# 490d C316 — Distinct antecedents for fixed17K and8395

24 September 2026. Step 3 of the ten-step authorization C314–C323.

Keeping8993=17K and8395 fixed, all five selected Flood boundaries have a unique derived cumulative Flood antecedent **h=i−2**, with the same cumulative phase as Noah. The five h values are5,4,3,2,1 as j increases3…7. They are already admitted annual stations. This is selection of another cumulative station, not a cumulative Gear operation.

The two-year ancestor difference supplies exactly the missing amount:

`N−f = (8993−8395)+(q_i−q_h) =598+2=600`.

This succeeds in all ten exact components, but changes the ancestor. It does not repair C315's failure under a common ancestor.

**C271's actual Flood ancestry must remain distinct.** It is cumulative LXX_OFF **Shem at indexi**, not cumulative Flood at h. Write `p_i=−5890+i`, `q_h=−5290+h`. Then

`p_i+8993 = q_h+8395 = f`, with `q_h−p_i=598`.

Both routes reach the same source Flood coordinate and phase. Their starting roles, indices and declared paths differ. C271's local translation5888/reflection layer is retained; the endpoint T8993 comparison does not erase that intermediate provenance.

| Shem j | Noah i / derived Flood h | SP state | C287 at i / j / h | Regular descent available |
|---:|---|---|---|---|
|3|7 /5|G3 primary|No /Yes /Yes|No starting alias|
|4|6 /4|G3 companion|No /Yes /Yes|No starting alias|
|5|5 /3|G2 primary|Yes /Yes /Yes|G3 start→G2 start|
|6|4 /2|G2 companion|Yes /No /Yes|G3 close→G2 close|
|7|3 /1|G1 primary|Yes /No /No|G2 start→G1 start|

Where C315's same-i8395 candidate is an admitted next-Gear Flood, the permitted regular one-Gear descent subtracts2 and agrees with the h-selection endpoint. This is a partial correspondence in three cases. At the upper boundary no initial alias exists; one cannot descend from an unadmitted G4. The five-case cumulative selection therefore has a larger domain than this regular descent. Full C287 support at all three tested indices survives only j=i5,h3.

## Verification and limits

54 main assertions and 15 frozen-input/predecessor checks passed. A second main replay produced byte-identical DATA and RESULTS. Separate review scope and agreement are recorded in the evidence. All frozen originals and standing controls remain unchanged. These are verification counts, not independent-witness counts.

No common-ancestor repair, source-role replacement or cumulative Gear. Direct rectangles and stronger all-K C287 membership must be distinguished.

Mirror/529 remains the focus: K=529, E=25/23, P=70/69. Global paired Mirror January AD1; local junction x=1 January AD2; no civil year zero. Regular Gears remain Noah/Shem/Flood only. SP minus-one companion is local to SP Noah/Shem. No cumulative/upstream Gear, new endpoint or phase, fitted anchor, global axis, z-law, canonical or graph edit. Capture now; canonize later. Source state, event identity, generated coordinate and phase ancestry remain distinct. Exact arithmetic and source membership do not establish intention or independent historical witnesses.

## Decision after this result

**C317, proposed and unexecuted:** Verify the five inherited same17K rectangles using cumulativeShem_i/Flood_i and source regularSP Flood/Noah, with exact phases and comparison to the strongerC287 form.

The source audit recovered an already recorded17K ancestry for the Flood endpoint. A full typed rectangle now tests whether the600 biography has a coherent529 transport without the alternate8395 re-expression.