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Source changed 2026-10-03 11:52:20 UTC · snapshot created 2026-10-03 11:53:41 UTC · last check 2026-10-03 14:10:16 UTC

C.31:4 - Solution

C.31 defines and constrains modularity and reusable-structure characteristic assertions as C.16-compatible characteristic heads, composite descriptions, lens-backed characteristic interpretations, temporal or scale-sensitive characteristic interpretations, causal-use-sensitive characteristic interpretations, or report-only proxies. It starts from action guidance and adds fields for beyond-local-repair use only when a use being made requires them.

C.31:4.1 - Ordinary output: ModularityVectorLite

ModularityVectorLite is the ordinary output. It names at most three characteristics under evaluation because the first task is to find the next repair, not to audit all possible modularity interpretations.

ModularityVectorLite:
  describedHolonRef:
  architectureQuestion:
  intendedArchitectureUse:
  claimScopeRef?: U.ClaimScope
  qualificationWindowRef?:
  architectureClaimRef?:
  selectedStructureRefs:
  structureKindRefs:
  threeLiveCharacteristicsAtMost:
    - characteristicRef:
      characteristicScaleRef?:
      evidenceRefs?:
      comparisonBasisRef?:
      currentCue:
      repairDirection:
      claimUseClass:
      forbiddenOverread:
  observedProblem:
  relatedClaimPatternLocatorsIfClaimed:
  stopCondition:

The vector is complete enough when it states what can be done next and what cannot be inferred. relatedClaimPatternLocatorsIfClaimed is a non-semantic locator field: if a characteristic is used beyond local repair, the exact subject assertion and its defining or constraining ClaimGraph remain separately required. Architecture scale-preference claims use the predicate defined in C.31.ASAP.

C.31:4.1a - Filled ModularityVectorLite

ModularityVectorLite:
  describedHolonRef: ProductPlatform@FieldPumpFamily
  architectureQuestion: which structural repair would reduce field-replacement and certification burden?
  intendedArchitectureUse: choose the next modularity repair for field service and procurement
  claimScopeRef?: field-service and procurement architecture claims
  qualificationWindowRef?: 2026Q2
  architectureClaimRef?: ArchitectureOf@PumpControllerPlatform
  selectedStructureRefs: PumpControllerModuleInterfaceStructure, PumpControllerEvidencePackageStructure
  structureKindRefs: ModuleInterfaceStructure, EvidencePackageStructure
  threeLiveCharacteristicsAtMost:
    - characteristicRef: InterfaceStandardizationShare
      currentCue: controller ports are named by the same API family, but three field variants still require adapter-specific wiring.
      repairDirection: narrow the interface grammar and name the allowed variation before counting the interface as standardized.
      claimUseClass: local repair cue
      forbiddenOverread: the public API label is not substitutability or procurement suitability.
    - characteristicRef: SubstitutabilityWidth
      currentCue: two alternate controller boards pass the bench test, but only one has the required thermal envelope and connector constraints.
      repairDirection: state the substitution conditions and the exception before using the alternative count.
      claimUseClass: report-only proxy until C.16 or selection use is being made
      forbiddenOverread: the alternate-board count is not a selection result.
    - characteristicRef: EvidenceReuseShare
      currentCue: electrical-safety evidence is reused, while environmental evidence is recreated per enclosure variant.
      repairDirection: split reusable evidence package from variant-specific evidence and add source-return condition.
      claimUseClass: local repair cue with possible evidence-package use
      forbiddenOverread: reused evidence is not assurance sufficiency.
  observedProblem: the team says the platform is modular because interfaces are public and evidence is reusable, but field replacement and certification still create variant-specific work.
  relatedClaimPatternLocatorsIfClaimed: A.6.M for the module-interface relation; C.31.RSA if report-only share becomes reusable-structure accounting; A.10 or B.3 only if an exact evidence-use or assurance-use assertion is being made.
  stopCondition: stop at local repair until measurement basis, comparability basis, and any selection or assurance use are declared under their subject patterns.

Near miss: a high interface-standardization count alone is not a C.31 improvement. If field-service work, source-return events, or variant-specific evidence increase, the vector records that proxy divergence and returns to repair rather than treating the count as architecture quality.

C.31:4.2 - Characteristic classes

Every C.31 head is classified before use:

ClassUseBoundary
DirectCharacteristicA C.16-governed characteristic can be named with subject, scale, unit or unitless interpretation, declared measurement basis, comparability basis, and repair action.It is not automatically a score or decision selector.
CompositeCharacteristicDescriptionThe head is a bundle or description with sub-slots, such as function-module alignment or flow-boundary alignment.Do not pretend the bundle is one raw measure.
LensBackedCharacteristicThe head depends on a model description or mathematical lens, such as compression or RG or coarsening lens.Apply C.29 for lens use that changes action.
TemporalOrScaleCharacteristicThe head depends on time window, repeated instance, scale variable, aggregation scope, or source-return condition.Apply C.31.ASAP for architecture scale preference, C.27 for temporal adequacy, and C.18.1 or C.19.1 when scale-law or general BLP preference claims are being made.
CausalUseSensitiveCharacteristicThe interpretation is used to claim effect or intervention success.Apply C.28 before relying on the claim causally.
ReportOnlyProxyThe interpretation is only a local diagnostic or communication aid.State forbidden overread and the subject pattern needed for any beyond-local-repair use.

