C.22:6 - Archetypal Grounding (Tell–Show–Show)

Tell–Show–Show hook (per E.8): in Show‑1 (continuous ODE) and Show‑2 (MIP) below, CHR guard‑macros and scale rules show which field supplied which Eligibility or Acceptance input. For the receiving use, explicitly annotate which S2 fields triggered each Eligibility and Acceptance decision (e.g., service_level@ordinal → ORD_COMPARE_ONLY, budget@ratio → unit alignment check).

A. Differential equations (continuous systems, solver choice). ProblemProfile. DataShape=ODE, stiff?=unknown, SizeAndConditionProfile={n≈10^3}, ObjectiveProfile={↓error@ratio, ↑throughput@ratio}, ConstraintRefs={budget-envelope relation, safety-predicate relation}, RegularityTraits={Lipschitz known?=unknown, Jacobian sparsity=high}, Missingness=MAR. Attachment. Selector consumes TaskSignature; eligibility filters MethodFamilies whose eligibility conditions require known stiffness or differentiability, with unknown yielding degrade or abstain per family. Acceptance treats safety_gate as an ordinal predicate, not an average (ORD_COMPARE_ONLY), and treats budgets with unit-aligned sums on ratio scales. The selector returns a Pareto set; no cross-ordinal weighting.

B. Mixed‑integer optimisation (planning and scheduling). ProblemProfile. DataShape=MIP, NoiseModel=deterministic, ObjectiveProfile={↓cost@ratio, ↑service_level@ordinal}, Constraints={SLA hard, workforce soft}, RegularityTraits={convex_relaxation=available}, SizeAndConditionProfile={vars~10^5}, Missingness=MCAR. Attachment. CG‑Spec forbids means over service_level (ordinal); Acceptance holds acceptance-gate thresholds; Eligibility checks convex-relaxation availability; Selection applies the lexicographic guard (assumption-fit before evidence-fit before resource). If this receiving use makes a named assurance claim about an exact target claim, including when a material-reliance rule requires it, use B.3 to obtain its separate assurance result from the relied-on evidence relations and the declared policy; otherwise this example adds no assurance fold. If the admissible comparison remains partial, return a Pareto set.

Current practice anchor: the 2026 SciML Problem Interface constructs an immutable problem value before solver use and supports explicit remake when problem fields change. C.22 adapts only that problem-before-selector separation; it does not import Julia types as FPF ontology.

C. Quality-Diversity archive and declared set (illumination). ProblemProfile. DataShape=policy‑search; ObjectiveProfile={↑reward@ratio, ↑coverage@ratio (report‑only)}, DominanceRegime=ParetoOnly, PortfolioMode=Archive, CharacteristicSpaceRef(d=3, characteristics=CHR‑typed), ArchiveConfig(grid, res=32×32×16, K=1, InsertionPolicyRef=elite‑replace, DistanceDefRef.edition=v1), EmitterPolicyRef=v2, Budgeting{eval=1e6}, TelemetryHooks{PathSliceId=…}. Include PathSliceId only when an E.18 path slice is current. Selection result. Selector may return an archive; coverage and illumination are reported but excluded from dominance (default). Any change of DistanceDefRef.edition or Emitter policy is editioned and logged in SCR.

D. Open‑ended environment generation (POET‑class). ProblemProfile. GeneratorIntent{GeneratorFamilyRef=…, EnvironmentValidityRegion=… (CHR‑typed), TransferRulesRef=…, CoverageMetric=…}, PortfolioMode=Archive. Selection result. Selector outputs {environment, method} pairs that pass Eligibility; TransferRules govern cross‑environment policy reuse; telemetry reports coverage and regret and IlluminationSummary with edition and policy‑id when improved.

