NOT.5:4 - Solution

Choose the receiving operation → construct the translation → obtain and return an answer → expose collapsed distinctions → repair the needed loss → establish the required return.

NOT.5:4.1 - Choose what must remain possible

Name the source notation, target notation and intended reader operation. Specify the source expressions admitted for this use and the context required to interpret them. A drawing may use position as meaning or only as layout; a spoken sequence may rely on a separately maintained beat. Carry the context that the question uses.

Decide what the recipient must return: a value, a construction, an explanation, a reconstructed expression or a proposed change. These demands can require different information. An answer expressed in target units or names needs a way back to the source question.

If a source choice is unresolved, preserve the alternatives or the unresolved status that matters to the question. A default introduced by the translation is an added decision. Accept it only when making that decision is part of the intended work and its basis is available.

NOT.5:4.2 - Construct target expressions from interpreted source structure

For every kind of source part used by the operation, give its target construction. Then give a rule for translating their composition. Preserve operand order, connections, scope and reference where the interpretation uses them. Copying labels does not supply those rules.

Translate an expression by following its construction. For a diagram, this can mean declaring its nodes and translating each directed connection; for a sequence, translating each event while retaining its position or duration. Derive the target composite from those contributions. NOT.2 supplies the formation and reference rules; NOT.3 supplies the reading operations.

When a source ingredient has no target counterpart, choose an explicit treatment. Extend the target, carry an annotation, leave a visible unresolved part, or limit the admitted source expressions. Make this choice from the receiving operation. Silently deleting the ingredient or guessing its counterpart leaves the recipient unable to locate the loss.

For a mathematical interpretation, MATH.18 develops preservation and reflection of the required constructions and assertions. For a bijective change of mathematical representation, MATH.7 transports the operations through the inverse. Use those arguments when their conditions hold; a correspondence between printed signs alone does not establish them.

NOT.5:4.3 - Perform the receiving operation and recover its answer

Translate a small source expression, perform the intended operation in the target and interpret the result as an answer to the original question. Show the return explicitly. If the target gives a list of numbered nodes, say which source nodes those numbers refer to. If it supplies only a bound or a set of possible answers, retain that limitation on return.

Compare this result with what follows from the source under its declared interpretation. A mismatch locates a failed translation rule, a missing premise or a target operation that answers a different question. Repair the affected correspondence before relying on that answer.

A target-side answer can be spurious for the source if the target admits additional possibilities. Retain the source restriction or construct the needed reflection argument. For example, allowing arbitrary real values does not preserve a source question that admits only whole counts.

One successful expression establishes that case. A reusable translation needs an argument for its admitted family, such as a rule-by-rule construction over expressions. A separating example can refute a proposed general claim. Additional checking is warranted when its result can change the use or repair of the translation.

NOT.5:4.4 - Expose distinctions the target collapses

Look for different admitted source expressions with the same target expression. Ask whether the required operation gives different answers on them. If it does, the target alone cannot determine that answer: the translation has removed something the work needs. Section :5.2 makes this failure visible through cue order.

If every collapsed pair gives the same needed answer, the loss need not obstruct that question. For a claim about the whole admitted family, justify this independence over that family rather than infer it from a few pairs. MATH.2 supplies the mathematical construction through equivalence classes when that form is useful.

Include differences in assumptions, unfinished choices, references and reading context when they can change the answer. Equal visible strings can have different interpretations under different contexts. Conversely, two differently laid out diagrams can express the same directed structure when position has no role in their interpretation.

For several translation stages, follow the information needed by the final operation through each stage. A later, richer format cannot recover a distinction that an earlier stage removed unless another input supplies it.

NOT.5:4.5 - Repair the loss needed by the work

Choose the least burdensome repair that actually restores the operation. Retain the original expression when an occasional return is enough. Add the missing distinction to the target when the recipient must work independently. Otherwise, carry supplementary information with a defined recovery rule.

Call that supplementary information a complement when the target and the supplement together permit the required source recovery. State what it contains and how the return uses it. In :5.2 the position of a cue complements its count; in :5.3 a retained phase duration selects one backward update. A statement that the conversion is reversible cannot replace this construction.

Keep the target and its supplement associated with the same source. If the target is edited, check whether the old supplement still permits the intended reconstruction. A stored position can become invalid after deleting an event. Locate that conflict instead of returning an invented original.

The repair may instead be an explicit narrower use. A cue count remains useful for inventory even when it cannot recover order. Retain that useful result and identify the additional contribution needed by an order-sensitive question.

NOT.5:4.6 - Establish the return that the work requires

For an unchanged round trip, translate and reconstruct the source at the required level: the same expression, the same interpreted structure or the same needed consequence. State which level is obtained. Recovering a directed graph up to layout does not recover where its boxes were drawn.

For a target edit, construct a backward update using the edited target and retained source information. Specify what remains fixed and what may change. In the ordinary single-view setting, check two properties: returning an unchanged view leaves the source unchanged; translating the updated source yields the requested view. These properties still leave a choice of update policy, worked in :5.3. They do not mean that all possible edits must be accepted.

When several views constrain a shared source, distinguish the user’s changed requirement from values merely copied from the earlier view. NOT.6 handles their propagation and possible conflict. An unchanged value in a submitted view is not necessarily an instruction to freeze it.

If conversion performs effects such as asking a reader for missing information or changing external state, include the relevant behavior in the return claim. Recovering the same output value need not undo those effects. CMP.12 supplies the computational correspondence when an executable implementation is required.

Stop once the chosen operation and required return work within their stated conditions. Retain the translation rule, any supplement and the loss that changes later use where the recipient can find them. Reopen the affected construction when the receiving question, source interpretation or admitted edits change.