{"id": "c110", "title": "C110 — Equal two-year residuals preserve the ratio without merging N04’s events", "filename": "490d_C110_Mirror_Report_20260922.md", "role": "Research action", "step": 110, "sha256": "57e104bdb8611406307ea0179d973cff8dbbba4fea91339046393c8833da4159", "bytes": 3475, "origins": ["C01–C479/reference/490d_C01_C265_Complete_Window_Archive_20260923.zip!/workspace/mirror_10_step_graph_confluence_20260922/C110/490d_C110_Mirror_Report_20260922.md"], "download": "/sources/57e104bdb8611406307ea0179d973cff8dbbba4fea91339046393c8833da4159.md", "format": "md", "derived": false, "tags": ["Regular", "Cumulative", "Rounded", "Mirror / 529"], "excerpt": "C110 — Equal two-year residuals preserve the ratio without merging N04’s events\n\n22 September 2026 · Step 8 of the authorized ten-step Mirror continuation (C103–C112).\n\nN04 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 ap", "content": "# C110 — Equal two-year residuals preserve the ratio without merging N04’s events\n\n22 September 2026 · Step 8 of the authorized ten-step Mirror continuation (C103–C112).\n\nN04 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.\n\n\\[\ne_F=d+k(11r^2-12r),\\qquad e_N=d+k(13r-12r^2).\n\\]\n\nEqual 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**.\n\n| Branch | d | eF | eN | d−e |\n| --- | --- | --- | --- | --- |\n| N02 | 25 | 0 | 0 | 25 |\n| N04 | 27 | 2 | 2 | 25 |\n\nThe 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:\n\n| Record class | Meaning of the selected comparison |\n| --- | --- |\n| Ordinary Creation | different member of the fixed Normal/G2 Creation field |\n| Conquest | different member of the fixed Conquest field |\n| Original Joseph | different original cumulative member |\n| MT Flood and Noah; SP Noah | authorized regular Gear comparisons |\n| Apparent row | unchanged source records |\n\nThis 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.\n\nOn 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.\n\n**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.\n\n**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.\n\n**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.\n\n**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.\n", "evidenceLinks": [{"id": "d-be42daca1d82dac9", "title": "File 62"}, {"id": "d-68301ab760bfbe2e", "title": "File 18"}, {"id": "d-d580afd48d6e12d6", "title": "File 61"}, {"id": "d-45851004c5864229", "title": "File 09"}]}