In C.31, declared basis and comparability basis name C.16-compatible measurement or comparison fields. They are not generic reason words and are not substitutes for evidence, assurance, cause, source, decision, or architecture-description relations.

C.31:4.3 - Measurement-head mapping

When a head becomes decision-facing or publication-facing, create MeasurementHeadMapping before relying on it:

MeasurementHeadMapping:
  sourceHead:
  knownMeasureFamilyOrPractice:
  fpfCharacteristicKind:
  scaleType:
  unitPolicy:
  declaredBasisNeeded:
  requiredEvidence:
  evidenceRelationRefs?:
  evidenceProvenanceRelationRefs?:
  sourceRelationRefs?:
  evidenceClaimAbsentBecause?:
  commonFalseUse:
  nonAdmissibleUse:
  repairAction:
  relationFunctionClaimRef?:     # only when this use depends on exact rule identity
  authoritySourceRef?:           # only when a non-pattern source carries relevant authority

Use an ordinary PatternID to locate the rule. Under E.10 L-EPI-PUB, relationFunctionClaimRef identifies the defining or constraining ClaimGraph only when interpretation, comparison, migration, publication or reuse depends on that exact rule identity. It is not a demand to establish a separate relation-function individual. When an external standard, policy or other non-pattern source carries the relevant authority, use authoritySourceRef for that source instead.

For example, an ordinary InterfaceStandardizationShare account states its subject, the counted interface population, conformance specification, ratio Scale, source/test basis and limitations. It needs no extra rule-identity claim merely to describe that share. If a comparison combines two editions that count partial conformance differently, cite the exact defining predicates through relationFunctionClaimRef before treating their shares as comparable. The comparison still needs its actual measurement and evidence basis; citing the predicate supplies neither test results nor assurance.

This mapping is not a measurement template by itself. It prepares a C.16-compatible characteristic card or a report-only boundary. When the head is decision-facing or publication-facing, the mapping names required evidence plus at least one evidence relation, evidence-provenance relation, or source relation. If no evidence claim is being made, evidenceClaimAbsentBecause states why the head remains local, report-only, or repair-only.

C.31:4.4 - C.31 characteristic card

Use the full card only when the use goes beyond local repair:

ModularityCharacteristicCard:
  characteristicRef:
  subjectRef or relationSubjectTuple:
  characteristicClass:
  scaleRef:
  unitInterpretation:
  declaredBasisRef:
  comparabilityBasisRef:
  requiredEvidence:
  evidenceRelationRefs?:
  evidenceProvenanceRelationRefs?:
  sourceRelationRefs?:
  evidenceClaimAbsentBecause?:
  proxyRisk:
  auditQuestion:
  nonAdmissibleUse:
  repairAction:
  relatedClaimPatternLocators:
  relationFunctionClaimRef?:     # same rule-identity condition as MeasurementHeadMapping
  authoritySourceRef?:           # relevant non-pattern authority, when used

Each card states its own C.16 well-formedness fields: characteristic, scale, unit or unitless interpretation, declared measurement basis, comparability basis, evidence relation, evidence-provenance relation, source relation, or evidence-claim-absent reason, non-admissible use, and repair action. When source material is used as evidence, the source relation is named. A source checklist, source-discharge slice, dashboard label, or inherited score is not enough.

C.31:4.5 - Seed characteristic heads and repair actions

These heads are seeds, not an exhaustive taxonomy. Use only the heads that change the next action.

