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Fig 1.

Transition diagram for a two-state system with disruption d and recovery r.

The diagram shows the state transitions between normal (x0) and degraded (x1) states under the disruption transformation d and recovery transformation r.

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Fig 2.

A canonical shock-propagation geometry with a unique collapse state x*.

The diagram illustrates a three-layer propagation network where disruptions propagate downward through dependency hierarchies until converging on a shared collapse configuration.

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Table 1.

Basis-pruning algorithm for minimal intervention set.

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Table 1 Expand

Table 2.

Shock-propagation simulation algorithm.

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Fig 3.

Manufacturing stage disruption propagation‌‌ example.

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Table 3.

Generator effects on manufacturing stages.

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Fig 4.

State transitions in manufacturing supply chain under minimal collapse set.

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Table 4.

Generator effects on agricultural regions.

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Fig 5.

State transitions in agricultural supply chain under sequential shocks.

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Table 5.

Generator effects on e-commerce hubs.

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Fig 6.

State transitions in e-commerce logistics supply chain.

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Table 6.

Shock propagation simulation algorithm.

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Fig 7.

Flow diagram for shock propagation simulation (Table 6).

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Table 7.

Basis-pruning procedure for minimal generating set.

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Fig 8.

Flow diagram for basis-pruning (Table 7).

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