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Cascade

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Description

A cascade is a directed chain of dependent events: an initiator fires, which fires the next event, which fires the next, and so on. The defining property is that each link’s firing is sufficient to fire its successor — not merely correlated with it, not merely making it more likely, but causally adequate to drive the next step. This propagation property is what distinguishes cascade from diffusion (where many local events probabilistically combine), from correlated failure (where multiple events share a common cause), and from feedback-loop (where the chain closes back on itself). The cascade’s structural shape is initiator + chain + propagation property. Remove the initiator and the cascade doesn’t start; remove enough of the chain (via bulkheads, circuit-breakers, or topology changes) and the cascade halts at the boundary; weaken the propagation property below sufficient-to-fire and the cascade dies probabilistically as it tries to spread. Cascade is the parent structural shape under which several catalog concepts specialize. Cost-cascade adds the cheap-default → expensive-fallback motivation and the conditional gating on cheap-path failure. Contagion adds the failure-state polarity and the dual-use coupling claim (the same edges carry productive flow). Chain-of-responsibility adds the handler-acceptance semantics and the early-termination guarantee. Each specialization preserves the directed-chain structure and adds domain-specific propagation semantics. Naming cascade as a primitive in its own right lets these specializations participate explicitly in the catalog’s structure-mapping operations — and lets other concepts (signaling cascades, trophic cascades, information cascades) attach to the parent without being forced into one of the existing failure-flavored or handler-flavored specializations. The polarity of a cascade is independent of the cascade structure itself. Apoptotic signaling cascades in cells are adaptive — the chain’s purpose is committed, irreversible cell death triggered by a controlled initiator. Trophic cascades in ecology can be either beneficial (sea-otter reintroduction restoring kelp forests) or destructive (sea-otter loss collapsing them) depending on which direction the chain runs. Information cascades in markets and social networks can produce efficient aggregation or destructive herding. The catalog’s contribution is making the shape explicit so that polarity becomes an additional property a specialization can name, rather than baked into the parent.

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Triggers

User-initiated: User describes a sequence of events where each triggers the next, asks how far a localized event might spread, or wants to understand whether a failure / change / signal will propagate. Vocabulary cues: “cascade,” “domino effect,” “knock-on,” “chain reaction,” “ripple effect,” “downstream,” “one thing led to another.” Agent-initiated: Agent observes a system where the initial event has potential downstream effects via directed dependencies. Candidate inference: “what’s the propagation property here — is each link’s firing sufficient to fire the next, or is the chain probabilistic; what bulkheads exist; where does the cascade terminate naturally?” If the system has named specializations (cost-cascade, contagion, chain-of-responsibility), prefer the more specific concept; cascade is the right fit when the structure is the directed-chain shape itself without the specialization’s added semantics. Situation-shape signals: Sequential failure analysis. Dependency-graph reasoning. Biological signaling pathways (caspase activation, MAPK cascade, complement system). Ecological trophic-level analysis. Power-grid stability discussions. DNS-resolution traces. Any situation where a single initiating event is followed by a directed sequence of dependent events.

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Exclusions

• Single-step causation — A causes B, with no further chain. The structural shape requires a sequence of contingent firings; a one-link “causation” is not a cascade. The diagnostic question: would removing any intermediate link still let the terminal event happen? If yes, the intermediates aren’t cascade-links; they’re parallel causes.
• Feedback-loop or cyclical systems — cascade is unidirectional and directed; feedback-loops are explicitly cyclical (output influences future input, possibly re-entering the same node). When the “chain” closes back on itself, the appropriate primitive is feedback-loop (or one of its polarity specializations), not cascade. A cascade can ignite a feedback loop, but the cascade itself is the acyclic directed propagation.
• Independent parallel events — when multiple events fire concurrently without causal dependency between them (a meteor strike triggering many failures at once, a regulatory change with simultaneous effects across firms), the structure is correlated firing, not cascade. The diagnostic test: is the second event caused by the first, or are both caused by something external?
• Chains where each link’s firing is insufficient to fire the next — when the propagation property is missing (each event merely makes the next “more likely” but routinely fails to fire it), the dynamic is closer to diffusion or probabilistic spreading than cascade. Cascade fires when the sufficient-to-fire-next property holds along the chain; below that threshold, the cascade dies out.

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Structure

The initiator is the cascade’s exogenous entry-point — the first domino, the patient zero, the tripped substation, the receptor binding, the predator removal. Its defining property is that it fires without itself being part of an upstream cascade-link; once it fires, the chain’s behavior is determined by the chain topology and the propagation property. The chain is the directed sequence of dependent events. It admits no cycles (a cycle would make it a feedback-loop, not a cascade), but it may branch — one event firing multiple downstream events is still a cascade, just one whose chain is a directed tree rather than a directed path. The chain has a natural direction (from initiator outward) and a natural terminus (either a sink event that has no further downstream dependencies, or a bulkhead that halts further propagation). The propagation property is the structural feature that makes each link sufficient to fire the next. In load-redistribution cascades (power grids), the property is “a tripped line’s load exceeds adjacent lines’ capacity, guaranteeing their trip.” In signaling cascades (biology), the property is “the upstream enzyme’s product is the downstream enzyme’s required substrate, and the substrate concentration exceeds the activation threshold.” In information cascades, the property is “observing N prior actors’ identical choice dominates one’s own prior, guaranteeing the same choice.” Without a propagation property, the chain is merely a sequence of correlated events; with it, the cascade runs to completion or to a bulkhead.

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Relationships

• cost-cascade — specialization of cascade where the chain is a tier of escalation and the propagation property is “cheap path fell short.” Preserves the directed-chain structure; adds the cost-differential motivation and the conditional gating on cheap-path failure.
• contagion — specialization of cascade with failure-state polarity and the dual-use coupling claim. The same edges that carry productive flow in mutualism carry failure in contagion; the cascade structure runs through the same topology.
• chain-of-responsibility — specialization of cascade for request-handling chains, where the propagation property is “this handler defers” and the chain terminates at the first handler that accepts. The early-termination semantics distinguish it from cascades that propagate to completion.
• keystone-species — keystone-species removal is one canonical initiator for cascades; the keystone’s disproportionate connectivity ignites a cascade out of proportion to its size. Reading the pair: keystone names the ignition site; cascade names the propagation that follows.
• phase-transition — cascades can drive system-level phase transitions when the propagation reaches threshold structures whose crossing produces qualitative state change. The cascade is the propagation mechanism; the phase-transition is the regime-change it produces.

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Examples