C.2.1:7 - Episteme morphing, viewing, and retargeting (normative)

C.2.1 governs episteme identity discriminators and neighboring relations. A.6.2-A.6.4 govern transformations between epistemes.

C.2.1:7.1 - Effect-free episteme morphing

For a morphism from episteme X to episteme Y, state by value:

1. which of claim content, EntityOfConcern, and effective reference scheme are preserved, restricted, bridged, or changed;
2. which exact viewpoint selection the use names, which exact empirical-grounding, claim-scope, model-use, evidence, or representation occurrences the arrow rule reads, and which endpoint facts it compares; the arrow changes none of those occurrences and makes none obtain or cease;
3. which claims in Y are preserved from or supported by X under the named morphism, the exact correspondence or retargeting relation governed by that morphism pattern, and any F.9 Bridge that governs cross-context sense use when current;
4. whether a separate operation application or Work actually produced or changed an episteme, and which direct pattern governs that occurrence.

The morphism declaration and its mathematical arrows are different objects. The declaration is a C.2.1 episteme, normally an A.6.0 FormalSubstrate signature, whose EntityOfConcern is the local mathematical family and whose claim content declares vocabulary, laws, and applicability. One arrow f : X -> Y is a local mathematical object identified inside that substrate by its exact endpoints, arrow rule or designator, and declared formal equivalence.

The mathematical statement f : X -> Y names no execution. When an exact operation application is current, A.6.1 separately identifies its argument and result bindings. For any precise performed-Work claim, use A.13 to identify the actual performer and A.15.1 to admit the dated Work independently. If that claim must also identify the assignment under which the Work was performed, check that relation separately through F.6. Identify the affected or newly constituted episteme, its C.2.1 discriminators, and any production or change relation under their direct governors. The same arrow may be used in several applications, and an arrow may relate already existing epistemes. No bare result, generic Work result, or universal production relation follows from an arrow or declaration.

A claim that one arrow is suitable for one exact use is another C.2.1 assertion. Its complete claim content names the arrow, use, conditions, and polarity. Evidence and reliance qualify that assertion; they do not identify the arrow or operation application.

C.2.1:7.2 - Epistemic viewing

A.6.3 governs an exact source-to-receiving viewing construction when one separately identified receiving episteme is constructed from one separately identified source episteme. That construction may preserve the exact EntityOfConcern while restricting claim content or specializing the effective reference scheme. It neither grants U.View membership nor performs work. Direct authoring and query generation can identify receiving epistemes without this construction relation.

E.17.0 independently asks whether one fixed receiving episteme E conforms to one fixed viewpoint episteme P; formally, whether EpistemeViewpointConformanceRelation(E,P) obtains. Only an obtaining relation gives the same E dependent U.View membership. A system may perform viewing, query, authoring, or rendering work, but neither that work nor an A.6.1 result position grants U.View membership or supplies C.2.1 identity.

Empirical grounding continues only while every mapped direct relation required by the receiving episteme’s exact covered claim subgraph obtains. Changing publication, current use, evaluator, or evidence alone changes neither the conformance of fixed E to fixed P nor grounding. Several source or receiving epistemes do not automatically form a multi-view family; identify any current collection under C.13 and any selected organization under A.22.

C.2.1:7.3 - Epistemic retargeting

A.6.4 governs a local class of effect-free arrows r : X -> Y whose exact endpoint epistemes concern different exact entities. It does not admit a durable U.EpistemicRetargeting kind. The A.6.0 FormalSubstrate signature that declares the class, one arrow r, a bounded-use assertion q, a current-case judgement, and any actual operation application remain different objects.

For one receiving use, q states one proposition with affirmative or negative polarity: whether r preserves the named invariant and makes the stated loss acceptable under named conditions. A separate current-case judgement compares exact current facts with that proposition and reports satisfies, fails, or cannot decide. The same r can have different q assertions and case results for different uses without changing arrow identity. A missing deciding fact yields cannot decide, names that fact, and states what would reopen the question; it does not create unresolved assertion polarity or require an assurance record.

Use A.20 only when the proposition is an internal constraint, A.10 only when an evidence-use claim is current, and B.3 only when an actual named assurance claim is current. Otherwise the named predicate and direct facts supply the case judgement. If the case also asserts a semantic relation between exact F.17 local senses, F.9 defines that separate Bridge and its bounded-use claim.

A system may perform exact retargeting work. Identify its enacted method, any exact A.6.1 operation application and binding, affected or newly constituted episteme, and actual change facts separately. The arrow itself performs no work, and the mathematical statement r : X -> Y infers no bare result or universal production relation.

Examples include retargeting from an episteme about a physical cabinet to one about a selected functional U.Structure, or from observations to a learned model, when the independently identified source and receiving entities really differ. For Cab-7 as the cabinet and Route-A as the selected functional structure, an independently stated behaviour-test result can supply q’s current-case basis; the judgement is satisfies only when that result meets q’s named conditions. The source expression Realises(Cab-7, Route-A) has no current direct relation governor here and therefore stops at A.6.RCD missing-governor; it contributes nothing to that judgement. For a Fourier representation change, identify the endpoint subjects under C.2.1. If the same signal remains the EntityOfConcern, use A.6.3.RT or the applicable representation-transition pattern. Use C.29 when a mathematical-lens choice, transfer or reliance question remains.