NOT.7:5 - Archetypal Grounding

NOT.7:5.1 - Turn prerequisite lookup into downstream search

A small dependency account gives the immediate inputs of four tasks:

This form answers “what does D need?” directly: B and C. The new working question is “after A changes, which tasks may need reconsideration?” The reader must repeatedly search the input column for dependents, then do so again for each newly found task.

Construct the reverse index: A → {B, C}, B → {D}, C → {D}, D → {}. Here an arrow goes from a supplied input to a task using it. Starting at A, follow arrows and retain newly reached tasks until none remains. The resulting set is {B, C, D}; D is retained once even though two paths reach it.

The repair changes the lookup arrangement and supplies a reading procedure. It does not add a new dependency. It makes the required direction directly available, but finding the immediate inputs of D is now less direct. Keep the original table as a complementary view if that operation remains frequent, using NOT.6 to maintain the connection.

Now remove C from D’s input list. Remove the arrow from C to D as well. A still reaches D through B. A reader who merely drops D from the downstream set has confused removal of one path with removal of every path. The changed case tests the reading operation, not the prettiness of the index.

This construction demonstrates the dependencies and operations preserved. It supplies no measured claim that every reader finds the index faster; the local display and reading conditions can change that comparison.

NOT.7:5.2 - Share a parameter while retaining a local exception

Three quoted amounts use the same tariff, 3 units per item, for quantities 2, 5 and 7. The expressions are 3*2, 3*5 and 3*7. Their intended common assumption is known, but the written expressions repeat it independently.

To make a common tariff change local, introduce p = 3 and write p*2, p*5 and p*7. A change to p = 4 then gives 8, 20 and 28. There is one tariff definition to change, while a reader of an individual expression now follows p to that definition. The definition must remain accessible.

The next request keeps the second quote at the old tariff and changes the others. A global change of p alone cannot express that request. Write the second expression as 3*5, with its fixed-tariff meaning stated, while the others remain p*2 and p*7. The amounts are now 8, 15 and 28. If later exceptions acquire their own shared rule, give that rule its own name.

For work dominated by common tariff changes, the shared parameter can be useful. For independently negotiated quotes, the assumption of a common tariff may be wrong. The notation repair therefore needs the subject’s sharing relation; identical printed numbers alone do not establish it.