Wound healing is a jamming→unjamming→re-jamming transition. A free edge unjams (shape index q rises above the vertex-model threshold q*=3.81), cells migrate collectively to close the gap, then confluence crowds the edge past the spinodal and the sheet re-jams (q falls below q*). Below a critical unjamming drive (~0.15) the wound never closes — a chronic wound.
Re-epithelialisation is an unjamming–rejamming cycle around the vertex-model shape index q* = 3.81. The free edge unjams (q↑ to 4.07), cells migrate, confluence re-jams the sheet (q↓ to 3.55); below a critical drive the wound fails to close.
A wound is an unjamming transition
A confluent epithelial sheet is a jammed solid: cells are caged by neighbours and cannot rearrange. The tissue's jammed-vs-fluid state is set by a single geometric control, the cell shape index q, with a vertex-model threshold at q* = 3.81: below it the sheet is jammed, above it it flows.
Injury frees an edge. The free-edge cue drives the edge cells across q*, unjamming them; in this run the shape index rises to qmax = 4.07, well into the fluid regime. The unjammed cells migrate collectively into the gap.
Closure is re-jamming
As the gap closes the free-edge cue vanishes and the confluent crowding bias takes over, pushing the edge field back below the spinodal so the sheet re-jams: the shape index settles to qfinal = 3.55, back below q*. The wound has closed and the tissue is solid again — a full unjam→migrate→rejam cycle.
The honest failure mode: chronic wounds
The same model predicts when healing fails. Below a critical unjamming drive of about 0.15 the edge never crosses q*, the sheet stays jammed, and the gap does not close — the substrate's picture of a chronic, non-healing wound.
The jam→unjam→rejam sequence and the chronic-wound threshold are simulation-verified shapes [V] Simulation-verified; q* itself is a cited anchor [L] Cited anchor. The absolute closure rate in µm·h−1 is open [O] Open (obstacle stated): it needs a measured single-cell migration speed.