At reference capacities, losing any one of Chinese nodes for a year stops more than a quarter of two years' lithium-ion cell output

Every minimal cut set of at most three losses, with its shortfall and its share of the risk

φ(S) is the least cumulative shortfall over 24 months when the nodes in S are out for the stated months, as a share of demand; a cut set fails (φ > α) and every immediate predecessor (one loss shortened by one level) does not. Each φ is a primal LP value with a matching dual (gap ≤ 10⁻⁶). P(S ⊆ Z)/L is the share of the exact lower bound L carried by S; shares overlap. Durations are 3, 6 or 12 months; h is months of input stock; σ the spare-capacity fraction reached after L months. Basis: production statistic, trade export proxy, imputed from the bill of materials.

The witness column shortens only the named loss, keeping all other losses unchanged; 0 months removes it. Every resulting shortfall is at most α. The controls also drive the PV cut table below.

One loss can cut a layer only where the rest of it supplies less than half the requirement: cells, precursor, cathode, anode, graphite, lithium carbonate and refined cobalt

Each bar is a country's 2024 output in years of the layer's requirement per year; a layer's total is its supply ratio S. A twelve-month loss of a node fails at α = 25% only if the rest of its layer falls below half the requirement over the year. Copper, aluminium and manganese hold 25–165 years of requirement because the model lets every tonne serve batteries: it has no competing demand, which makes upstream cuts harder to reach than in reality. Sources and bases: DATA.md.

Chemistry choice lowers the Li-ion scenario estimate from 48.6% to 28.8%

Same fixed reference capacities, node rates and outage lengths; only the recipes change. The cut controls default to chemistry choice. Both approved 24-month NCM-share ranges, [0,1] and [0.25,0.75], give the same failure event: every outage ends by month 12, and the restored second year can supply the reference mix and satisfy either aggregate share limit. This sensitivity is nonbinding under this horizon. All estimates below add residual failures to exact L; 20,000 draws, seed 8, exact-binomial 95% sampling intervals. Zero sampled residuals retain a positive upper endpoint. Full outages remain a scenario.

The following risk chart and severity study retain the fixed 50/50 reference

If every recorded export restriction were a full outage, failure would come about every other year (, L = ); counting only quotas and bans, (L = )

Onsets 2012–2024 from the OECD Inventory and national acts, pooled by product with empirical-Bayes priors; a country shock with ρ = makes losses in one country coincide; of spells last 12 months. L is the exact probability of containing an enumerated cut; U = min(1, L + P(more than three losses)) = is too loose to use, since about nodes are hit per year. The point estimate is L plus a Monte Carlo estimate of failures containing no enumerated cut, with exact-binomial 95% interval [, ], checked against crude Monte Carlo (). The registered predictive test failed (log-loss against for a constant), so these are scenarios under stated rates. The quotas-and-bans scenario (OECD codes M3, M4 and prohibiting acts) was added after the registered tests and is not one of them. Each estimate uses 20,000 draws from its scenario law. Intervals cover sampling uncertainty conditional on fixed inputs.

The severity study cannot yet replace full-outage assumptions

At α = 25%, h = σ = 0, the three scenario definitions give the following estimates and 95% sampling intervals. Only four isolated events survive the approved trade-data rules; no measure type reaches the five-event minimum. The registered severity calculation therefore assigns full loss to every onset. Its law is identical to full outage, so the table reuses that law's L-plus-residual estimate, rather than treating a different Monte Carlo draw as a change in risk. The paired reduction is zero in 20,000 draws; S3's five-percentage-point reduction is killed under this fallback rule. This does not establish that actual policies remove full capacity. Exports measure shipments leaving a country, not production.

BACI HS12 2012–2023; onset years 2014–2022. Equal-event-weight difference in differences compares the first full calendar year after onset with the preceding year, using surveyed unrestricted exporters of the same HS6. Country bootstrap: 2,000 draws. Losses below are unclipped changes relative to baseline export volume; negative values mean a relative export increase. All intervals have weak inference because there are fewer than ten treated countries. M3/M4 are quota/prohibition; M1 is export tax; M14 is other export measures; M5 is fiscal tax on exports; M6 is licensing. S1 and S2 are untestable.

