C169 — Changing the MT profile requires its own residual
23 September 2026 · Step 14 of 50, continuing C155.
Changing the selected MT profile changes the square-side residual without changing a held Creation→ordinary-Flood interval. The additional quantity ρ=M−f−190 makes that distinction explicit.
Hold P6's b4416, ordinary f2460 and Noah X3709; compare the four declared MT offsets:
| MT offset | M | δ | ρ | b+f−13K |
|---|---|---|---|---|
| 0 | 2460 | 191 | -190 | -1 |
| 60 | 2520 | 131 | -130 | -1 |
| 130 | 2590 | 61 | -60 | -1 |
| 190 | 2650 | 1 | 0 | -1 |
The first three M values belong to different profile selections; they are not relabeled as members of the retained +190 field. In each case δ+ρ stays equal to one, preserving the actual Creation residual −1.
This is a bounded profile comparison using the existing regular Cainan/Terah switches. It demonstrates why the single-δ formula cannot be carried unchanged between profiles. No switch is applied to Creation or to the cumulative chain in this test.
Evidence and scope
K=529. Positive BC base B denotes (B+1)t/Bn BC; reflected AD base A denotes AD At/(A+1)n. Their same-season civil span is B+A, after the no-year-zero correction. AD source projections are not historical AD occurrences. Generated coordinates and interval midpoints do not acquire event identity from numerical coincidence.
Regular Gears remain confined to Noah/Shem/Flood. Creation and Conquest use fixed source-field members; no fourth Gear is admitted. File_18/File_09 and the C127 graph are unchanged. C133–C155 source corrections remain controlling, with the C10 ancestry of the next-Flood-Gear rule now explicit. No historical campaign is rerun, no quarantined primer is reopened, and no N01/N03 expansion or missing Shem join is repaired. Original Reports 01–10 remain previously verified; interrupted original Reports 11–25 remain unestablished.
Sources: controlling File_18 §§2–3, 6A–6D; File_09 paired Mirror rules; selectively retained C05, C08, C10, C123, C128 and C133–C155 evidence. Specific dependencies are named in the body/certificate. 23 assertions passed; see RESULTS.json and CERTIFICATE.json. Assertions, selected field combinations and inherited identities are not independent historical witness counts.