# 490d Mirror checkpoint after C272

24 September 2026. Latest completed step: **C272 — fixed charts and the outer radius selection**. Continues C271; no restart.

## Completed finite comparison

For the six C271 positive families, use

\[
x=1+\rho+\delta,\quad\rho=1,\ldots,6,\quad\delta=-1/4,0,+1/4.
\]

Hold C268’s maps Φ_s,a(x)=a+s(x−1), with s=1196 or 1300, a=−4419 (N02) or −4417 (N04). Compare the resulting **72 image instances** only with the **48 distinct reflected pair centers** in the frozen C01 Noah/Shem/Flood register. No refitting, absolute values, side reversal or wider date lookup.

**Ten matching instances represent eight distinct target source records, all at radius 6 and all inherited from C268.** Radii 1–5 add no target matches. The remaining 62 image instances are 62 distinct generated coordinates, giving 70 distinct coordinates overall.

| Chain / scale | Inner image | Center image | Outer image |
|---|---|---|---|
| N02 / 1196 | 2458 MT G2 Flood start | 2757 SP G2 companion Noah death | 3056 MT G1 Noah birth |
| N04 / 1196 | 2460 MT G3 Flood start | 2759 SP G3 companion Noah death | 3058 MT G2 Noah birth |
| N02 / 1300 | 3056 MT G1 Noah birth | **3381 generated** | 3706 SP G1 primary Noah birth |
| N04 / 1300 | 3058 MT G2 Noah birth | **3383 generated** | 3708 SP G2 primary Noah birth |

Repeated centers 3056 and 3058 are shared stage endpoints, not extra event identities. The 299 midpoints remain sourced; the 325 midpoints remain generated. “Generated” means absent from this held target register, not absent from every historical or project context.

## Exact structural criterion

The intervals at scales 1196 and 1300 have widths 598 and 650 at every radius. The second inner endpoint minus the first outer endpoint is

\[
G(\rho)=104(\rho-6).
\]

They share an endpoint only at ρ=6. For radii 1–5 they overlap by 520,416,312,208,104 respectively. The equality is equivalent to (4ρ+1)/(4ρ−1)=25/23, already selecting C271’s outer radius. The general anchored 25/23 expansion identity holds for every radius; the shared adjacent-stage endpoint does not.

The successful outer row retains widths 6877→7475→8125=13(529→575→625), with gains 598 and 650. C272 establishes the finite extension limit of those calibrated charts, not a new independent witness.

## Source and phase qualifications

All six C271 input ancestries remain supported even where chart outputs fail to match a target. The outer input is cumulative LXX OFF Flood closing base 5283 and its induced regular SP G3 primary-Noah counterpart 3710. Target SP companion Noah deaths and target MT Flood/Noah events do not replace that input identity.

Seasonal input components become target pair centers under these scales; target half-year displays come from their own source records. The unit-magnitude maps of C270/C271 remain distinct operations. The charts are not new stored chronological edges or a universal source-preserving action.

Of the 72 images, 36 are negative. The target register is positive, bounded by 1956 and 3710. Fifty-six image instances lie below that minimum; sixteen lie inside the range. The six within-range misses are 2081,2083,2406,2408,3381,3383. No broader event identifications were attempted.

The scales were calibrated to radius 6 in C268. The match pattern is conditional on those scales, the two inherited anchors and the fixed target register; no probability or global uniqueness claim follows.

## Evidence and retained controls

Fourteen frozen inputs; **326 exact assertions**; six outputs replayed byte identically; independent mathematical and source-role reviews; certificate chained to C271. Authored report and checkpoint are not replay outputs.

File_18 SHA-256: `68301ab760bfbe2e874aedc5c8d943ced7a6219d34bc2859332a70713f9630d5`.

File_09 SHA-256: `45851004c5864229ebf6a896f9099819a08d8926715d3e97e4bc3985c4a3876e`.

C127 graph and C265 certificate unchanged. Keep K=529, E=25/23, P=70/69 and ρ=radius. Global Mirror remains January AD 1; local junction x=1 remains January AD 2. No civil year zero. Regular Gears remain Noah/Shem/Flood only. SP person companions and Flood closing boundaries remain distinct.

Capture now, canonize later. No canonical changes, cumulative/upstream Gear, primer reopening, z-law or new axis. Retain the 2500/7500 distinctions and complementary 7000/7500 interpretations. Original unprefixed Reports 01–10 and interrupted, unestablished original Reports 11–25 remain distinct from the C-series. The superseded AD 1905–1911 lookup remains unexecuted.

## Best next bounded step

**C273:** consolidate C266–C272 into one source-qualified dependency account: 17K correspondence → induced 7K shift → six-radius register → outer 25/23 bracket → 13K/598/650 chart connection. Separate inherited assumptions from derived consequences and identify the strongest unsupported link. Use only these completed steps and immediate dependencies; no new numerical search. **High is sufficient. C273 remains unexecuted.**

Publish completed reports and incremental evidence as work proceeds; await Dean’s next instruction.