Characteristic headIntended characteristic interpretationTypical scale or value formDeclared measurement or comparison basisDefect signalRepair directionEscalation trigger
InternalCohesionDensityDensity of typed relations inside a proposed module.ratio or graph-derived valuetyped dependency graph or DSMproposed module has insufficient typed internal dependency basissplit the proposed module, move relations, or reclassify as component relationcomparison, clustering, or publication use
ExternalCouplingDensityCross-boundary dependencies per module or interface.ratio or distributiontyped dependency graph, interface graph, integration defectshidden external dependencies dominate module boundaryexpose dependency, revise interface spec, split context, or accept bounded exceptionintegration risk, assurance, or release claim
InterfaceAlphabetSizeCount or entropy-like variety of interface types.count or entropy-like valueinterface registrytoo many interface variants erase modular benefitreduce variants, introduce interface grammar, split context, or document exceptionplatform grammar, candidate selection, or publication use
InterfaceStandardizationShareShare of interfaces conforming to declared specifications.ratio or percentageconformance tests and specificationsstandardization is low where reuse needs itdefine or narrow standards, add conformance tests, or stop at local exceptioncross-case comparison, certification, or procurement decision claim
InterfacePublicnessOpenness, publication, and vendor-neutrality value.ordinal or categorystandards, API specs, licensing, access termsopen label lacks substitutability relation, substitution policy, conformance expectation, or interface specificationrecover interface spec, substitution policy, and conformance expectationopen-architecture claim, procurement decision claim, or publication claim
SubstitutabilityWidthNumber or diversity of compatible alternatives for a slot or interface.count or diversity valueapproved implementations, vendors, testsonly one viable implementation existsrepair interface spec, loosen unnecessary coupling, or mark single-source exceptioncompetition, platform, or decision claim
ModuleTypeReuseRateInstances per module type or template.ratio or countproduct-line records, bills of material, template recordsreuse is claimed only by repeated namingdefine module type, allowed variation, and measurement basiscross-case reuse or product-line publication
TemplateCompressionGainDescription saving from template plus parameters compared with instance-by-instance descriptions.ratio or bits under declared methodcorpus or model-description methodcompression erases safety, law-domain, or source distinctionsadd source-return condition, split template, or apply C.29lens-characteristic or effect claim, publication, or decision use
FunctionModuleAlignmentCharacteristicFunctional elements and module relations align without unmanaged many-to-many exceptions.vector, ordinal, or bundle descriptionfunctional view and module relation recordsallocation hides many-to-many exceptionssplit function from module claim, revise allocation, or add correspondencecandidate decomposition or quality-composition claim
FlowModuleBoundaryAlignmentCharacteristicFlow topology crosses declared interfaces rather than hidden channels.vector, ordinal, or bundle descriptiontransformation-flow structure refs and interface refsflows bypass declared module boundariesexpose crossing, revise interface, or apply C.30.TFS-REL for the bounded architecture use of the selected transformation-flow structurepublication or assurance claim about that architecture use
ControlStructureSeparationCharacteristicControl responsibilities, rates, and boundaries are explicit enough for the architecture move.ordinal or vectorLCA or control description and temporal adequacy basiscontrol relation is hidden inside module labelapply C.30.LCA, C.27, A.3.3, or B.3 when a control, temporal, dynamics, or assurance claim kind is being madestability, assurance, or gate use
HiddenCouplingDiscoveryRateHidden dependencies discovered after integration or change.ratedefect and change recordsdependencies appear lateexpose side channel, revise interface spec, add sentinel, or reopen boundaryintegration risk, repeated release, or assurance claim
CrossBoundaryChangeReachHow many modules, views, or work items a local change touches.distributionchange-impact recordslocal change travels farther than claimedsplit relation, add interface grammar, revise allocation, or source returnrelease, decision, or comparison claim
WorkRepeatabilityShareDelivery, operation, or test work under repeatable method descriptions.ratiowork records and method descriptionswork repeats as bespoke effortdescribe the repeatable Method in a MethodDescription under A.3.2 or accept exceptionwork planning, evidence reuse, or scale use
EvidenceReuseShareEvidence package items reused across instances or contexts.ratioevidence graph and validity contextevidence is recreated or mis-scopedmove repeated evidence into reusable evidence or assurance packagecertification, safety-case, or assurance claim
RegulatoryBespokeResidueOne-off regulatory or acceptance content not covered by reusable structures.ratio or ordinalsafety, approval, or regulatory recordseach instance needs new regulatory argumentisolate residue, add reusable evidence package, or keep bounded exceptionsafety case, approval, or publication claim
LearningTransferCoefficientImprovement transfer from one instance or run to subsequent instances.slope or elasticityrepeated work data and learning curve recordsimprovement claim hides time or causal assumptionsapply C.27 for temporal adequacy and C.28 for causal usecausal, benchmark, or scale-preference use
BespokeResidueShareShare of structure not covered by reusable templates or rules.report-only share unless C.16 measurement basis is declaredRSA description and exception registerresidue is hidden under reuse scoreuse C.31.RSA and source-return conditionaccounting, comparison, or decision claim
RGFlowStabilityStability of characteristic vector across declared coarse-graining scopes.vector or ordinaldeclared multi-scope architecture graphscoarse-graining hides lower-scope hazardsapply C.29 for lens use and C.31.ASAP when an architecture scale-preference claim is being madeRG, scale, or lens transfer use
ExceptionCurveSlopeChange in one-off exceptions over a scale variable.slopeexception records against scale variableexceptions grow with scaleapply C.31.ASAP or accept bounded exceptionscale preference, publication, or decision claim

C.31:4.6 - Claim-scoped residual heads

C.31 uses residual heads only as qualitative repair cues. These heads do not create one complexity characteristic.

