Fold (with pivot and fulcrum)

Definition (canon)

Fold. The bifurcation type by which a sensor node fails. Pivot. What the node does at a fold — smooth relocation to a new state. Fulcrum. The inflection point of maximal gain and minimal restoring margin; the coordinate at which commitment occurs. A location, not a failure mode.

Use fold/hinge for geometry and pivot/fracture for behaviour.

The relaxation time diverges on approach, with exponent in [1/2, 1).

In plain words

Recovery from small pushes gets slower and slower as the node nears the edge, then the node settles somewhere new.

It is not

• A queue. A queue also slows, but its exponent lies in (1, ∞) and its pool grows without limit behind the step. A fold's state converges on a finite critical value. See queue.
• The location called the fulcrum. Fulcrum is where commitment occurs, not the fold itself.
• Announced by a scale-free cascade. That pairing is withdrawn (see cascade and the erratum).

What would defeat it

• Follows from the definition. A node meeting all three bifurcation conditions whose relaxation does not diverge on approach, or diverges with exponent outside [1/2, 1).
• Canon. Kill test 6, the fold/queue exponent test (Dropzone §9), is the instrument the series says is now carrying the discrimination.
• Simulation caution. Sweeping too fast can erase the divergence and mistype a fold as a hinge. See the ledger.