## A short operation inventory

| Operation | Construction | What must be retained |
|---|---|---|
| Select a declared source state | Use the finite source inventory with its row and event bindings. | No unlimited repeated variant addition is inferred. |
| Choose and accumulate a measure | X_i=a+sum of selected downstream weights. | A complete ordered field and anchor recover adjacent weights. |
| Round resolved row counts | Q(n)=5 floor((n+2)/5) on the positive integer count domain used here; retain e=Q(n)−n. | Order is preserved; additivity and exact invertibility generally fail. |
| Cap a resolved lifespan ledger | Y_i=min(L_i,B_i−F+1), with source-qualified count/death tags. | Monotone, idempotent, many-to-one. |
| Reverse admitted original components once | Strip and retain trailing-zero placeholders; reverse the remaining decimal core; restore placeholders. | Partition and digit register matter; no general additive law. |
| Apply an exact Key about a pivot | D(k,a)(x)=a+k(x−a); selected components may have separate declared roles. | Exact rational differences scale; integer-stage domains require divisibility. |
| Translate a specified field | Move precisely the source-declared nodes by the stated amount. | Internal differences survive common translation; scope cannot be enlarged. |
| Group or coarsen with retained measure | Sum declared blocks or identify source classes; carry multiplicities when needed. | Symmetry descends only when the grouping respects the action. |

These operations have different domains and information effects. Together they form a source-qualified network of constructions. They do not form one group of reversible date transformations.