B.1.1:4 - Solution
Use dependency structure first; use graph representation second.
B.1.1:4.1 - Dependency Structure Frame
DependencyStructure@Context:
dependencyQuestion:
intendedUse?:
claimScopeRef?: U.ClaimScope
qualificationWindowRef?
candidateNodeRefs:
selectedDependencyStructureRef?
dependencyRelationRefs:
relationParticipantRefs:
relationGroundingRefs:
partWholeRelationRefs?
boundaryCrossingRelationRefs?
orderRelationRefs?
temporalRelationRefs?
resourceRelationRefs?
representationRelationRefs?
evidenceRelationRefs?
publicationOrSourceUseRefs?
designRunTag?
definingOrTestingPatternRefs:
This frame records independently grounded relation claims and their participants. It is not itself a U.Structure. When the receiving use needs one selected dependency structure, recover all four A.22 identity discriminators: exact constituents, obtaining relation occurrences, applied constraints and named selection/use frame. The record refers to that structure and to the patterns defining its relations.
B.1.1:4.2 - Graph Representation
Use graph language only when a graph is the selected mathematical or representation lens:
DependencyGraphRepresentation@Context:
representedDependencyStructureRef:
nodeExpression:
edgeExpression:
graphPropertyChecks?
mathLensRef?
publicationOrViewRef?
The graph may express acyclicity, reachability, cutsets, weak links, flow, or traceability. Those checks apply to the graph expression and bear on the selected relation only when the rule for that relation admits the mapping. Use C.29 to state the mathematical representation correspondence, preserved and lost distinctions, and validation boundary on which that inference depends.
B.1.1:4.3 - Relation Grounding Guide
| If the edge means… | Recover… | Pattern that defines or tests the claim |
|---|---|---|
| part of the whole | part-whole relation over admitted holons | A.14, C.13, B.1 |
| an entity belongs to a world-side collection | the collection’s own belongs-to occurrence, or a separately grounded collection-as-whole claim | A.14, C.13, C.16, and the pattern that defines that collection’s rule |
| phase of the same carrier | temporal phase relation | the carrier’s identity and phase rules, A.14, and B.1.4 |
| ordered step or branch | method, process-view, Work, or order relation | A.3.1, A.3.2, A.15.1, or the pattern that defines the order relation; B.1.4, and C.29 when a lens is current |
| performed work part | work occurrence relation with evidence and timing | A.15.1 |
| external influence, signal, supply, measurement, or control | the exact obtaining relation and its participants; recover evidence provenance separately | A.3.4 for an actual transformation, C.16 for measurement, and the defining pattern for the particular supply or control relation; A.10 recovers the independently established support and bounded use |
| representation, dashboard, digital twin, or architecture description | description or representation relation, not parthood | C.2.1, E.17, C.30.AD, C.30.AD.BA |
B.1.1:4.4 - Graph Checks Are Conditional
Acyclicity, topological order, cutset, reachability, and flow checks are useful only after the graph is selected as a lens over a selected relation structure.
Do not infer:
- parthood from graph adjacency;
- independence from graph separation without a rule that makes the selected relation support that inference;
- performed work from a planned step graph;
- whole reidentification from a graph property without B.2;
- architecture from a graph without an exact described holon, selected structure, and architecture relation or claim.