lin-0126

9.9 Validated scalarization

After the obstruction profile and admission blocks are explicit, a numerical realization may use

\[ \mathcal L_D^{\mathrm{val}} = \Phi _0\bigl(\mathcal O_0(D)\bigr) + \sum _{k\in \Omega _D} g_k(\mathcal V)\lambda _k \Phi _k\bigl(\operatorname {INC}_k(D)\bigr), \]

where \(g_k(\mathcal V)\ge 0\) is selected from validation evidence. The model class must permit \(g_k=0\). An auxiliary tangent signal that does not help, does not transport semantically, or cannot be estimated reliably should not be forced into the objective.

Block	Typical null	Evidence	Failure response	Leakage barrier
Base structure	declared factorization holds	held-out routes or overlaps	repair or enrich model	freeze declarations first
Tangent structure	admitted lift is coherent	held-out probes	drop signal or revise site	fit gates on validation only
Task behavior	no practical improvement	task metrics and slices	reject candidate	separate final test
Safety/invariants	no forbidden regression	hard checks and red teams	automatic rejection	never trade against mean gain

Table 9.1 Admission blocks remain separately inspectable even when a final decision combines them.