C284 — Completeness with independent annual selectors
24 September2026. The j−2 pairing is released in this test.
The six2K/15K paths exhaust the3072 independent-selector comparisons in the held fields and two regular profiles. The first factor23 recovers the index relation; the second factor23 selects the state configuration.
Let cumulative Shem index j and cumulative Flood index i vary independently over0–7, and regular Flood index k over2–7. The two cumulative Cainan states and two regular profiles remain those of C283. No new chronology record is introduced. The source widths are
A=600+i−j+460(s−f), B=8393+k−i+460(f−r).
Because460 is divisible by23, the first width is divisible by23 exactly when2+i−j=0 in these short ranges. The second is divisible by23 exactly when−2+k−i=0. Thus i=j−2 and k=j. These are the source pairings previously held fixed, now recovered by the declared divisibility requirement.
This leaves48 rows, precisely C283's eight state patterns at six positions. Requiring a second factor23 leaves only s=1,f=0,r=1, with widths1058 and7935. There are six such rows, at j2–7.
| Filter in the full3072 domain | Count |
|---|---|
| First leg divisible by529 | 72 |
| Second leg divisible by529 | 96 |
| Total divisible by529 | 192 |
| Both legs divisible by23 | 48 |
| Both legs divisible by529 | 6 |
A divisible total alone is much less selective than divisible constituent legs. The failed cases are retained in the complete3072-row evidence ledger. Counts describe this finite arithmetic domain and do not estimate chance or intentionality.
This supplies a reduced grammar for the retained source pattern:23 divisibility determines the two-index offset and shared regular selector; the additional23 selects the mixed-Cainan/restored-MT configuration. The requirement of divisibility is explicit. It does not follow from chronology alone, nor does it impose equality of images under independent local translations. C276's distinction therefore remains intact.
Eight aggregate mathematical/domain checks compare the exhaustive ledger with these independently stated formulas and counts. Eight separate source-authentication checks pass. Exact replay agrees. No historical campaign was rerun, no new source event was added, and no canonical file was edited.
Best next bounded step — C285: broaden only the regular Flood endpoint to the already documented MT/SP/LXX Cainan/Terah/sojourn state domain. Test whether the six all-K paths remain the only admitted Flood realizations. High is sufficient.