# 490d Mirror checkpoint after C275

24 September 2026. **Latest completed: C275, provenance of the 529 placement premises.** Continuation, not a restart.

## Main finding

The supplied Mirror documents explicitly support the construction: common MT/LXX translation 5290, cumulative SP translation 4715, and additional Shem translation 598. The closing join and SP/MT reflection are displayed consequences. The bilateral theorem uniquely recovers MT placement if the closing join is required.

This is documented conditional determination. The initial assignments and their derived equalities must not be counted as separate independent determinations.

## Premise record

Let m, l, s be MT ON, LXX OFF and cumulative SP OFF Flood translations.

| Premise | Equation | Documentary status |
|---|---|---|
| A: MT closing join | 2m=10580 | Comprehensive handoff §§8–9 supplies 5290 then displays the join; bilateral §6 proves the converse conditionally |
| B: common MT/LXX shift | l=m | Explicit shared operation in comprehensive §8; the six-year raw source gap alone does not require equal shifts |
| C: SP/MT global Flood reflection | m+s=10005 | SP 4715 supplied in §14.1, reflection displayed in §14.2; uniquely recovered once MT 5290 and reflection are held |

File_18 controls MT 5296–5289, SP 4716–4709 and native LXX 5750–5743; removing cumulative Cainan 460 gives LXX OFF 5290–5283. The canonical MT row's “5290 → Christ” annotation is relevant compressed support, not a complete phase/operator specification.

Define residuals RA=2m−10580, RB=l−m, RD=l−5290. Then **RA+2RB=2RD**. With B held, A is equivalent to placing the LXX OFF opening at the existing global Mirror origin. MT opening at x=−6 is the same placement condition. Do not count these as additional constraints.

The retained **5296→3709→6 BC = 3K+7K** chain is source-qualified: MT cumulative ON, SP regular G3 companion Noah, retained Christ anchor. Its own text calls the 5290 span already established. It adds a sourced intermediate without independently choosing the 6 BC target.

The retained branch copy has upload suffix (1); the axis bibliography cites (2). Title, date, chain and roles identify the relevant material; unseen (2) byte identity is not asserted. The inspected copy matches its prior extraction hash.

## Retain C274 results

All three equations give m=l=5290, s=4715. Single omissions give:

- Omit A: m=l=5290+u, s=4715−u.
- Omit B: m=5290, l=5290+v, s=4715.
- Omit C: m=l=5290, s=4715+w.

No free value is selected. Matched source 600 minus assigned shift increment 598 preserves H=F−2 and RH=2−F. The source 17K correspondence and regular six bindings remain. Regular local radii 1–6 remain fixed when l remains fixed, including omission C. Cumulative SP and regular SP must remain distinct.

## Supplemental correction, retained without redirection

Dean's corrected LXX observation is verified separately:

| Source and +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. Compare Q1406 and Q1446 on the AD side.

LXX Creation→Jared is 960 versus MT's 460; MT/LXX offsets are 1380 at Creation and 880 at Jared. Gap difference 960−40=920→1000. **AD 3746/2300 is superseded.** File_18's introductory +1380 shorthand must not override the Jared rows. No canonical edit or upstream Gear transport.

## Verification and controls

Thirteen frozen existing inputs; nineteen audit passages and five separate supplement passages; **72 targeted checks**; five generated outputs replayed byte identically. Classification is authored; no machine proof of historical necessity or new independent-agent review is claimed.

File_18 SHA-256: 68301ab760bfbe2e874aedc5c8d943ced7a6219d34bc2859332a70713f9630d5.

File_09 SHA-256: 45851004c5864229ebf6a896f9099819a08d8926715d3e97e4bc3985c4a3876e.

C127 remains 208 nodes/382 duration edges; C265 certificate unchanged. Predecessor C274 certificate SHA-256: 23ab41af374a05812d024b1be7ef9b141086b11bbf9ca456b2255efd8b5968f6.

K=529; E=25/23; P=70/69. Global Mirror January AD 1; local junction January AD 2; no civil year zero. Regular Gears Noah/Shem/Flood only. Preserve source identities and phase ancestry, complementary Year 14/15 interpretations, and the distinction between source paths and large affine charts. No primers, canonical amendments, 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. Superseded AD 1905–1911 lookup remains unexecuted.

## Best next bounded step

**C276:** audit whether the retained 598/600 source rectangle requires the assigned 598 difference between Flood and Shem translation parameters, without reinstating the desired local join. Hold source nodes and phase labels fixed; use the existing 17K correspondence. Distinguish cross-index source duration from operator assignment. No new event scan or fitted landing.

**High is sufficient. C276 is proposed, not executed.** Await Dean's instruction.