HeadMeaningRelated claim pattern locator and assertion requirementRiskRepair direction
ComplexityGrowthPressurePressure to add, split, mediate, or stabilize a declared aggregation scope, interface grammar, control relation, evidence scope, work-method scope, abstraction scope, or source-return condition.C.30.ILC, C.31.ASAP when an architecture scale-preference claim is being made, G.5, C.11treating more apparatus as progressname the pressure and the repair direction; use set-return or decision patterns when the corresponding claim is being made
FrustrationResidualPersistent cross-scope residual after local repair.C.30.ILC, C.29-local cross-scope lens claimturning a lens-backed interpretation into proofkeep as residual cue or apply C.29 or C.30.ILC
ConflictResidualSlopeResidual grows or shrinks over declared scale variable, scale window, or coarse-graining scale.C.31.ASAP, C.29, C.27, C.18.1, C.19.1treating two points as universal lawdeclare window, lens-use boundary, and measurement basis or stop at report-only
DeclaredScopeAdditionCostAdded work, evidence, change-policy, latency, observability, accountability, or interface cost from a new declared aggregation or control scope.C.16, C.31, C.30.LCAignoring the cost of added structureidentify cost bearer and apply the measurement pattern if used for comparison
BespokeResidueGrowthOne-off exceptions grow with deployment spread, regulation, or project repetition.C.31.RSA, C.31.ASAP when an architecture scale-preference claim is being madeassuming all bespoke work is badsplit useful exception from repairable residue
InterfaceAlphabetGrowthInterface variants grow faster than reuse, substitutability, or integration payoff.A.6.M, C.31premature standardizationadd platform grammar, split context, or accept bounded variation
SourceReturnCostFrequency or cost of returning from a compressed, indexed, coarse, extracted, or accounting view to source-side structure records.C.29, source-return discipline, A.10over-compressionadd source-return condition or reduce compression
ControlNestingDepthRiskNested control relations create latency, accountability, observability, stability, or assurance cost.C.30.LCA, C.27, B.3, A.3.3LCA-as-proofapply control, temporal, assurance, or dynamics subject patterns when the corresponding claim is being made

C.31:4.7 - Proxy-risk discipline

Every decision-facing C.31 card includes proxyRisk and auditQuestion. If the proxy diverges from the value it was meant to represent, the card stops at report-only use or returns to repair.

HeadProxy riskAudit question
ExternalCouplingDensityTeams hide dependencies instead of reducing them.Did integration failures or source-return events fall?
InterfaceStandardizationSharePremature standardization blocks useful variation.Did exception slope or workarounds rise?
InterfacePublicnessOpen label without substitutability.Are alternative implementations actually viable under declared conditions?
TemplateCompressionGainCompression erases safety, law-domain, or source distinctions.Did source-return events or bounded exceptions rise?
EvidenceReuseShareReused evidence becomes stale or mis-scoped.Does evidence remain valid in the new context?
RGFlowStabilityCoarse-graining hides lower-scope hazards.Are source-return conditions triggered?

C.31:4.8 - Rejected shortcut

The expression ModularityScore = average(all measures) is not admissible as a C.31 result. A local score is admissible only when the scoring method, codomain, polarity, characteristic basis, comparability basis, and use boundary are disclosed through the governing scoring or comparator pattern. Without that, keep the result as report-only or return to ModularityVectorLite.

C.31:4.9 - Lowering and currentness conditions

Lower or reopen a ModularityVectorLite, ModularityCharacteristicCard, or report-only proxy when any of these conditions changes the characteristic use:

  • proxy audit worsens, such as more integration failures, workarounds, source-return events, stale evidence reuse, or bounded exceptions;
  • measurement basis, comparability basis, scoring method, codomain, polarity, unit policy, or declared characteristic basis changes;
  • evidence relation, evidence-provenance relation, source relation, evidence-claim-absent reason, or source-return condition changes;
  • described holon, architecture question or intended use, ClaimScope or qualification window, architecture claim, structure kind, characteristic head, or repair direction changes;
  • a report-only proxy is used for comparison, selection, publication, assurance, benchmark, causal-use, cross-case reuse, decision, procurement, or architecture scale-preference;
  • C.31.RSA, C.31.ASAP, C.16, C.25, C.29, C.30.STRAT, A.6.M, C.30, C.30.ASV, A.10, B.3, A.20, A.21, G.5, or C.11 changes the boundary for the neighboring claim being made.

Admissible repair results are: keep the result report-only, split or rename the characteristic head, update basis or evidence fields, revise the repair direction, change relatedClaimPatternLocatorsIfClaimed, lower a score to a local proxy, or stop C.31 use for the beyond-local-repair claim and constitute the exact subject assertion under its predicate.