory: The Geopolitical Manifold 3.1 Manifold Structure We model the global system as a continuous configuration manifold Mgeo with nodes representing nation-states and edges representing bilateral relationships. Definition 3.1 (The Geopolitical Manifold).A configuration space Mgeo equipped with: 1. A metric tensor gij encoding interaction friction (trust/cost) 2. A flux field  Vrepresenting directed flows (trade, energy, capital) 3. A constraint field  Crepresenting topological bounds (treaties, alliances) Definition 3.2 (Metric Tensor).The metric tensor gij is defined by diplomatic trust. Geodesic distance represents the friction of bilateral interaction. High trust implies short distance; low trust implies long distance. Assumption 3.3 (Symmetry).The topological bond is symmetric: HAB =HBA. Helicity is a property of the relationship, not the individual actor. This symmetry assumption is empirically testable and approximately holds for our data: the correlation between HAB and HBA computed from directional trade flows is r= 0.94 (see Appendix A.4). 4 Davis Framework Foundations Before presenting the helicity framework, we situate it within the broader Davis Framework for geometric inference (Davis, 2025)—a mathematical structure connecting seemingly disparate problems across fluid dynamics, field theory, and complex systems.1 4.1 The Davis Law The foundational equation governing inference from incomplete information is: C=τ K(2) where Cis inference capacity (the degree to which unobserved states can be determined), τis topological budget (the holonomy constraint on valid paths), and Kis curvature (the geometric complexity of the configuration space). This law governs when unique solutions exist to completion problems—from sudoku puzzles to world models to geopolitical forecasting (Davis, 2025). Applied to conflict prediction: capacity Crepresents the predictability of conflict onset; topology τrepresents alliance/treaty constraints; curvature Krepresents the friction of diplomatic adjustment. High curvature (rigid alliances, low trust) reduces predictive capacity unless topological constraints are correspondingly tight. 1The Davis Framework is published at Zenodo with DOI 10.5281/zenodo.17771796. The mathematical derivations—including the Davis Law C=τ/K, the mass gap formulation, and the Navier-Stokes connection— can be independently verified from the posted manuscript. Page 5 Topological Conflict Prediction Davis Framework 4.2 The Navier-Stokes Connection The deepest mathematical connection is to fluid dynamics citepdavis2025field. In the incompressible Navier-Stokes equations: ∂u ∂t + (u ·∇)u =−∇p+ν∆u, ∇·u = 0 (3) the central question is whether singularities (blow-up) can form. The Beale-Kato-Majda criterion (Beale, Kato, & Majda, 1984) states that blow-up occurs if and only if vorticity becomes unbounded: RT∗ 0∥ω∥L∞dt =∞. In the Davis Framework, we interpret fluid dynamics as geodesic flow on a configuration manifold Mfluid: Navier-Stokes Geopolitics Velocity field u Economic/diplomatic flows  V Vorticity ω=∇×u Curvature of trust dynamics Helicity H=Ru ·ω dV Alignment-flux coherence H=V×A Viscosity ν(damping) Diplomatic friction (stabilization) Blow-up (singularity) War (catastrophic discontinuity) The regularity principle: bounded helicity prevents singularity. In fluids, conserved helicity constrains vortex stretching. In geopolitics, positive helicity (aligned flows and trust) constrains escalation. 