Resurgence — a perturbatively invisible effect and its instanton are one fact
builds_on: and related:Scope. Phenomena invisible to every order of a perturbative expansion. Evicted from the vocabulary (v4 §12) as a resident.
| phenomenon | suppression | small parameter |
|---|---|---|
| tunnelling | e^(−S/ħ) | ħ |
| confinement | e^(−2π/β₀α_s) | α_s |
| Cooper pairing | e^(−1/λ) | λ |
| black-hole information | e^(−S_BH) | G |
A shared form with no shared theorem is a cross-reference. The theorem is resurgence: the perturbative series is not Borel summable, its sum is ambiguous by an amount of order e^(−S/g), and that ambiguity is cancelled exactly by the instanton's. The two sectors are halves of one trans-series and neither is defined alone — so the invisibility and the instanton's existence are the same fact, provably. That upgrades the table from a cross-reference to an edge.
And it makes the fourth row's open problem precise. Replica wormholes look like an ensemble average over theories. In ordinary field theory the non-perturbative sector completes one theory's trans-series; if gravity's wormholes only make sense averaged, nothing is being completed, and the fourth row belongs to a different family.
Placement. A cross-reference upgraded to an edge; sits beside the trace-identity bridge family ([[CASE-16]]) at rung-vocabulary-v5.md §8.1.
36 source lines, no addenda.