# C110 — Equal two-year residuals preserve the ratio without merging N04’s events

22 September 2026 · Step 8 of the authorized ten-step Mirror continuation (C103–C112).

N04 does not have the same literal junction identities as N02. Let eF be ordinary-row Flood minus apparent-row Flood, and eN ordinary-row Noah minus apparent-row Noah. Its source records give eF=eN=2.

\[
e_F=d+k(11r^2-12r),\qquad e_N=d+k(13r-12r^2).
\]

Equal residuals still eliminate d and give kr(23r−25)=0. Thus N04 preserves the same ratio, while its anchor equation is now **d−e=25k/529**.

| Branch | d | eF | eN | d−e |
| --- | --- | --- | --- | --- |
| N02 | 25 | 0 | 0 | 25 |
| N04 | 27 | 2 | 2 | 25 |

The apparent row remains 1904→2456→3056. N04's ordinary rows are 2 later in the reflected coordinate than N02's, but those shifts have different source meanings:

| Record class | Meaning of the selected comparison |
| --- | --- |
| Ordinary Creation | different member of the fixed Normal/G2 Creation field |
| Conquest | different member of the fixed Conquest field |
| Original Joseph | different original cumulative member |
| MT Flood and Noah; SP Noah | authorized regular Gear comparisons |
| Apparent row | unchanged source records |

This is not one global Gear action. In particular, the ordinary Creation and Joseph member changes cannot inherit the Noah/Flood Gear label. The two residuals are linked by the same authorized regular G1/G2 comparison and are not two independent observations.

On the reflected counterpart diagram all centre differences reverse sign: N04 has d=−27 and e=−2, giving d−e=−25. With widths oriented in the reflected direction, the same eliminated ratio equation holds. This reverses orientation without introducing another Mirror axis, an extra year, or a new scale.

**Validation.** 10 exact arithmetic/structural checks passed. The 19 frozen dependencies passed hash verification; all three generated outputs replayed byte for byte in isolation, and the original dependencies remained unchanged. This step reads completed certificates and does not execute their campaigns.

**Scope and provenance.** Controlling File_18 and File_09 remain unchanged. Regular Gears apply only to Noah/Shem/Flood; SP person companions only to Noah/Shem. Creation and Conquest fields remain fixed. Native LXX ON, explicitly derived OFF, independent Flood start/close, and paired suffix inversion at January AD 1 remain in force. No civil year zero, upstream Gear transport, primers, Rounded campaign, or localized −33 is introduced. These are new continuation reports, not recovered historical Reports 11–25. Evidence is conditional on the supplied project model, not a proof of literary intention or independent historical dating.

**Source locators.** File_09 §3 and Appendix A (paired Mirror); File_18 §§2.1.3, 3.1 and 6A (regular fields and cumulative source members); File_61 §11.2 (original backward Joseph +110); File_62 collateral-scope guards; C05 admitted apparent field; C43 frozen graph; C95 and C100–C102 named carrier rows; preceding current certificates. The forthcoming 529 × 4 × 2 cycle has not been explored. The declared phase model does not infer an unstated birthday or event month from an annual source row.

**Best next bounded step — High sufficient.** Test which assumptions determine ratio, scale and origin in the reduced junction model, and distinguish that parameter count from the fixed graph rank.