Field projection — Grounding Certificate / Drift

Grounding certificates aim to keep monitors tied to value-relevant state under conservative abstraction. Class-green coverage can hold while the true environment drifts off-class — nonrealizability blocks inferring deployment safety from class certificates alone.

What decision changes?

Treat class-level grounding green as evidence about the certified abstraction, not as discharge of off-class drift risk without explicit coverage extension.

Grounding certificates and conservative-abstraction agendas ask monitors to stay tied to value-relevant state as ontologies shift. This project separates class-level coverage from deployment-level safety: a monitor can be green on the certified class while the true environment drifts off-class.

Lean proves class_certificate_not_deployment_safety on a finite toy: narrow class certificate plus in-class robustness can hold while the true environment is nonrealizable under the represented class and unsafe for the deployed policy. MB9 forward discharge remains a bridge; the separation is load-bearing for claim calibration.

What grounding-certificate work keeps that this crosswalk does not replace: proof-carrying code pipelines, conservative extension lemmas, and engineering protocols for ontology updates. Relocating drift as a separation does not automatically produce drift detectors.

Formulas

ClassCertificate(S)  μS. InRepresentedClass(μ)\text{ClassCertificate}(S)\ \equiv\ \forall \mu\in S.\ \text{InRepresentedClass}(\mu)
Field object: every environment in plausible set S is marked checked relative to the represented class. (ch43)
ClassCertificate(S)  RobustUnderAmbiguity(π,S)  ¬SafeIn(μtrue,π)\text{ClassCertificate}(S)\ \wedge\ \text{RobustUnderAmbiguity}(\pi,S)\ \wedge\ \neg\text{SafeIn}(\mu_{\text{true}},\pi)
Non-converse separation: class-green plus in-class robustness while true environment is off-class and unsafe. (ch43)
GroundingCertificate  GroundingViable\text{GroundingCertificate}\ \Rightarrow\ \text{GroundingViable}
Forward bridge packaging: MB9 grounding certificate soundness (bridge assumption). (ch03)

Lean source

Machine-checked declarations on the shared finite domain — each links to the theorem in the repo.

  • class_certificate_not_deployment_safety (counterexample) — Finite separation: class certificate and in-class robustness do not imply safety in off-class true environment.
  • epistemic_coverage_finite_shape_not_deployment_safety (counterexample) — Interface re-export of nonrealizability separation for epistemic coverage packages.
  • MB9_grounding_certificate_soundness (bridge) — Bridge MB9: grounding certificate supports grounding viability when assumptions hold.