A.6.3.RT:4 - Solution — preserve practical content across a representation change

A.6.3.RT:4.1 - Ordinary representation move

Produce the useful target first:

1. Name the user action the new representation should help: compare, inspect, traverse, calculate, communicate or replay. Identify the user’s familiarity with the notation when that changes what they can do with it.
2. Point to the source material. Recover the givens, constraints and partial construction, including the claims, commitments, uncertainty and source references that must survive. Keep unknowns identifiable as unknowns.
3. Choose an available scheme and a target representation suited to that action. Identify the formation and interpretation rules needed for this use; a familiar notation can be named without reproducing its grammar.
4. Make the smallest target that supports the action. Arrange its parts so they can be used together: for example, keep a shared element recognizable in two groupings, or align a sequence of signs with a temporal reference. Explain any meaning-bearing mark, position or timing whose interpretation is not already clear from the selected conventions. A.6.3.RT.OE develops this construction when the expression’s parts must be prepared for the intended operation.
5. Compare target and source. Mark what is preserved and foregrounded; what is rearranged, omitted or harder to recover; and which visible links or interpretations were added by the representation.
6. Try the intended operation when a short trial can decide whether the expression is useful. Apply the relevant mathematical, physical or other subject Method. Use the result to judge or repair the expression.
7. State the representation and reasoning-medium delta only as far as it changes use or blocks a likely overread.
8. Close with admissible use, non-admissible use, and a concrete return trigger and destination.

The first result is the expression and its representation note. If working with the expression establishes a new claim, its construction or argument supplies the source for representing that claim. Do not describe the new conclusion as content preserved from the original givens; sharing an EntityOfConcern does not establish that preservation.

Choose another available scheme when the current one cannot express a needed distinction. If new signs or rules are needed, develop the scheme through notation-design work. The scheme’s description can use A.6.0 for a reusable vocabulary, laws and applicability, and A.6.1 for declared operations when those are needed. Those declarations describe the designed rules. RT uses the selected rules to construct particular expressions.

Use this compact note for ordinary work:

A.6.3.RT:4.1.a - Exact episteme-construction branch

Open this branch only when the receiving use makes exact claim identity material: the target must travel independently, be cited or disputed, cross a scheme boundary for consequential use, be considered for admission as receiving episteme Y in a generated or decode-mediated case, or meet an exact-identity requirement from a named public, evidence, or assurance receiver.

Then establish exact A.6.3 construction v : X -> Y:

1. identify source episteme X and receiving episteme Y independently under C.2.1 by claim content, exact EntityOfConcern, and effective U.ReferenceScheme;
2. require the same exact EntityOfConcern; a changed concern requires A.6.4;
3. state how claims in X and any named additional source epistemes construct the claims in Y;
4. state the relation between endpoint schemes, preserved and foregrounded content, admitted loss or recoverability, prohibited strengthening, applicability, use, and return; and
5. cite every exact correspondence relation on which v actually depends. Scheme difference, similar content, adjacency, or a visible edge proves none.

A source model, graph, publication occurrence, form, carrier, table, or display does not substitute for X; a target table, diagram, notation, page, or file does not substitute for Y. If the target has no recoverable claim content, exact EntityOfConcern, or effective reference scheme, keep it as a useful rendering or candidate carrier and do not assert exact RT yet.

An exact v performs no Work and is not a relation occurrence. A system may perform representation-transformation Work under A.15.1; methods, source-use relations, A.6.1 bindings, and any A.15.PROD inception claim remain separate. E.17.0 independently decides viewpoint conformance and dependent U.View membership. E.24.PUB independently identifies publication occurrence, form, carrier, audience, and bounded use. Completing the exact construction does not itself authorize reliance.

A.6.3.RT:4.1.b - Later-specific six-participant occurrence

Use RepresentationSchemeTransitionRelation@Context only when the actual transition occurrence is itself needed and all six exact participants plus actual Work are present. The suffix @Context retrieves one independently selected A.1.1 BoundedModelUseStructure : U.Structure; it introduces no generic context kind or description-context field.

