Every individual carries a personal threshold map — the invisible line between resisting a decision and taking it. These thresholds don't erode gradually. They hold under pressure, accumulate damage invisibly, and collapse suddenly at a trigger that looks disproportionately small from the outside. Threshold Theory models the mechanics of that collapse before it happens.
In structural engineering, the Wöhler curve describes the relationship between cyclic stress amplitude and the number of cycles a material can sustain before fracture. The material doesn't yield — it holds at full strength, accumulates microscopic damage, and then fails suddenly at a load that would previously have been trivial.
We apply this directly to decision thresholds. A person's resistance to a category of decision — exfiltrating data, violating rules of engagement, making an impulsive financial trade — is not a static number. It is a material with fatigue properties. Each near-miss, each rationalisation, each cycle of pressure-and-recovery erodes the threshold by a small, invisible amount.
The result is that the dangerous moment rarely looks dangerous. The individual appears stable. Their recent behaviour is unremarkable. But the accumulated damage in their threshold structure means the next trigger — however minor — will produce a fracture event rather than a resistance response.
Subject USR-1402 — Senior Security Analyst, Level 3 access. Baseline threshold profile established. Inject stress events to watch how each dimension drifts independently. Near-misses ratchet down thresholds permanently. Acute stress suppresses them temporarily. Watch for the fracture line.
The red collapse line marks zero threshold. When any dimension crosses it, the model flags a fracture window — the subject is now capable of acting on that category of decision under any trigger.
Given a subject's current threshold level, ongoing drift rate, and the frequency of stress cycles they are experiencing, the model computes the predicted time to fracture across each dimension.
This is the operational intelligence no existing system produces. Not "is this person at risk" — but "this person will cross the security threshold in 14 days unless the following conditions change."
Adjust the parameters to model different subject profiles and operational environments. The output is a predicted collapse date per dimension — the number that goes in the operational briefing.