Solar is more concentrated still: each of China's four PV stages is a cut set on its own, and on the shared network a battery loss and a PV loss together suffice

PV chain polysilicon → wafer → cell → module (BACI HS22 2024; MIIT China output; 2.0 g Si/Wp), demand set to the undisrupted module output. On the shared network each sector's shortfall is measured in its own annual output, so the two count equally and failure is more than α of their sum. The cut-set controls above also select this PV configuration. PV rates borrow the all-product prior except polysilicon, the only PV product the OECD survey covers.

The failure threshold and allowed outage length change the scenario lower bound most

Fixed 50/50 reference. Each interval spans the saved E1 values for one input, with other inputs at α = 25%, D ≤ 12 months, h = σ = 0. Spare-capacity cases ramp over six months; the ramp comparison fixes σ = 0.5 because ramp has no effect with zero spare capacity. The dotted line is the headline L. These are parameter ranges, not confidence intervals. Sources: Li-ion result bundle and the fixed onset law, 2012–2024. Endpoints appear on hover.

Country attribution changes with the selected losses, chemistry and recourse

For each country, P(some cut set containing one of its nodes is contained in Z)/L, computed exactly for the cut-set controls above. A cut set with nodes in two countries counts for both, so country shares overlap.

Japan’s output data remove one cell triple; five Chinese singletons remain

METI 2024 sealed-cell output totals 5,136,311 kAh: 16.436 GWh at assumed 3.2 V or 19.004 GWh at 3.7 V. The conversion is imputed. Both variants remove the China cells 6-month + Poland and US cells 12-month triple from the seven chemistry-choice cuts, leaving six. These capacity variants are separate from the reference cut controls and probability comparison; their onset probabilities have not been refitted. German Prodcom sold carbonate (24,728 tonnes, both purity grades, imputed proxy) changes no headline cut. Sold output is not actual production.

The competing-demand sensitivity reserves non-battery uses, applying global battery shares 76% Co and 16% Ni proportionally to countries. Cu/Al/Mn availability of 100%, 10% or 1% is assumed. Demand stays fixed. A positive baseline shortage is shown; when it exceeds 25%, the sole minimal cut is the empty set. Thus one empty cut means failure without any outage, not a new single-node chokepoint. N1 and N2 survive.

All cases: α = 25%, h = σ = 0, 24 months, outages ≤ 12 months, at most three losses. Complete lattice lists have primal/dual and shorter-duration certificates. Source: supply-4ae36c1. China tariff-line partner batches match the preview rows, but repeated dimensions, a precursor sum above its BACI parent, and four empty graphite queries prevent a complete-flow or production claim. Korean domestic physical cell output remains unlocated, so its flagged trade basis is retained. Data, licences and limitations.

Registered tests: the network adds information beyond concentration, and the probability claims are scenarios

The table reports the fixed-mix reference tests. W3's registered chemistry-choice claims both survive: a full-year Chinese precursor or refined-cobalt loss has zero shortfall. Kill conditions were committed in HYPOTHESES.md before any probability was computed. Outcomes and the cut sets they withdraw or qualify: FINDINGS.md.

Natural hazards enter only as a scenario: no production site has located capacity

Located capacity covers 0% of every layer, below the registered 70% threshold, so hazards are not matched to sites. Instead each country with nodes loses a fixed fraction of all its capacity; the table lists the losses that fail at α = 25%, with the years 2012–2024 in which GDACS issued an orange or red alert for the country. An alert is not a loss.

Every number on this page is read from a named result bundle

Runs . Reference risk code , chemistry risk code , capacity code . Reference source lock . Raw inputs are frozen with URL, date, SHA-256 and licence in SOURCES.lock; derivations are in MODEL.md. Data: CEPII BACI (Etalab 2.0), USGS (public domain), MIIT, Cochilco, Xu et al. 2020 (CC BY 4.0), OECD Inventory of Export Restrictions, GDACS. No investment or price claim is made.