30.1A correction with an identified object
Provisional translation allowed reading to continue with a disputed term explicitly marked. A correction can do more: it can name the object being corrected. At minimum it should identify the exact source version affected and the proposition that changed. That pair of identifications is enough to give downstream work an address rather than a topic.
Consider the declared dependency graph G01. Source S0 supports summaries A and B; A informs C; unrelated source T informs D. Suppose S0 is revised. Because A and B are declared dependents of S0, and C is a declared dependent of A, the changed source makes A, B, and C reachable review candidates. D has no declared path from S0 and does not join that candidate set under the stated edges.
The identification does two kinds of work. Naming the version prevents a downstream summary from being examined against the wrong historical state of S0. Naming the changed proposition narrows the question reviewers must answer: whether the inference in A, B, or C still holds given that particular revision. Without both, the instruction "S0 was fixed" leaves ambiguous whether the maintained copy as it now stands or an old version retained as history is meant, and which of its claims moved.
One qualification governs everything that follows. Reachability here computes review candidates, not findings of error. A, B, and C may all remain supported after the correction. Equally, unchanged wording or an unchanged numerical total is not a clean bill of health: S0 could have changed its explanation while retaining the same total, and a downstream inference might have depended on the discarded explanation. Finally, the graph records declared dependencies only. A dependency that was never entered into G01 will not be reached by this computation, so the candidate set is bounded by what the graph honestly declares rather than by what actually bears on each summary.
Once the correction names its object, the question of downstream inspection becomes computable rather than intuitive. A vague assertion that “the topic is wrong” tells a reader nothing about which derived objects inherit the problem: the assertion identifies neither the premise in dispute nor the relations through which the dispute might travel. An identified source version and changed proposition, by contrast, can be matched against the declared dependencies.
In G01, those dependencies are the edges S0→A, S0→B, A→C, and T→D. When S0 changes, reachability yields the review candidates A, B, and C. D is outside that set because no declared path runs from S0 to it. This gives the correction an initial scope without prejudging its result. The relevant limit is that reachability is a candidate computation, not a finding that A, B, or C is false; a descendant may recompute unchanged even when its explanation has shifted. Nor does the absence of a path to D establish independence, since undeclared dependencies lie outside the graph.
Within the declared scope, three events must remain distinct. Notification says that a premise has changed. Recomputation asks what, if anything, derived from that premise now differs. Renewed judgment decides whether a downstream summary or decision remains warranted. These can come apart: a corrected source may revise its explanation while retaining the same numerical total, and equal output strings do not show that every associated inference is still supported.
Likewise, maintenance and history separate. A maintained copy may be revised while an older version remains identifiable as history; the fact that both exist does not tell downstream readers which one their summaries presently depend on. Determining that dependency is the next problem.
30.2Dependencies and stale links
Once the correction identifies its object, the declared graph can be consulted rather than the whole record searched. In G01, a change to S0 makes A, B, and C reachable along declared edges, since the paths S0→A, S0→B, and S0→A→C are present. D is not reachable, because its only incoming declared edge comes from T. This computation yields review candidates, not findings. Nothing in reachability says that A, B, or C is false, and the absence of a path to D does not establish independence from S0: undeclared dependencies lie outside the graph.
A link can mislead in the opposite direction. A pointer from C to A may continue to resolve long after the target has been superseded, and long after the source S0 behind A has been corrected. Resolution is a property of the pointer and the address it names; evidential currency is a property of the relation between the target's present content and the inference drawn from it. A live link is therefore not a current evidential dependency, and unchanged prose in C is not insulated by the fact that its reference still works. Equal output strings, and even an unchanged numerical total, leave open whether the corrected source now offers a different explanation that no longer supports the earlier inference.
Separating the events keeps review bounded. Reachability of A, B, and C determines which objects are candidates for notification; recomputation updates a summary or total where the correction bears on it; renewed judgment decides whether an inference still stands. These can come apart: a descendant may be recomputed without renewed judgment, or judged again without any change to its output. The qualification to retain is that this path computes candidates and stages of attention, not the standing of each descendant. Whether an old version should remain identifiable for auditing the earlier reasoning is the next question.