4.3 The Mass Gap and Singularity Prevention The key insight from the Davis Framework is the mass gap ∆—the geometric cost of extreme behavior. In Yang-Mills theory, ∆ >0 implies confinement. In Navier-Stokes, ∆ <∞implies regularity. In geopolitics, ∆ represents the cost of war. Definition 4.1 (Geopolitical Mass Gap).For a dyad (A, B): ∆AB =Z|∇A|2−H2 AB VAB dt (4) This measures the competition between alignment gradients (diplomatic effort) and helicity-flux mismatch (structural instability). When ∆ >0, gradients dominate—the system can absorb shocks through diplomatic adjustment. When ∆ <0, the mismatch dominates—the trap has formed. Proposition 4.2 (Singularity Criterion).Conflict becomes structurally inevitable when ∆AB < 0persists for duration τc. The critical duration τcscales inversely with flux: τc∼1 √VAB (5) High-flux relationships snap faster once the trap forms. This explains why Russia-Ukraine (high energy flux) progressed from L4 to conflict in 72 days, while US-China (lower direct flux) has remained at L3 despite similar alignment collapse. Page 6 Topological Conflict Prediction Davis Framework 4.4 The Geometric Trichotomy The Davis Framework classifies all systems by the parameter: Γ = m·τbudget Kmax ·log |S|(6) where mis constraint count, Kmax is maximum curvature, and |S|is solution space size.  Γ>1: DETERMINED — unique equilibrium, stable, predictable  Γ≈1: CRITICAL — phase transition, early-warning signals  Γ<1: UNDERDETERMINED — multiple equilibria, chaotic, unpredictable The international system operates in the critical regime: enough constraints (treaties, norms, economic interdependence) to make conflict non-random, but not enough to make it impossible. This is precisely why prediction is difficult but not hopeless—and why topological measures like helicity provide discriminatory power. 5 The Helicity Framework 5.1 The Master Equation Building on the Davis Framework foundations, we define scalar helicity as the product of flux magnitude and alignment: HAB(t)=VAB(t)×AAB(t) (7) 5.2 The Flux Term The flux term VAB measures economic integration. Range: [0,∞). VAB(t) = TAB(t) ¯ Tglobal +αEAB(t) ¯ Ecritical (8) where:  TAB = bilateral trade volume (constant 2020 USD), normalized to median G20 bilateral flow  EAB = energy dependency (share of primary energy consumption from partner)  α= 4.0 = strategic multiplier, derived from GDP elasticity estimates (Hamilton, 2003) 5.3 The Alignment Term The alignment term AAB measures diplomatic orientation. Range: [−1,1]. AAB(t) = tanh k·Svote +Rtreaty 2−σ(Xsanction) (9) where:  Svote = UN General Assembly voting similarity (Voeten ideal point distance, rescaled to [0,1])  Rtreaty = treaty/alliance index from ATOP (Leeds et al., 2002)  σ(X)=1−e−βX = sanction penalty, with Xfrom GSDB severity scale  β= 1.0, k= 2.0 (see Appendix A.2 for calibration) The tanh transformation ensures bounded output and smooth regime transitions. The steepness parameter k= 2.0 ensures 95% saturation at boundary conditions. Page 7 Topological Conflict Prediction Davis Framework 5.4 The Integration-Alignment Divergence Theorem 5.1 (Integration-Alignment Divergence).Let (A, B)be a bilateral dyad with helicity HAB(t). The system enters a conflict trap when: 1. The constraint field inverts: AAB <0(diplomatic hostility) 2. The flux magnitude persists: ZV>+0.5(above-average integration) 3. The helicity is anomalously negative: ZH<−2.0(two standard deviations below baseline) Interpretation: Trust has collapsed while economic flows persist. The system cannot equilibrate because geometric inertia (contracts, infrastructure, supply chains) prevents the topological break from propagating. War is the catastrophic discontinuity that forces flux to zero. 5.5 Conservation and Stability Assumption 5.2 (Helicity Conservation).In stable regimes, d dt H≈0. Perturbations in Vare matched by adjustments in A(and vice versa) through diplomatic and economic feedback loops. This assumption is empirically grounded: for dyads that never experienced MIDs in our sample, the mean absolute quarterly change in His 0.08, compared to 0.31 for dyads that eventually experienced conflict (Welch’s t= 4.7, p < 0.001). The singularity regime violates conservation: the restoring force (diplomacy) fails to dampen the inertial force (flux). 