# 490d Mirror checkpoint after C268

24 September 2026. Latest completed step: **C268 — the LXX seasonal bracket meets the 13×529 chain**. Continues the existing C01–C265 research and redirected C266–C267; no restart.

## Current result

The C267 positive LXX closing Flood pair has local inner/center/outer points **27/4, 7, 29/4**, at radii **23/4, 6, 25/4** from x=1. Its source is LXX OFF cumulative Flood closing pair 5284t/5283n BC, translated by 5290. The local chart η(x)=1000(x−1) gives 5750/6000/6250. The negative counterpart is the reflected translated LXX Shem closing pair, centered at −5.

C268 compares that fixed triple with the two established C01/C206 chains, keeping Creation anchors a=−4419 and −4417.

| Scale in Φₛ,ₐ(x)=a+s(x−1) | Widths from Creation | N02 target centers | N04 target centers |
|---:|---|---|---|
| 1196=4×299 | 6877, 7176, 7475 | 2458, **2757**, 3056 | 2460, **2759**, 3058 |
| 1300=4×325 | 7475, 7800, 8125 | 3056, **3381**, 3706 | 3058, **3383**, 3708 |

The first center images 2757/2759 are the retained SP G2/G3 companion Noah-death reflections. The second center images 3381/3383 remain generated; neither is in the frozen 48-record C01 event register. This distinction was already established in C209.

The input half-year becomes 598 or 650 years. The scales have ratio **1300/1196=25/23**. With E=25/23, g(x)=1+E(x−1) and Pₐ(y)=a+E(y−a),

\[
\Phi_{1300,a}=P_a\circ\Phi_{1196,a}=\Phi_{1196,a}\circ g.
\]

The arithmetic identity is general affine geometry; the retained endpoint and midpoint source labels provide the finite chronological content. C268’s addition is the explicit correspondence with the LXX bracket, not a new discovery of the earlier 299+299 and 325+325 constructions.

## Source and phase limits

- Local seasonal components map to long-chain **pair centers**. Restoring target components center±1/4 is a separate display operation. Raw E dilation gives width 25/46, differing from the restored components by ±1/46, as already documented in C224.
- At scale 1196, the third macro endpoint requires generated local x=717/92. At scale 1300, the first requires generated x=629/100. Neither is on the quarter-year phase lattice. One scale can reproduce the full numerical chain without making every local preimage sourced.
- Scale 1300 gives the full 10-fold to 13-fold relation: 5290/5750/6250 multiplied by 13/10 gives 6877/7475/8125, measured from the selected Creation anchor.
- The target roles are mixed: MT Flood, SP companion Noah death, MT Noah birth and SP primary Noah birth. There is no assertion that these are the same event as the local cumulative LXX Flood pair.
- Local reflection J₁ maps under one chart to reflection about **a**. Global Mirror reversals require reflecting the target anchor too: Φₛ,₋ₐ(J₁x)=−Φₛ,ₐ(x). No new Shem chain follows.
- The two Creation anchors remain distinct fixed source-field members. Their charts differ by target translation +2; no Creation Gear is introduced.

## Retained controls and evidence

C267 still gives 2500 as a generated LXX whole-field midpoint radius, 5750/6250 as seasonal radii and 7500 as a whole seasonal-envelope length. Keep 7000/Year 14 and 7500/Year 15, and envelope sum versus union, distinct. C266’s 5+1+1 sequence and source qualifications remain in force.

C268 freezes fifteen immediate inputs. **127 assertions passed; six generated outputs reproduced byte identically; two independent reviews completed.** Source tags, exact maps, phase/reflection calculations, generated-point limits and replay records are retained in the evidence packet. The certificate links to C267; the artifact manifest inventories all other payloads. The authored report/checkpoint are not replay outputs.

File_18 SHA-256: `68301ab760bfbe2e874aedc5c8d943ced7a6219d34bc2859332a70713f9630d5`.

File_09 SHA-256: `45851004c5864229ebf6a896f9099819a08d8926715d3e97e4bc3985c4a3876e`.

The C127 208-node graph and C265 certificate remain unchanged. Keep K=529, E=25/23, P=70/69 and ρ=radius. Regular Gears remain Noah/Shem/Flood only. Capture now, canonize later; no canonical amendment, cumulative Gear, upstream Gear, z-law, new global axis or primer reopening. Original Reports 01–10 and interrupted, unestablished original Reports 11–25 remain distinct from this C-series.

The former C266 AD 1905–1911 historical endpoint search remains unexecuted. C266 instead completed the authorized axis endpoint ledger; C267 and C268 followed that redirect.

## Best next bounded step

**C269:** trace the source connection between the LXX closing pair and the retained N02/N04 cumulative members at bases 5287 and 5285, using only their existing LXX OFF field and 868 attachments to fixed SP Creation. Test whether existing source-labeled paths support the comparison beyond common field membership and affine rescaling. Preserve endpoint roles and phases. **High is sufficient.**

C269 is proposed, not executed. Publish completed reports and incremental evidence as work proceeds; await Dean’s next instruction.