A surviving link may still fail to identify which evidential relation needs attention. That distinction carries into version handling. When a maintained copy is revised, the prior version should remain identifiable as history, because it records what earlier reasoning relied on. Preserving it is an audit aid: it lets a reviewer reconstruct why a conclusion was drawn at the time. It must not be presented as the latest account, and its continued availability does not extend its claim to current support.
In G01, that separation matters because a correction to S0 can leave some outputs visibly unchanged. A numerical total may survive while the explanation supporting it changes. Equal strings therefore do not show that every inference associated with them remains supported. A summary C may read exactly as before even though its declared premise chain runs through A to S0; unchanged wording is not a license to skip renewed judgment.
The revision path should distinguish four events. Notification reaches the holders of downstream items. Recomputation updates what follows mechanically from the correction. Renewed judgment re-examines whether the inference still holds. Receipt by downstream readers concerns whether the updated account has actually arrived. None entails the next: sending notice is not recomputation, recomputation is not judgment, and an updated copy is not read.
On the declared edges of G01, a change to S0 makes A, B and C review candidates. That computation says only that these items lie on a declared path; it does not find any of them false, and it cannot exclude dependencies that were never declared. The qualification is therefore internal to the method: reachability allocates scrutiny, while the substance of each inference still has to be decided separately. Where no declared path exists, as with T and D, the graph is silent rather than reassuring.
30.3Which descendants are affected
Keeping the old version identifiable as history answers one question; the next is how far a correction must travel. In the proposed correction graph, the declared edges run from S0 to summaries A and B, from A to C, and from the unrelated source T to D. These edges record dependencies that someone has declared; they do not themselves establish that any inference in the chain is valid.
When S0 is corrected, the graph yields a definite candidate set. A and B sit directly downstream of S0 and must at least be flagged. C is two steps away, but the path S0 → A → C is declared, so C joins the set as well. D remains outside it: the only path into D runs from T, and no declared edge connects S0 to D. The computation is therefore local on this graph's scale—a correction to one source marks A, B and C for possible review and leaves D untouched.
The word "possible" carries weight. A flag places an object in a review queue. Sending a notification, receiving it, recomputing an output and reaching a new judgment are separate events; traversal does not prove any of them occurred. A and B may need revision, recomputation, or neither; C may depend on the part of A that the correction did not alter. The graph does not decide among those outcomes. It answers only which descendants can no longer be assumed to have escaped the change. Nothing licenses skipping a descendant merely because its prose happens to be unchanged.
This is why the candidate set is defined by the declared edges rather than by the underlying world. The graph supports a routing proposal: reachability identifies candidate objects. Contacting responsible readers would require an additional mapping from objects to recipients and an actual delivery step. Because its edges are declarations rather than proofs of valid inference, the traversal establishes only that these descendants lie on a declared path from the changed source.
Because the declared paths from S0 lead to A and B and then from A to C, all three belong to the candidate review set, while D does not. That result routes attention; it does not determine any verdict. A dependency edge records that one item was taken from or informed by another, so C’s position in the graph makes renewed examination appropriate without establishing that C’s conclusion is now false. The graph answers where a changed source might have traveled; examination of the surviving material answers whether anything has actually failed.
The absence of a path to D carries a narrower meaning. Under the declared edges, D is outside the propagation from S0 because T, not S0, informs it. If D also relied on S0 through an edge that was never recorded, the graph would omit that relationship and fail to flag the affected item. That is a separate risk in dependency declaration: reachability is reliable only over what has been made visible. It cannot compensate silently for dependencies the graph never knew.
The distinction between direct and transitive dependence gives the candidate set a practical scope. A and B may each need review as direct dependents, and C as a transitive one, yet their eventual responses need not match. A premise may have to change, a derived item may survive intact, or an interpretation may need reconsideration. Even an unchanged total or identical output text leaves open whether the inferences attached to it remain supported. Thus the graph can narrow the work to a tractable set without promising that every reachable item was wrong—and without treating every unreachable item as secure beyond the declared record.