6 Detection Logic: Alert Levels 6.1 Z-Score Normalization For each dyad, we compute rolling Z-scores against a 60-month historical baseline: ZH=H(t)−µH σH (10) ZV=V(t)−µV σV (11) The 60-month window balances responsiveness to regime changes against stability. Sensitivity to this choice is examined in Section 7.2. 6.2 Practical Mass Gap Computation The mass gap ∆ from Section 4.3 is computed as a rolling sum over window W= 12 months: ∆AB(t) = t X τ=t−W|A(τ)−A(τ−1)|2−H(τ)2 V(τ) + ϵ(12) where ϵ= 0.01 prevents division by zero. The first term captures diplomatic effort (alignment gradients); the second captures structural instability (helicity-flux mismatch). When diplomatic adjustment cannot keep pace with structural stress, ∆ <0. 6.3 Alert Level Definitions The detection algorithm combines Z-score thresholds with mass gap criteria: Page 8 Topological Conflict Prediction Davis Framework Level Name Mass Gap Z-Score Criteria Interpretation 0 Stable ∆ ≥0ZH≥0 System healthy. 1 Stress ∆ <0 OR ZH<−1.0 Trap forming. Friction rising. 2 Decoupling ∆ <−1.0ZH<−1.5, ZV<0 Managed exit via flux reduction. 3 Divergence ∆ <−1.5ZH<−2.0, ZV>+0.5The Trap. 4 Singularity ∆ <−2.0A<0, ZV>+1.0Conflict imminent. Table 1: Alert level definitions. Detection uses BOTH mass gap ∆ and Z-score thresholds. Level 1 triggers on either criterion; higher levels require both. The key insight: ∆ <0 can trigger Level 1 (Stress) before Z-scores cross threshold, providing earlier structural warning. The Z-score criteria capture statistical anomaly; the mass gap captures geometric instability. Together they provide both sensitivity and specificity. Escalation Logic: If ∆ <−1.0 and Z-scores indicate a lower alert level, the system escalates by one level (e.g., Stress →Decoupling). If ∆ <−2.0 with A<0 and ZV>0, the system triggers Singularity directly regardless of ZH—this captures cases where the trap has formed but helicity hasn’t yet crossed threshold. Note on Level 4 criteria: The original Z-score-only classifier required ZH<−2.0. The mass gap enhancement relaxes this: if ∆ <−2.0 (trap confirmed geometrically), the ZHthreshold is not required. This is how the 2013 Russia-Ukraine case triggers Stress rather than Stable. 7 Data and Methods 7.1 Sample We construct a panel dataset of 156 directed dyads among 42 states (all G20 members plus 22 additional states with high conflict risk) observed monthly from January 1990 to December 2022 (N= 61,776 dyad-months). For historical validation, we separately analyze the US-Japan dyad from January 1930 to December 1945 using archival sources. 7.2 Data Sources Variable Source Processing Bilateral trade (TAB) UN Comtrade Constant 2020 USD (PWT deflator) Energy dependency (EAB) IEA, BP Statistical Review Share of primary energy Voting similarity (Svote) Voeten UN Data Ideal point distance, rescaled Treaty status (Rtreaty) ATOP v5.0 Binary →categorical index Sanctions (X) GSDB Severity score (0–10) Conflict events UCDP/PRIO, MID v5.0 Fatalities ≥25 Table 2: Data sources and processing. 7.3 Missing Data Trade data coverage is 94% for the modern sample. Missing values are interpolated linearly for gaps ≤6 months; longer gaps are coded as zero trade (conservative assumption). Energy dependency data is annual; we assign the annual value to all months within the year. Page 9 Topological Conflict Prediction Davis Framework 2. Reduce flux: Managed decoupling to reduce V. Painful economically, but exits the trap via Level 2 (Decoupling) rather than Level 4 (Singularity). The worst policy is to maintain high flux while allowing alignment to deteriorate—yet this describes much of Western policy toward Russia from 2014–2021 (maintaining gas purchases while imposing limited sanctions). For corporations, the framework enables supply chain risk assessment. Dyads in Level 2+ should be flagged for diversification. Insurance and reinsurance pricing can incorporate helicity scores. 10.3 Limitations 1. Integration wars only: The framework predicts conflicts arising from weaponized interdependence. It does not apply to wars between already-decoupled states (low flux) or proxy conflicts (indirect engagement). 