# 490d Mirror checkpoint after C276

24 September 2026. **Latest completed: C276, the 598 source relation and translation increment.** Continuation, not a restart.

## New result

Source 598 and the retained 17K correspondence alone leave the translation increment free. Requiring the selected cross-index images to align fixes it at 598, while leaving one common translation free.

Let f and h be cumulative LXX OFF Flood and Shem translations; δ=h−f. Let F(q)=q+f, H(q)=q+h and G(q)=−q−h.

| Cumulative source | Index | Center | Reflected regular counterpart under +8993 |
|---|---:|---:|---|
| S: Shem closing | 7 | −5883 | R=3110, SP G3 Flood start |
| I: Flood interior | 5 | −5285 | P=3708, SP G2 primary Noah birth |
| L: Flood closing | 7 | −5283 | N=3710, SP G3 primary Noah birth |

I−S=P−R=598; L−I=N−P=2; L−S=N−R=600. The 598 is cross-index; the 600 is same-index/same-Gear.

For R_N(y)=y+α and R_F(y)=−y+β, source transport gives α=f−8993 and β=8993−h. Rank 2 in four unknowns leaves two free parameters, so δ is not determined.

Add **X: H(S)=F(I)**. Its residual is δ−598. X therefore fixes δ=598; rank becomes 3 and one common translation remains free.

With p=f−5285:

\[
F(I)=H(S)=p,\quad G(S)=-p,\quad F(L)=p+2.
\]

The cross-index pair reflects about x=0; the same-index pair reflects about x=1. Its radius is |p+1|. Baseline f=5290, h=5888 gives p=5 and images 5, −5, 7, but X alone does not force that placement, radius six, 7K Noah subtraction or the 5750/6250 chart bracket.

## Dependencies and limits

The source-only image midpoints are (598−δ)/2 and (600−δ)/2; their difference is always 1. These diagnostics introduce no new adopted axis.

Equivalent X descriptions—cross-index alignment, global image reflection, δ=598, and the same-index J₁ reflection—are one scalar condition, not independent witnesses.

C270's intercepts −3703/3105 were induced from 5290/5888. Holding them fixed would import the result. The unreduced MT join is **2m+δ=11178**; C274's 2m=10580 already substitutes 598. Neither MT join equation is imposed here.

Generally R_F(y−600)=600−δ−R_N(y). Do not extend C271's fixed-J₁ match counts to free δ. No all-profile necessity follows from this one rectangle.

The source ±1/4 components are retained; reflection reverses order without reattaching phases. Co-location preserves distinct source identities.

C127 stores S→I, I→P and S→R as duration edges. L is absent as a stored node; its +8993 route is inherited from C254 through C269. No edge or historical event is added.

## Supplemental correction

| LXX +8464 landing base | Reflected AD anchor | Gap | ×25/23 |
|---|---:|---:|---:|
| Creation 5494 BC→AD 2970 | Conquest 1406 | 1564=68×23 | 1700 |
| Jared 4534 BC→AD 3930 | Exodus 1446 | 2484=108×23 | 2700 |

Full pairs: 5495t/5494n BC→AD 2970t/2971n; 4535t/4534n BC→AD 3930t/3931n. LXX Creation→Jared 960 versus MT 460; offsets 1380/880. Difference 960−40=920→1000. **AD 3746/2300 superseded.** Awareness only; no research redirection or upstream Gear transport.

## Verification and standing controls

Sixteen frozen inputs; **70 checks passed**; six generated outputs replayed byte identically. Author review only. File_18, File_09, C265 certificate and C127 unchanged; graph remains 208 nodes/382 duration edges. Full hashes are in the evidence integrity record.

Predecessor C275 certificate SHA-256: 9f07d37f74b9bfb9e21984b5efa17fe53f22d545af152e208b21c629af3f7c47.

K=529; E=25/23; P=70/69. Global Mirror January AD 1; established local junction January AD 2; no civil year zero. Regular Gears Noah/Shem/Flood only. Preserve source identities, phase ancestry, complementary Year 14/15 interpretations, and the distinction between source paths and affine charts. No canonical/graph amendments, primers, new axis or z-law. Capture now, canonize later.

C-series reports remain distinct from original unprefixed Reports 01–10 and unestablished interrupted original Reports 11–25. The superseded AD 1905–1911 lookup remains unexecuted.

## Best next bounded step

**C277:** extend the same tagged 598 alignment across the existing six C271 bindings, checking counterpart availability and source-index/register boundaries. Add no events or fitted landings.

**High is sufficient. C277 is proposed, not executed.** Await Dean's instruction.