Notification therefore has a limited job: it tells maintainers of A, B and C that their declared premises may have moved. It neither recomputes anything nor renews the judgment by itself. Once those items are identified, the response can be assigned according to what each item actually depends on.
30.4Recomputation versus judgment
Once the correction to S0 makes A, B and C reachable, the candidate set is only the first output of review. It does not say what work each candidate requires. Two responses must be kept apart. Recomputation reruns a derivation with the corrected input: A's derived count is recalculated under the procedure that produced it. Renewed judgment asks whether an interpretation or a decision remains warranted in light of the corrected source.
The two questions have different conditions of success. Recomputation is bounded by the declared edges and the operative procedure; given the correction and the same rules, it yields a value to be recorded against the corrected copy. Judgment is not settled by that value alone. It considers what the quantity supports, how A bears on C, and whether the earlier conclusion was framed in terms the corrected source still sustains. Renewed judgment may confirm the earlier conclusion; what differs is that the confirmation is now deliberate and traceable rather than merely inherited from an unchanged claim.
The distinction supplies the division of labor within the revision path. Notification identifies the affected candidates, recomputation updates derivations, and renewed judgment restores or withholds the standing of interpretive claims. These are three events, and they need not complete together: a maintained copy may be recomputed and recorded while an old version remains identifiable as history and a downstream reader has not yet received notice. In G01, D lies on no declared path from S0, so neither response is triggered there; a hidden dependency would fall outside the graph and therefore outside this account of the trigger.
That partition also answers the cost objection in part. Reachability creates candidates for review, but it does not oblige every candidate to undergo judgment of the same depth; the kind of response is settled only after the candidate is identified.
Once recomputation and renewed judgment are kept apart, a further distinction is needed: an output can survive recomputation unchanged while the argument attached to it does not. Suppose a corrected S0 produces for A the same numerical total as before. The count needs no adjustment, yet A's explanation may still rest on the premise that has just changed. Restating the total leaves the output in place while making its supporting account stale.
In the stipulated graph, the declared edges are S0→A, S0→B, A→C, and T→D. A change to S0 therefore makes A, B, and C reachable review candidates: A and B directly, C through A. D has no declared path from S0 and so is not a candidate under this graph. Each candidate nevertheless raises a different question. For A, recomputation may confirm the total while judgment examines whether the inference summarized by A still holds. For B, the numerical result may itself move. For C, what is at stake is whether the interpretation inherited through A remains warranted after A's premise has changed.
In a larger graph, reviewing every descendant might exceed the available budget, and repeated notifications might burden recipients. Neither cost nor fatigue is measured by this small example. Reachability narrows attention to declared descendants; selecting among those candidates would require a further triage rule. But its limit is equally sharp. Reachability is a computation of review candidates, not a finding that any reachable descendant is false; and if a dependency was never declared, the graph cannot surface it. Hidden dependencies remain outside this graph even though they may exist.
The practical consequence is that identical output strings or totals do not demonstrate that every associated inference remains supported. An unchanged summary can depend on a changed premise, so preserving the text and preserving its standing are separate operations. Distinct events—reachability, notification, renewed judgment, and receipt by downstream readers—should not be collapsed into a single verdict of "affected" or "unaffected."
30.5Withdrawal and historical versions
Withdrawal does more than remove a sentence from use: it changes the standing of claims that were supported by it. In G01, when S0 is withdrawn, A and B lose an active premise, and C loses support through A. That change of status is a consequence of the declared dependencies, even if none of the downstream summaries has yet been rewritten. The inferential step is therefore from withdrawal to suspended support, not from withdrawal to falsehood. A, B and C become review candidates, not refuted claims.
This matters for outputs that look stable. A recomputed summary may retain the same numerical total or the same wording while its explanation no longer rests on the premise it once relied on. Treating textual or numerical identity as evidence of unaffected support would repeat the error identified for recomputation. Conversely, a renewed judgment need not alter the prose: if a replacement premise licenses the same summary, the summary can stand, but it now stands on a different basis, and that difference belongs in the record.