RepresentationSchemeTransitionRelation@Context <: U.Relation:
  TransitionModelUseStructureSlot = <TransitionModelUseStructureSlot, U.Structure, U.StructureRef constrained to one exact BoundedModelUseStructure>
  PreservedEntityOfConcernSlot = <PreservedEntityOfConcernSlot, U.Entity, U.EntityRef>
  SourceRepresentationEpistemeSlot = <SourceRepresentationEpistemeSlot, U.Episteme, U.EpistemeRef>
  ReceivingRepresentationEpistemeSlot = <ReceivingRepresentationEpistemeSlot, U.Episteme, U.EpistemeRef>
  SourceRepresentationSchemeDescriptionSlot = <SourceRepresentationSchemeDescriptionSlot, U.Episteme, U.EpistemeRef>
  ReceivingRepresentationSchemeDescriptionSlot = <ReceivingRepresentationSchemeDescriptionSlot, U.Episteme, U.EpistemeRef>
  direction = SourceRepresentationEpistemeSlot -> ReceivingRepresentationEpistemeSlot

The six SlotSpecs and direction are the exact RelationSignature. X and Y have the same exact EntityOfConcern and their own effective schemes. Each scheme-description episteme is independently constituted: its claims describe one exact endpoint scheme, its EntityOfConcern is that scheme, and its own effective reference scheme makes the description interpretable. A scheme label or visible notation fills no scheme-description slot.

A positive occurrence obtains only when all of the following hold together:

1. all six participants resolve exactly, and the BoundedModelUseStructure was independently selected because its model-use organization changes this transition use;
2. A.13 identifies the actual performer, and A.15.1 independently admits the dated representation-transformation Work. If the current use also needs to say exactly which assignment covered that Work, F.6 checks that separate relation against the same A.13 assignment; F.6 identifies neither performer nor assignment, and a missing or failed attribution leaves the Work intact. The Work uses all six participant values collectively through its governed inputs, result, references, A.6.1 bindings, or a combination of these;
3. exact v : X -> Y states claim construction, endpoint-scheme relation, same EntityOfConcern, preservation, loss or recoverability, prohibited strengthening, applicability, use, and return; and
4. every depended-on correspondence is an exact separately governed relation or claim.

Work, performer, assignment, method, operation application, source-use relations, and any inception claim are not seventh participants or identity discriminators. Work alone proves neither v nor the occurrence. Conversely, an inspectable v without the selected model-use structure and exact Work remains an ordinary exact construction.

The occurrence is participant-determined by the complete six-participant tuple. Changing any participant identifies another occurrence. A repeat Work episode, evidence change, publication, form, carrier, layout, transition-description edition, or C.29 output does not reidentify an unchanged tuple. A changed C.2.1 discriminator of X or Y first identifies another episteme and therefore another tuple.

A.6.3.RT:4.1.c - Transition description and source-relation epistemes

Describe the occurrence durably only after it obtains and a receiving use needs that description. The transition-description episteme is identified under C.2.1 by claim content about the exact six-participant occurrence, that occurrence as EntityOfConcern, and its own effective U.ReferenceScheme. Editing its claim graph creates another description episteme without changing the occurrence.

Its claim content may make these values recoverable; they are not extra participants or identity fields:

At least one of loss and recoverability is explicit; both are explicit when distinctions are lost and a recovery route is claimed.

When v cites a claim about one exact source relation, identify any reference-bearing episteme independently by its own C.2.1 triple: claims designating that relation and stating its exact kind, signature, defining pattern, and use in v; the source relation as EntityOfConcern; and its effective scheme. The episteme is not the relation, and citation does not make the relation obtain.

Publication may expose X, Y, the occurrence, or its description; forms, carriers, C.29 representations, and publication occurrences substitute for none of them.

A.6.3.RT:4.2 - Progressive use and local vocabulary

Use three levels, without copying one level’s burden into another:

• Ordinary target: target representation plus compact note.
• Exact construction: add X, Y, v, endpoint schemes, exact source dependencies, and claim-level loss/return when the receiving use triggers them.
• Actual transition occurrence: add the six-participant relation, Work, and optional occurrence-description episteme only when that historical relation is itself material.

Use detailed vocabulary only when it changes the next representation decision or blocks a concrete overclaim:

• semiotic mode — the meaning-bearing relation doing the main work, such as structural likeness, trace, conventional code, model-mediated correspondence, or decode-mediated recovery;
• factor delta — the representation-factor change material to review;
• source dependencies of v — the identified source claims and relations on which the construction depends, including which are needed jointly for each part of it and any required precedence between those parts. This dependency structure can branch or join;
• source-return references — links or other locators used to reopen source material for omitted detail or a changed question;
• decode-mediated case — a case whose receiving interpretation depends on a declared decoding or access relation;
• actionability shift — an apparent change in what users think they can do, which is not work authority, gate status, or permission; and
• recoverability evidence — evidence that omitted content can be recovered well enough for the declared use.

