What the common grammar retains
The compact account reuses rules across many outputs. Its input cost includes source choices and placement, not only the numerals in a formula.
| Family | Retained source information | Generated together |
|---|---|---|
| Ordinary genealogies | Selected rows, order, named change supports, terminal and count convention | Complete Regular/Cumulative differences and interior ladders |
| Regular variant field | Terah, Cainan and Sojourn choices; applicable support | Eight offsets and their consecutive gaps |
| SP cap | Native births, baseline lives, inclusive capacity rule | Nine capped outputs and located reduction488 |
| SP rectangle | The source fields, standard frames, −215 state, week/decade openings and endpoints | Two equal Key gains, retained9200 and Priestly10000 |
| Moses family | Selected MT path, late event edges, Moses1526 and named cuts | Twenty-five coordinates, five blocks and related cycle spans |
| Inverse/Keys | Original component words, retained-zero policy, appointed factor and pivot | Whole transformed paths, shared totals and exact rational prefixes |
| Covenant | Local ages and offsets, lifespans, terminal, state and phase | Regular field, stack, clutch columns and forced/conditional joins |
| Counts/NT | Category labels, source order, templates, named slots, scale and grouping | Recoverable registers, comparisons and permitted symmetries |
The five-amplitude row model describes differences rather than replacing all source rows. The century amplitude is derived from those paired rows. Similarly, measured Covenant gaps and cumulative prefixes are consequences once their input path is given.
Residuals and clipped excesses have a different role: they retain information discarded by a chosen representation. Keeping them permits exact recovery, but does not count as generating that information from the rounded or capped output.
No numerical description-cost weights were fixed for this study. The result is therefore a transparent structural compression, not a globally minimal model or a statistical ranking of possible source histories.