C282 — A source-qualified 2K + 15K = 17K route
24 September2026. This step follows the state and role qualifications established in C279–C281.
Dean's598+460=1058 observation now participates in a complete tagged comparison:2K+15K=17K. Each of the six retained rows has the same regular MT Flood endpoint and two qualified cumulative intermediates.
For each j2–7, take cumulative LXX ON Shem, cumulative LXX OFF Flood at index j−2, and the regular MT ON/Terah+60 Flood endpoint of C280. The first difference is598+460=1058=2×529; the second is8395−460=7935=15×529. The sum remains8993=17×529.
| j | LXX ON Shem signed | LXX OFF Flood signed | Reflected MT Flood |
|---|---|---|---|
| 2 | −6348 | −5290 | 2645 |
| 3 | −6347 | −5289 | 2646 |
| 4 | −6346 | −5288 | 2647 |
| 5 | −6345 | −5287 | 2648 |
| 6 | −6344 | −5286 | 2649 |
| 7 | −6343 | −5285 | 2650 |
The alternative intermediate is the native ON Flood boundary460 earlier than the listed OFF boundary. That route has widths598+8395. Hence both routes share their source and target:
1058+7935 = 598+8395 = 8993.
This joins the squared23 carrier to actual state-qualified endpoints. It goes beyond observing that the scalars happen to add: the frozen source records determine the two paths, and both ±1/4 seasonal components reach the same target component.
The interpretation remains a comparison between parallel chronology states. Moving from an ON Shem source to an OFF Flood source does not narrate a physical life through both Cainan settings. The regular endpoint uses130 Cainan and60 Terah; the460 in the first leg belongs to the cumulative ON/OFF difference. No regular460 insertion is substituted.
All six rows arise from one translated pattern. The mixed-state route is derived from the existing8395 realization and the source-qualified460 exchange; its equalities are not independent confirmations of those inputs. It adds no stored graph edge or new event. The absolute local placement is still separate.
Thirty-one mathematical/domain checks and seven source-authentication checks pass, with identical replay. The complete two-route ledger is included in the evidence. Author review only.
Best next bounded step — C283: enumerate only the two retained cumulative states for Shem and Flood and the two retained regular endpoint profiles. Determine whether the2K/15K split is the only all-K split in that small state domain, preserving every failure. High is sufficient.