lin-0057
3.6 Observation and scalarization
A computation eventually needs measurements. LINCS separates their selection from the structural declaration.
An observation is a map
into a space \(Z\) of inspectable witnesses. A scalarization is a further map \(\sigma :Z\to \mathbb R\), possibly depending on data, probes, uncertainty, or an experimental design.
Different observations of the same obstruction can answer different questions. A supremum norm emphasizes worst-case disagreement; an empirical mean estimates average disagreement under a sampling law; a hypothesis test asks whether the available evidence distinguishes the obstruction from a null; a decision functional asks whether the failure changes an action.
11. Scalarization is not forbidden. It is postponed until the type, location, and evidential status of the failure are explicit. ↩
A scalar diagnostic may guide repair only relative to its declared observation map, sampling regime, and support. A low value outside that contract does not establish that the categorical obstruction has vanished.