E. Physical manufacturing method-family eligibility. Problem-side episteme. PartFamilyFinishingProblemCard-E2 : U.Episteme is the exact C.22.2 ProblemCard for a shop that must finish AlloyPartFamily-17 on one machine under ShopInspectionScheme-E4 and a production-window ClaimScope. The receiving question is which available finishing-method families can be compared without presuming one of them. TaskSignature. SurfaceFinishingEligibilitySignature-E1 declares EntityOfConcernRef=AlloyPartFamilyFinishingTarget-17, effectiveReferenceScheme=ShopFinishing-Scheme-A, TaskKind=surface-finishing work, ScopeSlice(G)=AlloyPartFamily-17 during [2026-09-01T00:00Z, 2026-10-01T00:00Z), ObjectiveProfile={surface roughness Ra@ratio in micrometres with downward polarity, throughput@ratio}, ConstraintRefs={geometric-tolerance relation, heat-distortion relation, resource-envelope relation}, and material-hardness condition as a live unknown with an explicit measurement relation and unknown-handling policy. The TaskSignature makes eligibility reviewable; it does not select grinding, honing, polishing, or another method and does not establish that any part was finished. Assignment. FinishingMethodEligibilityUse-E1 : U.Episteme states the exact receiving eligibility-comparison use. TaskSignatureAssignmentRelation(PartFamilyFinishingProblemCard-E2, SurfaceFinishingEligibilitySignature-E1, FinishingMethodEligibilityUse-E1) has exactly the problem-side episteme, signature, and receiving-use episteme as participants. It obtains only while that exact signature is actually adopted as the task-typing declaration for that exact card and the use stated in FinishingMethodEligibilityUse-E1, under ShopFinishing-Scheme-A, the declared part-family scope, ShopInspectionScheme-E4, and the production window above. Withdrawal of that adoption or change of a participant or qualification ends this assignment occurrence; a shared row, carrier, or publication does not make it obtain.

F. Clinical rehabilitation method-family eligibility. Problem-side episteme. CohortRehabilitationProblemCard-E3 : U.Episteme is the exact C.22.2 ProblemCard for a rehabilitation service with Cohort-2026-Q3 and a stated capability-change question under clinical safety constraints. TaskSignature. RehabilitationFamilyComparisonSignature-E1 declares EntityOfConcernRef=RehabilitationCapabilityChangeTarget-4, effectiveReferenceScheme=ClinicalRehabilitation-Scheme-C, TaskKind=rehabilitation-method-family comparison, and ScopeSlice(G)=Cohort-2026-Q3 in the declared care setting during [2026-08-01T00:00Z, 2026-11-01T00:00Z). It also declares outcome characteristics with their scale kinds, contraindication and resource constraints, and unknown tolerance or comorbidity values preserved as unknown. Include the evidence relations and follow-up windows only because this comparison use relies on them.

C.22 makes the comparison inputs explicit. Diagnosis and treatment recommendations remain claims governed by the applicable clinical patterns. For a separately current evidence or benefit claim, apply its evidence or clinical evaluation pattern; for a named gate decision, use A.21; for a care-permission claim, use A.2.8.PER and its GrantedPermissionRelation@Context predicate; for decision authority, recover the applicable authority predicate. Return missing-governor under A.6.RCD only when no governing rule can state or test that exact needed relation claim.

If clinical Work occurs, recover each exact actual performer System through A.13 and let A.15.1 independently admit the dated Work and its enacted Method. Add an assignment occurrence, its declared species, and F.6 only when this clinical account or its receiving use expressly consumes precise assignment-bound attribution through the same obtaining A.13 assignment; F.6 identifies neither assignment nor performer, and missing or failed F.6 leaves the Work intact. A local system-role kind, classification, or assignment can remain a neighboring fact, but it establishes none of the permission or authority relations above. Assignment. RehabilitationInterventionFamilyComparisonUse-E1 : U.Episteme states the exact receiving comparison use. TaskSignatureAssignmentRelation(CohortRehabilitationProblemCard-E3, RehabilitationFamilyComparisonSignature-E1, RehabilitationInterventionFamilyComparisonUse-E1) has exactly the problem-side episteme, signature, and receiving-use episteme as participants. It obtains only while that exact signature is actually adopted for that exact card and the use stated in RehabilitationInterventionFamilyComparisonUse-E1, under ClinicalRehabilitation-Scheme-C, the declared cohort and care ClaimScope, the qualification window above, and the stated evidence-use conditions. Withdrawal of that adoption or loss of a participant or qualification ends this assignment occurrence; cohort labels, records, carriers, and organizations add no signature field or fourth participant.