# 490d Mirror checkpoint after C271

24 September 2026. Latest completed step: **C271 — the SP three-Gear radius register**. Continues C270; no restart.

## Completed finite test

Held maps on reflected regular coordinates:

\[
T(q)=q+8993,\quad R_N(y)=y-3703,\quad R_F(y)=3105-y,
\]

\[
J_1(x)=2-x,\quad\eta(x)=1000(x-1),\quad3703=7\times529.
\]

Domain: SP regular Noah births, primary/companion, and independently typed Flood starts/closes in G1–G3, full-430 comparison frame. Twelve source records, 24 actual seasonal components, 36 Noah/Flood cross-pairs. No Noah deaths or new regular Shem map.

**Exactly six pairs preserve the held local reflection:**

| Cumulative index j | Gear and binding | Reflected Noah / Flood | Cumulative Flood / Shem BC bases | Local centers | Radius |
|---:|---|---|---|---|---:|
| 2 | G1 companion / close | 3705 / 3105 | 5288 / 5888 | 2 / 0 | 1 |
| 3 | G1 primary / start | 3706 / 3106 | 5287 / 5887 | 3 / −1 | 2 |
| 4 | G2 companion / close | 3707 / 3107 | 5286 / 5886 | 4 / −2 | 3 |
| 5 | G2 primary / start | 3708 / 3108 | 5285 / 5885 | 5 / −3 | 4 |
| 6 | G3 companion / close | 3709 / 3109 | 5284 / 5884 | 6 / −4 | 5 |
| 7 | G3 primary / start | 3710 / 3110 | 5283 / 5883 | 7 / −5 | 6 |

The cumulative LXX OFF source indices are retained annual selectors, not cumulative Gears. For g=1,2,3 and c=0 primary/start or c=1 companion/close:

\[
j=2g+1-c,\qquad \rho=2g-c.
\]

Primary/start gives radii 2,4,6; companion/close fills 1,3,5. Flood close remains an event boundary, never a person companion.

## Complete failure criterion and phases

For arbitrary selected Noah N and Flood F:

\[
\Delta=R_F(F)-J_1(R_N(N))=N-F-600
=2(g_N-g_F)-c_N+c_F.
\]

All thirty nonmatching pairs have Δ≠0. The same residual appears in both seasonal components. Within one Gear, companion/start gives 599 and midpoint 1/2; primary/close gives 601 and midpoint 3/2. Neither relocates the held axis.

Matching phases obey local images j+δ and 2−j−δ, δ=±1/4. Half-year separation is preserved; the Flood branch reverses order. Original BC seasonal ancestry remains distinct as in C270.

The six positive η brackets are 750/1250, 1750/2250, 2750/3250, 3750/4250, 4750/5250 and 5750/6250, with corresponding negative pairs. Their outer/inner ratios are 5/3, 9/7, 13/11, 17/15, 21/19 and 25/23. **Only the outer radius 6 gives E=25/23 within this finite register.**

G1 companion/close includes local center 0, whose pair is **1t BC / AD 1n**, not civil year zero. Local junction x=1 remains January AD 2; global Mirror x=0 remains January AD 1.

## Coverage and limits

Six of eight boundary records are covered in each cumulative field, j=2–7: five elapsed years between first and last centers. Indices 0/1 would require Noah 3703/3704 and Flood 3103/3104, absent from the held register. They remain generated regular coordinates.

Selected local center sets are [2,7] and [−5,0] at integer steps. Junction 1 is not a source image here. The omitted index-0 images at 0 and 2 coincide numerically with selected index-2 images on opposite source roles; this does not fill source coverage.

All twelve cumulative preimages are existing LXX OFF endpoint records. Their systematic T8993 pairing remains a derived comparison, not twelve new graph edges, six independent 17K witnesses or historical event identities. C269’s path qualifications and C268’s distinct 1196/1300 rescalings remain intact. The original C266 translations are inherited, not independently derived here.

## Evidence and controls

Ten frozen inputs; **271 exact assertions**; six evidence outputs replayed byte identically; independent mathematical and source-binding reviews; certificate chained to C270. 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. Regular Gears remain Noah/Shem/Flood only; the adjacent companion remains SP-local to Noah/Shem. Capture now, canonize later. No canonical changes, cumulative/upstream Gear, primer reopening, z-law or new global axis.

Retain the 2500/7500 classifications and complementary 7000/7500 interpretations. C-series reports remain distinct from original unprefixed Reports 01–10 and interrupted, unestablished original Reports 11–25. The superseded AD 1905–1911 search remains unexecuted.

## Best next bounded step

**C272:** compare the six positive radius pairs and their centers with C268’s fixed 1196/1300 charts at its two inherited anchors. Check all images against the frozen regular event register, retaining generated status where no source record exists. Hold all anchors, scales and offsets fixed. **High is sufficient. C272 is proposed, not executed.**

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