# C293 — The 13K arrangement and the fixed 8K reflection

24 September2026. Uses the retained13K and8K carriers with their operations stated.

**The common-offset1,3,5,7 arrangement is centered at4K+i, not uniformly at4K.** Under the fixed composition J(y)=4232−y, only the i=0 inner pair matches, and that row lacks its outer Noah partner. None of the complete common-offset rows closes under this fixed reflection.

After translating the cumulative pair by13K, its centers are K+i and3K+i. The retained regular endpoints are5K+i and7K+i. Both pair sums are8K+2i. Consequently the fixed reflection about coordinate4K=2116 requires regular partners5K−i and7K−i; the actual common-row partners exceed them by2i.

At i=0 the inner comparison is1587↔2645. The first point is the generated13K image of the cumulative LXX OFF Flood opening; the second is the reflected restored MT G1 Flood close. Their sum is4232. The outer generated point529 would need Noah3703, which remains absent.

For the complete SP rows i2–5, the fixed-reflection residuals are4,6,8,10 years. These are not phase errors: both ±1/4 components retain exactly the same residual after reflection reverses the component order. A separate reflection centered at4K+i would close each numerical row, but this study does not adopt row-dependent axes.

The operation J is the composition of the existing global Mirror with the8K translation. The global Mirror remains fixed at January AD1. Naming its comparison center at signed coordinate2116 neither moves that global axis nor asserts a new civil-year convention.

This tests the complete common-offset family, not all independent indices in the full cumulative fields. The negative result should not be extended beyond that domain. Twenty-six mathematical/domain checks and eight authentication checks pass; exact replay agrees. Author review only.

**Best next bounded step — C294:** release the common annual offset while keeping13K and8K fixed. Search the full inherited LXX ON Shem and OFF Flood fields against the existing regular endpoint register. This checks whether another source-qualified pairing closes the fixed reflection without changing an axis or bridge. High is sufficient.