State the actual use, loss, evidence, and return once. Use A.10 or B.3 only when a specific evidence or assurance claim is current.

A.6.3.RT:4.3 - Direct and correspondence-mediated constructions

In a direct exact construction, Y is constructed from X and fixed declared configuration. State the claim construction, endpoint-scheme relation, same exact EntityOfConcern, preservation, loss/recoverability, prohibited strengthening, applicability, use, and return; no generic correspondence object is required.

In a correspondence-mediated exact construction, Y depends on additional source epistemes or governed relations among their claim-bearing contents. Recover each needed direct relation and, when v cites a claim about it, the exact C.2.1 assertion episteme. A correspondence table, model, graph edge, or scheme difference is neither the relation nor proof that it obtains.

Both profiles retain the same exact EntityOfConcern. A correspondence by itself establishes neither an F.9 Bridge nor any substitution, comparative-review, evidence, or publication claim. Add C.29 only for a current mathematical modeling or reasoning use.

A.6.3.RT:4.4 - Recurring moves and useful deltas

Recurring move shapes include tabulation, diagramming, structured-notation shift, and a same-EntityOfConcern correspondence-mediated representation shift.

In ordinary language, say what changed and why it helps: “the table foregrounds row comparison”, “the diagram foregrounds dependency shape”, or “the notation foregrounds explicit argument positions”. Add salience, topology, actionability, calibration, interactivity, or semiotic-mode detail only when it materially changes use or misuse risk.

A.6.3.RT:4.5 - Preservation, loss, decode, and composition

A.6.3.RT:4.5.a - Preservation and conservativity

The ordinary move preserves the practical content named for the use. The exact branch preserves the same exact EntityOfConcern across independently constituted X and Y while changing scheme and often reasoning medium.

Check for unsupported strengthening when a target:

• upgrades a source-visible relation into dependency theory or another relation not present in the source;
• turns geometry, notation, embedding proximity, or decoder output into ontology-by-default;
• adds a Bridge, substitution, comparative, mechanism, temporal, or control claim that the source does not state and that has not been independently established under its governing pattern;
• collapses source alternatives, uncertainty, or bounded scope into one wider commitment; or
• treats decode-mediated recovery as direct givenness.

Check each target-side connective against the source or exact same-EntityOfConcern correspondence. A clearer, more structured, or more formal target does not establish a broader reliability claim.

A.6.3.RT:4.5.b - Loss and recoverability

State which distinctions, inspection possibilities, uncertainty cues, or local qualifiers are lost, foregrounded, rearranged, or harder to recover. The target may remain useful under a reliability claim bounded by the source or with an explicitly narrowed admissible use. If it remains honest only through a declared narrower use and source return, A.6.3.CSC is primary.

A.6.3.RT:4.5.c - Decode-mediated entry

A latent or decode-mediated case stays bounded until it has source material for the same concern, a decoding or access relation, recoverability evidence for the intended use, admissible and non-admissible use, remaining user action, and source return. When exact reliance is claimed, recover exact source episteme X, receiving episteme Y, construction v, and the source dependencies of v defined in §4.2.

A latent region, activation pattern, embedding, probe result, decoded rendering, publication form, or carrier may help locate the case but fills no episteme endpoint. Missing recovery evidence keeps the result exploratory, report-only, or blocked.

A.6.3.RT:4.5.d - Composition and reopen rule

Repeated same-regime normalization may be idempotent; heterogeneous representation shifts are generally order-sensitive. For an ordered sequence of representation shifts, compare the source and target of each shift and carry forward the loss from earlier shifts. Keep the source and target, content under test, scheme delta, preserved and withdrawn commitments, loss/recovery, and remaining action recoverable at every step.

Reopen the affected account when source content, endpoint identity, recovery assumptions, pins or provenance, correspondence or counter-witness disposition, primary semiotic mode, intended publication or receiving use, or accumulated loss changes. A changed EntityOfConcern requires A.6.4; a changed target-side claim uses the pattern that defines that exact claim.

A.6.3.RT:4.6 - Boundary triggers