Order from closure on real quadratic spaces: terminal, minimality, orientation (Geometry of the vacuum, floor −1)

Two declared conditions on a finite-dimensional real quadratic space — that it carries a volume cell, and that it is indefinite — are taken as PREMISES (not results), and we ask what they force. Closure of two-dimensional isometry generators under the Lie bracket induces a partial order on configurations: its direction is not chosen, its terminal is enumerable (coordinate-generated), and under the two premises its minimum is unique and asymmetric — the signature (3,1). This is MINIMALITY under declared premises, NOT selection: (3,2), (4,1), (3,3) satisfy the same conditions and are nowhere excluded. Independently of the premises: a 2-plane in so(p,q) closes if and only if it is Killing-degenerate; two different descriptions of the structure (closure and stabilizer) yield one list of classes — consistency, not independent confirmation, since both factor through the same axis-splitting by construction; and the Pfaffian is the only invariant we measured that survives on the generic stratum, while the whole Lie structure sits on degeneracy strata. The work contains no physical reading of any object: the words that carry one have no definition at this level. No action principle (out of scope: geometry does not describe an action). Every theorem carries its limits explicitly; every number is checked by a self-contained probe whose reference output ships with it — the check is a diff, and it is language-blind.