# 490d Mirror checkpoint after C332

24 September2026. **C332 complete; C333 unexecuted.** 1 steps remain in the current authorization. Read this checkpoint and report first; frozen predecessor records retain earlier findings. Current decisions override stale archive instructions. Do not repeat completed research.

## Current result

950+108 is equivalent to the right2K edge and selects b2;490 selects primaryrail. Together they retain02and22 at i3/5. Adding two17K selects22conditionally. No independent source prescription is established.

The new death partition supplies **a precise one-sided condition, not an independent rule coupling both+2 choices**. Within C319's held menu,950+108 selects the regular choice b=2. Adding actual MT-Noah→SP-Noah-death490 selects the primary rail. The cumulative choice a remains0 or2. Adding the existing two17K condition then selects22 conditionally.

C319 defines S=p−460+a and R=f−460+b with a,b independently0 or2, while SP Noah N is fixed. Matched SP death D=N−950 gives:

`D−R = 110−b`.

Thus D−R=108 is equivalent to N−R=1058 once Noah950 is held. It restates the right2K edge. Actual same-Gear MT Noah M gives M−D=490 for primary SP stations and491 for companions, independently of a and b.

| a /b | Source-admitted rows | With950+108 | With490 | With both | All-K rows |
|---|---:|---:|---:|---:|---:|
|0 /0|5|0|3|0|0|
|0 /2|3|3|2|2|0|
|2 /0|3|0|2|0|0|
|2 /2|3|3|2|2|3|

The two primary rows i3 and i5 retain both new conditions in **02 and22**. In each matched pair the N,M,D,R coordinates and source identities are identical; only the cumulative S member changes. For i3,02 uses S=−6347 while22 uses S=−6345. Both use N3706, M3246, D2756 and R2648. The new death path cannot by itself decide between those two existing cumulative endpoints.

The additional two17K requirement is R−S=N−q=8993, which C319 already shows requires a=b. Combined with b=2 and primary490, it leaves precisely22 at i3 andi5. This is a valid conditional uniqueness result. It does not establish an independent source prescription for imposing or coupling the conditions, and the new108 arithmetic does not add a constraint beyond the right2K edge from which it follows.

All20 inherited annual controls and40 same-phase components are retained. Fourteen annual controls are jointly source-admitted. Six admitted rows have950+108; nine have490; four have both; two have both plus the two17K condition. Formal upper rows whose R or S is absent remain unadmitted. In particular, a missing Gear4 MT Flood is not created to retain108.

This is C319's i3…7 slice. C287's separately admitted i2 companion row remains preserved in C331; it was not rejected by this narrower control domain. The complete four-row2K result and the three-row all-K subset in this menu must not be confused.

The result preserves the useful source-qualified950/108 and primary490 partitions while locating the remaining choice exactly: the cumulative+2 selection must be justified through an additional stated condition or source rule. Arithmetic alone does not supply that historical prescription.


## Retained context

C323 remains the completed predecessor synthesis. Retain the six-coordinate OFF600 rectangle family and three nativeON/restored-MT primary counterparts; the full same-Gear Noah-bound SP→MT biography translates by460, with source textual502 a distinct binding. C314 reversal requires i+j=10 and opposite cumulative phases. C313/C315 same-ancestry500/600 failures remain. C287 full domain is i2…5. The paired+2 choices produce its all-K form, but the00 control also retains two17K paths. The optional combined support criteria alone isolate i=j5. No source-prescribed selector has been established. Corrected LXX8464 supplement remains awareness only (1564→1700;2484→2700;920→1000); AD3746/2300 is superseded. Earlier reports, original unprefixed reports and Engine series remain distinct.

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.

## Verification

163 main checks and 17 frozen-input/predecessor authentication checks passed. A second main replay produced byte-identical DATA/RESULTS. Independent review and its scope are recorded in the evidence. All frozen originals and standing controls remain unchanged. Verification counts are not independent-witness counts.

## Best next bounded step

C333: Synthesize C324–C332, verify the sealed report/evidence chain and source integrity, and publish the final C333 checkpoint, reading index and recovery packages. Do not execute C334.

The bounded source, geometry, context, modal, dependency and529-control questions are complete. A verified synthesis is the remaining authorized step and will preserve both the positive new partitions and their exact scope.

Continue within the authorized batch, reassessing after the next completed result.