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.
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.