# 490d Mirror checkpoint after C274

24 September 2026. **Latest completed: C274, the single-premise placement omission audit.** Existing research continues; no restart.

## Current conclusion

Given the held source coordinates, phase convention and Shem translation increment 598, the three placement equations are an irredundant sufficient set for the three-variable affine problem. All three together fix MT/LXX Flood 5290 and cumulative SP Flood 4715. Every single omission leaves one free parameter.

This proves restricted algebraic irredundance, not historical necessity of the premises. The 598 assignment itself has not been audited or relaxed.

## Equations and complete solution families

Let m, l, s denote MT ON, LXX OFF and cumulative SP OFF Flood translations. Shem translations are each Flood translation plus 598.

| Premise | Equation |
|---|---|
| A: MT closing join | 2m=10580 |
| B: common MT/LXX shift | l=m |
| C: SP Flood is global Mirror of MT Flood | m+s=10005 |

| Case | m | l | s | Rank |
|---|---:|---:|---:|---:|
| All three | 5290 | 5290 | 4715 | 3 |
| Omit A | 5290+u | 5290+u | 4715−u | 2 |
| Omit B | 5290 | 5290+v | 4715 | 2 |
| Omit C | 5290 | 5290 | 4715+w | 2 |

The free parameters are integers for the inherited annual-center/quarter-phase lattice; rational extensions are formal only. The baseline is a reference origin, not a fitted value. No free value has been selected.

The omitted residuals are 2u, v and w. All retained residuals vanish identically. Baseline coefficient determinant: 2.

## Invariants and released quantities

Every profile retains H=F−2 and RH=2−F=J1(F), hence local reflection about x=1. This follows from source gap 600 and shift increment 598, independently of A/B/C.

The inherited selected MT opening, cumulative SP closing and LXX closing radii are:

| Case | MT | Cumulative SP | LXX |
|---|---:|---:|---:|
| All three | 7 | 5 | 6 |
| Omit A | abs(u−7) | abs(5−u) | abs(6+u) |
| Omit B | 7 | 5 | abs(6+v) |
| Omit C | 7 | abs(5+w) | 6 |

These track source-selected endpoints. A moving selected endpoint need not remain the field's furthest endpoint. Each individual field still spans seven center-years and has seasonal-envelope length 7.5; combined joins, ordering and union lengths must be recalculated for changed placement.

Retain T(q)=q+8993. The induced regular maps are RN(y)=y+l−8993 and RF(y)=8395−l−y. For all translations,

RN(yN)+RF(yF)−2 = yN−yF−600.

Thus C271's same six source bindings among 36 comparisons remain; its thirty exclusions also remain. This is an algebraic consequence, not a new enumeration. With delta=l−5290, local centers are j+delta and 2−j−delta, j=2,…,7; actual radii are abs(j−1+delta). The 7K shift is 3703−delta.

**Omitting C leaves l fixed, so regular SP radii 1–6 and the 7K maps remain fixed while cumulative SP moves.** Do not conflate the regular SP radius-five pair with the cumulative SP closing radius.

The j=7 Noah-side signed display components are 5750+1000delta and 6250+1000delta. Original bracket coordinates are not fixed when delta is free. No E-ratio fitting or chart refit was performed.

## Controls and retained limits

Fifteen frozen inputs; **139 targeted exact assertions**; six outputs replayed byte identically. Review is author consistency review only. No historical campaign rerun, new source-event search or canonical/graph edit.

File_18 SHA-256: 68301ab760bfbe2e874aedc5c8d943ced7a6219d34bc2859332a70713f9630d5.

File_09 SHA-256: 45851004c5864229ebf6a896f9099819a08d8926715d3e97e4bc3985c4a3876e.

C127 retains 208 nodes/382 duration edges; C265 certificate unchanged. Predecessor C273 certificate SHA-256: c6217745a9340e2380f0a4ec53e9f8e4ebe3b2b16090de2120b00927d92abc23.

K=529; E=25/23; P=70/69. Global Mirror remains January AD 1; local x=1 remains January AD 2. No civil year zero. Regular Gears remain Noah/Shem/Flood only; no cumulative/upstream Gear, primer reopening, new axis or z-law.

C269 source connectivity remains established. The source translations remain different operations from the large 1196/1300 charts. C272 remains a baseline result and was not extended to changed placements. C271's source gaps at indices 0/1 remain. Preserve source identities, physical phase ancestry, sourced/generated midpoint distinctions and complementary Year 14/Year 15 readings.

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. Capture now, canonize later.

## Best next bounded step

**C275:** trace A/B/C to exact passages in the supplied original Mirror/529 documents and their immediate references. Distinguish source-coordinate relations, declared placement conditions and derived restatements. Ask whether each passage independently fixes placement or presupposes it. Hold 598 fixed; no new event scan, free-parameter selection or chart refit.

**High is sufficient. C275 is proposed, not executed.** Await Dean's next instruction.