2. Structural, not proximal: We predict the conditions for conflict, not the trigger. Lead times are weeks to months, not days. 3. Major power focus: Validation is concentrated on G20 and high-risk states. Generalization to minor power dyads requires further testing. 11 Conclusion We have presented a mathematical framework for conflict prediction based on the topological properties of bilateral economic-diplomatic relationships. The Integration-Alignment Divergence theorem identifies the structural configuration in which war becomes effectively inevitable: when diplomatic trust collapses while economic integration persists. Validated on 47 militarized interstate disputes, the helicity model achieves F1 = 0.73 with mean lead time of 58 days—outperforming realist, liberal, and event-based baselines. The Russia-Ukraine case demonstrates operational utility: Level 4 was triggered 72 days before the February 2022 invasion. The policy implication is stark: integration without alignment is dangerous. High-flux relationships with deteriorating trust must be either diplomatically repaired or carefully decoupled. The alternative is the trap—and the trap ends in war. Ethics Statement. This research analyzes publicly available aggregate data on state-level behavior. No individual human subjects were involved, and the work was exempt from IRB review per Brown University policy. We acknowledge potential dual-use concerns. Conflict prediction systems could theoretically be misused for military planning, preemptive strikes, or market manipulation. We advocate for use in diplomatic early warning and humanitarian preparedness, not military targeting. The 72-day mean lead time is designed to enable diplomatic intervention, not operational planning. We also note the risk of self-fulfilling prophecy: public prediction of conflict could accelerate escalation. For this reason, we recommend that operational deployment include human-in-theloop review and avoid public release of specific dyad alerts without diplomatic consultation. Data and Code Availability: Replication code and processed data available at https: //github.com/nurdymuny/helicity. Raw data sources are public as cited. The 47 conflict events are listed in Supplementary Table S1. Page 16 Topological Conflict Prediction Davis Framework Appendix A: Technical Details A.1 Alignment Bound Proof Lemma 11.1. The alignment term AAB ∈[−1,1] for all valid inputs. Proof. Let x=k·S+R 2−σ(X). Since S, R ∈[0,1], we have S+R 2∈[0,1]. Since σ(X) = 1 −e−βX with β, X ≥0, we have σ(X)∈[0,1). Therefore S+R 2−σ(X)∈(−1,1], and x∈(−k,k]. Since tanh : R→(−1,1), we have A= tanh(x)∈(−1,1) ⊂[−1,1]. A.2 Parameter Calibration Strategic weight α= 4.0:Derived from Hamilton (2003), who estimate that oil price shocks have GDP elasticity 4×larger than equivalent trade shocks. Sanction decay β= 1.0:Calibrated to the GSDB severity scale such that σ(X)=0.5 when X= 0.69 (median severity). Steepness k= 2.0:Chosen so that tanh(k·1) = 0.96, ensuring 95% saturation at boundary conditions. A.3 Rolling Window Justification The 60-month window corresponds to typical diplomatic memory: sufficient to capture regime changes (new administrations, treaties) while avoiding noise from quarterly fluctuations. Empirically, 60 months minimizes out-of-sample prediction error in cross-validation. A.4 Symmetry Verification Computing directional helicity from asymmetric trade flows (TA→Bvs TB→A), we find Corr(HAB, HBA) = 0.94 across all dyad-months. The symmetry assumption is empirically justified. A.5 Baseline Model Specifications  Realist (military balance): Predicts conflict when CINC ratio >2 : 1 between dyad members (Correlates of War National Military Capabilities v6.0). Alert when the weaker state’s CINC <0.33×stronger state’s CINC.  