The record should therefore keep the withdrawn version identifiable as history while marking its changed status. A maintained copy can be revised, and an old version can remain recoverable together with the dependency facts in force when it was produced. Historical identifiability is what makes a later reader able to tell whether a summary was supported by S0 at the time or reconstructed after its withdrawal. This does not yet settle how widely historical versions are exposed; keeping history and giving unrestricted access are separate questions.
One qualification constrains the whole procedure. Reachability in G01 computes candidate descendants under declared edges: A, B and C, while T and D lie outside the S0 path. It does not certify that every candidate is unsound, and it cannot see dependencies that were never declared. Withdrawal can therefore prompt a bounded recomputation and renewed judgment, but it cannot by itself certify that the affected set is complete.
Retaining an identifiable historical version does not commit an archive to presenting withdrawn material without restriction. The record can acknowledge that the withdrawn statement once existed, record when and on what basis its status changed, and preserve enough context to reconstruct why earlier summaries were made. That treatment keeps revision history intelligible without reinstating the claim as a live premise. Access to the historical object and endorsement of its content are separate matters, and the scope of preservation need not determine the scope of exposure.
In G01, a change to S0 makes A, B, and C reachable review candidates because the declared edges connect S0 to A and B, and A to C. It does not make their current versions false. The graph records declared dependencies, not the validity of any inference along them. D is untouched by this calculation only because no declared edge leads to it from S0; a hidden dependency would be outside the scope of the graph.
The practical implication is to separate the revision path into distinct events. A change to S0 first triggers notification that previously relied-on premises may now be stale. Recomputation then determines which descendants remain reachable and whether any explanation, total, or inference must be checked. Renewed judgment records whether each descendant is retained, amended, or withdrawn. Receipt by downstream readers is a further event, since a correction has not reached those who rely on a summary merely because its calculation has been updated.
Equal strings can conceal a changed premise: a corrected source may alter its explanation while leaving a numerical total unchanged. Preserving both the old and current versions therefore supplies history rather than proof. A maintained copy may be revised while its predecessor remains identifiable as history, but that visibility must not be taken as a license to leave superseded claims circulating in decision contexts.
30.6Prioritizing revision effort
Keeping the withdrawn statement identifiable as history does not require revising every descendant at once. Revision effort is better allocated by three explicit criteria: the decision the downstream item currently supports, the declared dependency path from the changed source, and the plausible consequence if that premise is altered. In G01, a change to S0 makes A, B, and C reachable review candidates, because S0 supports A and B and A informs C. T and D lie outside that reach, since the only edge into D comes from T.
The three criteria order distinct kinds of work rather than collapse them into one. Notification asks who must learn that the premise changed; recomputation asks which derivations or totals should be checked; renewed judgment asks whether an identified decision still rests on support that the corrected premise provided. A downstream owner may need notice without recomputation, or recomputation without a new decision. Conversely, where a decision has a fixed schedule or a consequence that the change could plausibly alter, renewed judgment should not wait behind lower-consequence recomputation. A numerical total may remain the same while its explanation changes, so equality of output strings or totals is not by itself a reason to close the review.
The limit is that reachability is a review-candidate computation, not a finding that A, B, or C is false. G01 records declared dependencies only; an undeclared dependency from S0 to D would place D outside the computed reach despite a genuine link, while an undeclared dependency from A to some other item would omit a real candidate. Criteria therefore yield a defensible order of attention under the graph as declared, not a proof that unexamined items are unaffected. Each event—reachability, notification, recomputation, renewed judgment, and receipt by downstream readers—remains separate and should be tracked accordingly.
Priority in revision work is an ordering of review effort, not a prevalence estimate. Prevalence asks how often a kind of object, defect, or source condition occurs; priority asks which affected decision deserves attention first. These are different quantities, and neither substitutes for the other. A low-frequency correction may still warrant early review when it changes a premise on which an important decision rests.
