490d C389 — Cumulative source test of the reflected E/J square
24 September 2026. Step 6 of 10 in the C384–C393 authorization.
The existing17K corner exchanges preserve the E/J identity algebraically, but neither reflected square is source-complete in the frozen cumulative menu. Three new points are missing in each case.
The two original full430 states use the already recorded diagnostic exchanges x↦C−x, with C=−2639 at i3 and C=−2635 at i5. These are the C375 source-corner comparisons, not newly adopted global Mirror axes. Let S be the existing native cumulative Shem point paired with the held regular Noah N.
| Regular point | Reflected coordinate | Cumulative availability |
|---|---|---|
| Noah N | S | Existing |
| Next Noah N+2 | S−2 | Existing |
| Original J Flood pivot A | S+1058 | Existing |
| MT Noah input x | S+460 | Existing |
| MT Noah output x+2 | S+458 | Existing |
| E image: Shem input | S+500 | Absent |
| Next Shem output | S+498 | Absent |
| Transported J Shem-death pivot | S+1098 | Absent |
The table applies to both source states. Ten of sixteen labelled point slots are admitted; six are absent from the48-record cumulative Noah/Shem/Flood menu. The familiar cumulative598→600 repair is recovered on the existing lower route. The new upper route requires points40 beyond the corresponding prior repair input and pivot.
Conjugating both affine coefficients verifies the reflected identity exactly. Its required outer side is(S+1098)−(S−2)=1100, again42 beyond2K. This algebraic fact does not supply the missing cumulative sources.
Reflection reverses the inherited component offset. Both±1/4 possibilities were checked with that ancestry reversal; none supplies the missing endpoints or pivot. No cumulative Gear, new endpoint, phase, or global axis is introduced.
Sources: C379 identifies the two original17K joins; C385 supplies the new regular squares; C365 is the frozen cumulative source menu. The negative availability statement is explicitly confined to that menu.
Verification and limits
40 main checks and 17 frozen-input/predecessor authentication checks passed. A second main replay produced byte-identical DATA/RESULTS. These checks and the source interpretation were performed by the root agent; no new independent-agent review is claimed. All frozen originals and standing controls remain unchanged. Verification counts are not independent-witness counts.
The result is not a proof that a cumulative counterpart can never exist. It is a complete membership check for the stated frozen menu and existing two corner exchanges; no missing point is promoted to a source.
Mirror/529 focus: K=529, E=25/23, P=70/69. Global paired Mirror January AD1; local junction January AD2; no civil year zero. Regular Gears are Noah/Shem/Flood only. SP minus-one person companions remain local to SP Noah/Shem; Flood close is a separate boundary. No upstream/cumulative Gear, new endpoint or phase, fitted anchor, global axis, primer reopening, canonical or graph edit. Capture now; canonize later. Source identity, context, modal binding, generated coordinates and phase ancestry stay distinct.
Decision after this result
C390, proposed and unexecuted: Enumerate the finite coherent regular Noah/Shem/Flood family comparisons without prefiltering on529 or common P/J hits. Ask which adjacent-Gear Noah→Shem E/J squares actually pass, retaining source context, boundary and rail labels.
The Mirror lift is now bounded by a concrete source obstruction. An unconditioned finite family census can show whether the regular result is selective or merely a generic consequence of the source lifespans.