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Pathway Reachability Analysis

Analytic route model — instantiates Exposure Pathway Interruption

Treats exposure as a graph problem — computes whether a hazard can still reach a target after a proposed cut, and exposes the substitute routes that keep it reachable.

Before you cut anything, you need to know which cut actually disconnects the target. Pathway Reachability Analysis turns a diffuse "this hazard is dangerous" into an explicit directed graph — sources on one side, vulnerable targets on the other, every route between them as edges — and then computes whether any path still connects them. Its defining move is that it places no control of its own: it is the reasoning step that identifies which links, if severed, would disconnect the target, and — crucially — re-checks whether severing them merely reroutes the hazard down a substitute path. Every other mechanism in the archetype acts on one link; this one reasons over the whole route graph so those actions land in the right place.

Example

A plume of solvent from a closed landfill sits near a cluster of residential drinking-water wells. Analysts build the pathway graph: aquifer flow paths, a preferential fracture zone, and an old agricultural drain nobody had mapped. The reachability check shows which wells are currently connected to the plume under existing pumping. The severable-link inventory lists candidate cuts — a hydraulic-barrier well, sealing the drain, relocating an extraction well. Then the counterfactual test: if we pump the barrier well, does the plume reroute toward the school's well instead? It does. The output is not a control but a ranked map — which cuts genuinely disconnect wells versus which only move the plume — that tells the interruption effort where a barrier is worth building and where it would just migrate the problem.

How it works

  • Build the source-pathway-receptor model as a directed graph, with each transport route an edge.
  • Compute reachability from every source to every target, and check coverage — are all the ways a target can be reached actually represented?
  • Enumerate the links whose removal would disconnect one or more targets (the cut set / articulation points).
  • For each candidate cut, re-run reachability to see whether a substitute route reopens the connection.

What distinguishes it: it is the only sibling that reasons over the entire graph at once, so it catches the shortcut a single-link fix would miss.

Tuning parameters

  • Graph granularity — how finely routes are decomposed. Finer graphs surface hidden shortcuts but cost more to build and can drown the signal.
  • Edge labeling — whether edges carry capacity, likelihood, or travel-time weights. Richer labels let you rank routes by flux, not just existence.
  • Reachability criterion — "any path at all" versus "any path carrying more than a threshold flux." A stricter criterion prunes negligible routes but can dismiss a rare high-consequence one.
  • Cut-search scope — single-link fixes versus a minimum-cut set. Broader scope finds cheaper multi-point cuts but expands the search.
  • Scenario count — how many hypothetical cuts you counterfactually test before committing.

When it helps, and when it misleads

Its strength is that it stops controls from being placed at the wrong link: it shows which cut disconnects the target and which merely reroutes, and it drags hidden shortcuts into view. Its central failure mode is that the analysis is only as complete as the edges someone drew — an unmapped route (that agricultural drain) makes a confident "no path remains" dangerously wrong, the classic garbage-in problem of any model. And it is easily run backwards: assemble the graph after a control is chosen and quietly omit the substitute path, so the model "proves" the favored cut works. The discipline that guards against this is to represent unmapped-pathway uncertainty explicitly and to validate the graph against field evidence — a tracer test, a smoke test, a real probe — rather than trusting the diagram.[1]

How it implements the components

  • pathway_graph — it constructs the directed source→target route graph the whole archetype reasons over.
  • reachability_and_coverage_check — it computes whether any path still connects a target and whether every reaching route is represented.
  • severable_link_inventory — it enumerates the links whose removal would disconnect targets, the menu the intervention mechanisms choose from.
  • counterfactual_pathway_test — it re-runs reachability after each hypothetical cut to catch substitute routes before they are found in the field.

It computes but never acts: breakpoint_priority_rule is executed by Route Closure or Segmentation, the multi_barrier_control_stack is built by Barrier Interposition and Filtration or Scrubbing, and hazard_specification with source_and_reservoir_inventory belong to Source Elimination or Substitution.

Notes

This is diagnosis, not intervention — it says where to cut, never that the cut has been made. Keeping it separate is what lets a team improve the map (add the drain, run a tracer) without re-litigating every control decision, and its severable-link inventory is the shared input that Route Closure or Segmentation and the barrier mechanisms consume.

References

[1] Reachability and minimum cut are standard graph-theory notions: reachability asks whether a directed path connects two nodes; a minimum cut is the smallest set of edges whose removal disconnects them. Framing an exposure pathway this way is what makes "cut the smallest sufficient set of links" a precise question rather than a slogan. ↩