Release and the three endings

Three endings are available:

1. Constructed. The action, gauge fixing, and one tree are named, and the completed observable transforms correctly on the frozen algebra through the frozen order.

2. Proved obstructed. The gauge identity acquires a nonzero defect on that algebra at the frozen order, or the tree kernel leaves the declared domain.

3. Unresolved. The action, the gauge condition, or the propagator is unnamed.

The ending reached is (1) for the gates as frozen in Section sec:frozen: classical identity through ${\kappa }^2$, quantum-metric background identity through ${\kappa }^1$, one tree at ${\kappa }^2$. The ${\kappa }^2$ quantum-metric identity is not frozen; its defect is displayed. A sheet that froze that identity on this field content would reach ending (2) with Proposition prop:witness as the witness. The defect is not removed by shrinking the algebra.

A missing object is recorded as missing, not as a no-go. Nothing in this manuscript depends on a state for the graviton.