Consider the maintained copy that may be revised while its old version remains identifiable as history. The copy’s correction can be uncommon in the set of maintained objects yet consequential for a particular decision. Reachability, notification, renewed judgment, and receipt by downstream readers are distinct events, so limited circulation does not by itself settle urgency. If a changed premise affects a decision that is still live, the appropriate response is earlier review even though the correction affects few objects. Conversely, a common defect may be safely scheduled later when it leaves the relevant decision unchanged.
This qualification matters for the ordering criteria already introduced. Decision impact, dependency, and plausible consequence should determine priority under explicit criteria; frequency may help describe scale, but it is neither necessary nor sufficient for urgency. A correction is not automatically high-priority merely because it is common, nor low-priority merely because it is rare. The relevant question is what decision would change if the premise were accepted, and whether that change is plausible and material in the current setting.
Nor does notification ensure renewed judgment, or renewed judgment ensure receipt by every downstream reader. These are possible stages, not inevitable ones. Priority should therefore be assigned at the point where a particular decision and dependency are identified, while uncertainty about later reception remains attached to that claim rather than converted into a general estimate of how often such corrections occur.
30.7A visible unresolved queue
A revision queue should record not only which objects are affected but why each remains unresolved. In the maintained-copy setting already noted, a changed source can leave a summary’s wording unchanged while the premise supporting it has changed. The summary is therefore an affected object; pending recomputation or renewed judgment is the reason it remains open. A bare list of titles would preserve the first item while losing the second.
An entry therefore needs an object identifier, the dependency linking it to the changed premise, the operation still owed, and a condition for closure. The last field matters because recomputation and renewed judgment are distinct: recalculating a figure asks whether its value follows from current inputs, while reconsidering a conclusion asks whether the resulting claim should still be accepted. If both are owed, one entry should say so rather than treating either completion as closing the whole case.
This record also disciplines comparisons. Two encodings of a queue—one separating dependency from closure condition, another collapsing both into a status label—can be compared only when the task and inputs are fixed: the same changed premise, the same candidate objects, and the same standard for deciding what is owed. Even then, the count of pending entries measures open obligations under that encoding. It does not measure how common errors are, how serious they are, or whether later correction is inevitable. An entry is necessary for tracking an obligation but not sufficient to discharge it; it makes later correction possible and trackable.
An entry also has to survive a second premise change. If the source changes again before the closure condition is met, the recorded reason should be revised rather than the object being silently treated as pending for the original reason. Otherwise the queue correctly identifies the object while misdescribing what remains owed.
A queue of unresolved objects, with the reason each remains pending, is an inventory of unfinished work. Its evidential scope is narrow: it shows that a task was noticed and deferred, not that any correction was propagated. On the maintained-copy illustration, where a revision sits beside an older version preserved as history, the queue can show which objects the change touches and what stays open. It cannot show which downstream summaries have been recomputed or which readers have been notified.
The distinction is between necessary and sufficient conditions. A queue entry is necessary for managing the revision path: without a record of what was left undone, a later maintainer cannot reconstruct the remaining work. But it is not sufficient for propagation. Recording an object as pending is consistent with every subsequent outcome. The correction may reach downstream readers, it may trigger recomputation without notification, or it may stay untouched indefinitely. Reachability, notification, recomputation, renewed judgment, and receipt are separate events, and each can fail while the queue still looks orderly.
Conditional on a queue that lists only unresolved items, its length measures outstanding work among the objects it tracks. It does not measure reader coverage. Comparing queue sizes across two encodings is meaningful only when the task and inputs are fixed: both encodings must cover the same affected objects and treat "pending" as ending at the same stage of the revision path. Otherwise a shorter queue may reflect narrower scope or a looser threshold for completion, not faster correction.
The queue therefore prompts downstream verification; it does not certify it. An empty queue is equally inconclusive. If no entry records receipt, an absent pending item shows only that no unfinished task was logged, not that readers have seen the correction.