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.