# 490d Mirror checkpoint after C317

24 September 2026. **C317 complete. C318 unexecuted.** 6 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

Five600 rectangles and ten phase rectangles share two17K paths. Their duration rank is3. Replacing both lower corners by−458 recoversC287 only at i3…5; no independent second17K constraint follows.

The five selected biographies support a coherent **600-year rectangle with two17K translations**, using the existing C271 source identities:

| Symbol | Coordinate | Source role |
|---|---|---|
|p|−5890+i|Cumulative LXX_OFF Shem|
|q|−5290+i|Cumulative LXX_OFF Flood|
|f|3103+i|Regular SP selected Flood boundary|
|n|3703+i|Regular SP Noah birth|

For i3…7, `q−p=n−f=600` and `f−p=n−q=8993=17K`. Source pairs, regular roles, Gear/person rail and both exact phases are admitted. In ordinary BC chronology Shem precedes cumulative Flood; the reflected output is a later-numbered Noah compared with the Flood boundary. Coordinate order is not a substitution of event identity.

The cross-width matrix, rows p/q and columns f/n, is **[[8993,9593],[8393,8993]]**. This is not an all-K rectangle:600 is not an integer multiple of529. The six pairwise duration equations have rank3 and leave one common translation free. In particular, once the source and output600 sides and one8993 path are fixed, the second8993 path is forced. Five annual stations and ten phase checks are not independent historical measurements of17K.

Comparison with the stronger C287 form retains q and n but replaces the other corners by `S=p−458` and `R=f−458`. Its side becomes600+458=1058=2K and its cross-widths become[[17K,19K],[15K,17K]]. The new corners change source type/context: cumulativeON Shem at i+2 and regular MT restored-context Flood. This is not a free movement of an unchanged source event.

Both corners are admitted only at i3,4,5 within the current five-case domain. For i6/7 the ON-Shem indices8/9 and regular required Flood2651/2652 remain unavailable. The coherent direct600 rectangles at those rows do not supply the missing all-K corners.

## 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

46 main assertions and 14 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

C318: Audit the paired458 replacement as explicit source-state operations: cumulative CainanON plus annual-index change, and regular SP→MT Flood comparison plus declared restoration and Gear change. Check every intermediate source state and boundary.

This is the substantive link between a valid600 biography and the2K+15K framework. Its source operations and domain must be established before treating the numeric458 coincidence as a permitted composition.

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