Bounded additive sibling spill gives a polynomial actual route bound

A finite additive repair certificate assembles actual steps of a relation R. A leaf has excess e<=b and an actual route of cost<=Ce. A nonleaf records one initial R-edge or stationary step, followed by child repairs. Child dimensions strictly drop, each child excess is at most the parent e, and sibling excesses sum to at most e+b. Internal parents have positive dimension and e>b. Then the certificate gives an actual route of its recorded cost, and that cost is at most Ce+(1+b*C)hmax(e-b,0). Fixed b and C give a quadratic bound. The certificate is a conditional interface: dimension/excess tags are not automatically geometric, and arbitrary polytopes are not asserted to admit it. The cyclic fixed-slack obstruction and its adaptive routes are separate work.