Part VII. Robust curved certificates and noisy geometry
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The preceding block discovered a curved probability domain from exact operators. Exact preservation is not the same as stability under uncertainty. In the worked continuous model, every pure boundary state can remain on the boundary. A perturbation too small to be conspicuous in a coefficient table can then move a predicted state outside the probability domain.
This block separates three operations. A numerical procedure proposes a geometry. An exact checker decides whether the submitted polynomial family has a declared margin on that geometry. A separately stated uncertainty set determines which other families share the guarantee. If a repair changes the operators, its prediction cost is retained rather than called an exact coordinate change.
The resulting construction is broader than the preceding exact conformal search. It accepts nonconformal polynomial families and certifies a full coefficient box around a repaired estimate. The reference example uses a deterministic perturbation, not an empirical confidence region. Statistical coverage is a conditional theorem, not a conclusion of that example.
Lorentz-positive maps, robust convex constraints and Bernstein positivity certificates have classical antecedents [R8, R13, R21, R22]. The following arguments are self-contained specializations connecting them to the signal model's representation and evidence contracts. The nine propositions continue the numbering at 71. Their count is not a novelty claim or a count of Lean proofs.