# 490d Mirror checkpoint after C319

24 September 2026. **C319 complete. C320 unexecuted.** 4 steps remain in the current C314–C323 authorization. Read this checkpoint and its report first; use the frozen predecessor checkpoint and certificate for inherited state. Do not repeat completed work or follow stale archived next-step paragraphs.

## Current finding

The00 and22 choices both retain two17K paths. Only22 gives2K sides/allK in the fixedfour-case test. Of20annual/40phase cases,14/28are source-admitted; allKsurvives3annualcases.

**The two17K transports do not force the paired two-year selection.** With all source contexts held fixed, define `S=p−460+a`, `R=f−460+b`, with a,b independently0 or2. The cumulative annual choice is a; the regular Gear-coordinate choice is b. q and n are unchanged.

| a /b | Left/right short spans | S→R | q→n | Joint source rows | All-K rows |
|---|---|---:|---:|---:|---:|
|0 /0|1060 /1060|8993|8993|5|0|
|0 /2|1060 /1058|8995|8993|3|0|
|2 /0|1058 /1060|8991|8993|3|0|
|2 /2|1058 /1058|8993|8993|3|3|

The exact formulas are short spans1060−a and1060−b, with cross-width matrix[[8993+b−a,10053−a],[7933+b,8993]]. Thus two17K paths require a=b, allowing both00 and22. Requiring the all-K subdivision selects22 within this fixed four-choice domain.

All20 annual and40 same-phase configurations are enumerated. Fourteen annual and28 phase configurations are source-admitted; eight annual cases have two17K paths, and three have the all-K form. The00 choice is source-valid across all five rows. In the mixed choices one side can fail its endpoint domain independently; the22 upper failures remain.

The result is a sensitivity test, not a randomization or a probability estimate. Conditional uniqueness under the all-K requirement is not a source rule selecting that requirement or the matching annual/Gear choices. It does show exactly which extra choices convert a source-valid1060 rectangle to the1058 rectangle. The three all-K rows here are the i3…5 subset; C287's separately admitted i2 row has not disappeared.

## Retained context

C277–C310 and C311–C313 remain completed. C311 found no prescribing annual selector in its three-source audit; C312 admitted four complete cumulative transports and five SP targets; C313 found a center500 match only at j5 and no same-ancestry exact component500 match. The +155 regular normalization is local. C287 complete four-node indices remain2…5; direct17K admission is weaker. The original AD1905–1911 proposal remains unexecuted. Supplemental Engine ReportIII explicitly derives the LXX OFF field; older182/777 and mixed Cainan headings yield to File_18. Corrected LXX crossover8464 observations remain awareness only:1564→1700 and2484→2700, difference920→1000; AD3746/2300 is superseded. C-series and original unprefixed/Engine report series remain distinct.

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.

## Verification

121 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.

## Best next bounded question

C320: Close the finite coverage boundary: census all eight retained LXX_OFF Shem/Flood annual pairs against the existing regular Noah/Flood contexts under the same17K transport. Explicitly locate the omittedSPG1 companion and any LXX aliases, without new endpoints or variants.

The five-case test cannot represent the whole admitted rectangle family. Completing this small held-domain census will explain which source rows are excluded by the earlier reversed500 requirement and prevent a subset count being mistaken for the fullC287 domain.

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