Limitations
The current formalization is intentionally bounded.
It does not establish that the current candidate structural properties are complete.
It does not establish universal necessity, mutual independence, or joint sufficiency of those properties.
It does not assume that more evidence always produces more evidentiary capability.
It does not assign systems a universal scalar assurability score.
It does not infer that a more assurable system is safer, more trustworthy, or more likely to satisfy the evaluated claim.
It does not replace an assurance argument or determine its final conclusion.
Capability Profiles and Claim Resolution
The capability-ordering and claim-resolution mechanisms are distinct.
Strict Structural Assurability dominance does not imply improved claim-resolving power. Additional claim-material capabilities may leave the observation model's ability to resolve a claim unchanged.
The formalization does not derive a system-specific observation model directly from evidence accessibility, resource feasibility, materiality, or capability semantics.
Approximation Transfer
The approximation-transfer theorems establish sufficient conditions under which claim-resolution results can be transferred between abstract and concrete observation models.
Applying these results to operational systems requires independent justification of the relevant assumptions, including:
- admissibility and realizability of the modeled worlds;
- preservation of claim truth;
- faithfulness of the modeled observations; and
- the applicable relationship between abstract and concrete observations.
Witness-level transfer requires exhibiting only one concrete resolution-failure witness rather than specifying a global mapping.
Under the current definitions, however, a global failure transfer can also be constructed from one realized witness using a claim-dependent mapping. Neither construction independently establishes a faithful relationship with an operational system.
Finite-World Examples
The representative architecture examples establish that the formal relations can express strict dominance, equivalence, and incomparability. A separate observation-model construction demonstrates claim-resolution failure.
The precinct-vintage and deployment-shift examples demonstrate claim-relative resolution and failure under explicitly stated assumptions.
These examples do not establish empirical properties of actual precinct-data pipelines or deployed classifiers.
In particular, the deployment example uses a finite population with exact correctness values. It does not establish statistical sampling guarantees, confidence intervals, or bounds on deployment-accuracy estimation error.
The counterexamples demonstrate that particular admissible world pairs defeat the stated resolution guarantees. They do not establish that the omitted assumptions are necessary in every possible observation model.
Future extensions should preserve these distinctions unless the formal theory is intentionally revised.
Dimension-Specific Separating Constructions
The generic SeparatingConstruction interface remains unrestricted and
accepts caller-supplied difference relations.
The four dimension-specific constructions
provide profile-grounded, dimension-locked alternatives for
observability, evidence coverage, traceability,
and reconstructability.
Independence, integrity, and controllability do not yet have corresponding dimension-specific constructions.
For independence and integrity, establishing the assurance significance of a profile difference requires additional assumptions concerning evidence provenance, admissibility, and trust.
For controllability, connecting interventions to claim resolution requires representing how the evaluator's observations depend on permitted interventions and applicable resource constraints. The current claim-resolution model does not represent those interactions.