490d C384 — E ladder and P/J repair: the first mixed diagram

24 September 2026. Step 1 of 10 in the C384–C393 authorization.

The existing two-year source translation commutes with the Noah-held E ladder; the direct E/P and E/J mixed squares do not. This is the first distinction needed before combining the C343 ladder and C383 composition law.

The retained primary rows are:

|Row|SP Noah N|Restored MT Flood R|Base MT Shem H|Base MT Flood F|Restored MT Noah M| |---|---:|---:|---:|---:|---:|---:| |i3|3706|2648|2556|2456|3246| |i5|3708|2650|2558|2458|3248|

For E_N(x)=N+(25/23)(x−N), R→H→F realizes1058→1150→1250 in both rows. All six recorded endpoints N,M,D,R,H,F translate by2. Accordingly, E_(N+2) after T₂ equals T₂ after E_N as whole affine maps, and R,H,R+2,H+2 form a source-qualified square. Matched existing offsets±1/4 preserve this comparison. T₂ is a coordinate comparison between recorded contexts, not a newly adopted chronology protocol.

At i3 the P/J repair is M3246→3248, using J pivot R2648 and P pivot B3108. Applying the E ladder for the next row then reaches existing SP Shem birth3208. The opposite route starts with E_3706(3246)=3206, the existing SP Shem birth in the first row. Applying the next P/J pivots2650 and3110 does not reach3208:

These are affine-map defects, not rounding errors. The failed outputs are fractional and absent from the integer-centered frozen regular menu.

Static affine conjugacy still holds: E_N after F_a equals F_(E_N(a)) after E_N for either ratio. Its source limitation is different. E_N sends M to the sourced SP Shem birth, but sends M+2 to3206+50/23 (and the corresponding i5 value), not an admitted endpoint. Static conjugacy and moving source transport cannot be conflated.

Sources: C340 DATA supplies the five labelled ladder alternatives; this test uses only its two primary same-Gear ladders. C379 supplies the common P/J repairs; C286 verifies the SP Shem images. C341 and C382 retain the phase and moving-frame distinctions. All are frozen in the evidence packet.

Verification and limits

23 main checks and 18 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.

Only the two retained primary E ladders and their one adjacent pair were tested. A valid translation square does not make P/J a translation on all endpoints. Static conjugacy does not establish source closure or physical-time phase transport.

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

C385, proposed and unexecuted: Solve the unique pivots required to transport the existing P/J repair through the moving E ladder, then test their membership in the full frozen Noah/Shem/Flood register. Include all four previously admitted regular common P/J repairs and their SP/LXX context aliases without creating pivots.

The initial defect may reflect unavailable source pivots rather than an algebraic impossibility. Computing the required pivots once and checking the finite existing menu is the narrowest way to decide.