Liberal (trade/GDP): Predicts peace when bilateral trade/GDP >1% for both states (inverse prediction). Conflict alert when trade/GDP <0.5% for either state. Trade data from UN Comtrade; GDP from World Bank WDI.  GDELT Goldstein: 30-day moving average of Goldstein tone scores for dyad-specific events. Alert when ZGoldstein <−2.0 (two standard deviations below 180-day rolling mean).  Random baseline: Uniform random assignment with base rate matching observed conflict frequency (47/61,776 = 0.076% per dyad-month). A.6 Historical Data Processing (US-Japan 1930–1945) For the US-Japan case, we construct proxy variables from archival sources:  Trade (T): League of Nations International Trade Statistics (1930–1939); US Department of Commerce Foreign Commerce and Navigation (1940–1941). Converted to constant 1940 USD using BLS CPI deflator. Page 17 Topological Conflict Prediction Davis Framework  Energy (E): US oil export records to Japan from Hamilton (2003) and US Tariff Commission reports. Expressed as share of Japanese petroleum consumption from Japanese Ministry of Commerce and Industry records.  Alignment (A): No UN voting existed. We proxy using: (1) treaty status from COW Formal Alliances v4.1 (defensive alliance = 1, neutrality pact = 0.5, no treaty = 0, hostile =−0.5); (2) diplomatic representation level (ambassador = 0.2, charg´e = 0.1, recall = −0.3); (3) public statements coded from Foreign Relations of the United States (FRUS) volumes.  Sanctions (X): Binary coding from State Department records: moral embargo (1938) = 0.3; scrap metal embargo (1940) = 0.6; oil embargo (1941) = 1.0. The historical case uses annual data interpolated to monthly; modern validation uses true monthly observations. A.7 Out-of-Sample Validation Details Training set (1990–2014): N= 31 conflict events across 156 dyads. Test set (2015–2022): N= 16 conflict events. Metric Training (1990–2014) Test (2015–2022) F1 Score 0.75 0.69 AUC-ROC 0.86 0.79 Mean Lead Time 74 days 68 days Russia-Ukraine L4 Date — 2021-12-22 Table 8: Out-of-sample validation. Model trained on 1990–2014 data only. The out-of-sample F1 (0.69) is lower than full-sample (0.73), as expected. Russia-Ukraine Level 4 triggers 8 days later (Dec 22 vs Dec 14) in the out-of-sample model due to slightly different baseline estimates. Cross-validation: 5-fold temporal CV (non-overlapping 6-year windows) yields mean F1 = 0.71±0.04 (std across folds). This confirms the single train/test split result is representative. Page 18 Topological Conflict Prediction Davis Framework Appendix B: Supplementary Table S1 — Conflict Events Table S1 lists all 47 militarized interstate disputes (MIDs) in the validation sample. # Dyad Region Conflict Date L4 Alert Lead (d) Max Lv 1 Russia–Ukraine Europe 2022-02-24 2021-12-14 72 4 2 Armenia–Azerbaijan Caucasus 2020-09-27 2020-08-15 43 4 3 India–Pakistan S. Asia 2019-02-26 2019-01-08 49 4 4 Saudi Arabia–Yemen M. East 2015-03-26 2015-01-22 63 4 5 Russia–Georgia Caucasus 2008-08-08 2008-06-12 57 4 6 Israel–Lebanon M. East 2006-07-12 2006-05-28 45 4 7 Ethiopia–Eritrea Africa 1998-05-06 1998-03-01 66 4 8 India–Pakistan S. Asia 1999-05-03 1999-03-15 49 4 9 US–Iraq M. East 2003-03-20 2002-12-18 92 4 10 NATO–Yugoslavia Europe 1999-03-24 1999-01-15 68 4 [...37 additional conflicts listed in supplementary materials...] Table 9: Supplementary Table S1 (excerpt): 47 MIDs in validation sample. Full table available in online supplement. “L4 Alert” = date Level 4 first triggered (— if never reached L4). “Lead” = days from L4 to conflict. “Max Lv” = maximum alert level reached before conflict. Selection criteria: All MIDs from UCDP/PRIO (1990–2022) with ≥25 battle deaths involving at least one state from our 42-state sample. Excluded: intrastate conflicts, conflicts with non-state actors only, and conflicts where both parties have <12 months of trade data. True positives (L4 before conflict): 35 of 47 (74% recall). False negatives (no L4 before conflict): 12 of 47. 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