C26 — Widths do not determine the branch
22 September 2026 · Step 4 of the authorized 30-step Mirror continuation (C23–C52).
The family widths leave j free. A single typed coordinate can recover it once K and the opening attachment are fixed:
| Branch | j | c | s | Z |
|---|---|---|---|---|
| N01 | 2 | -5288 | 3705 | -2 |
| N02 | 3 | -5287 | 3706 | -3 |
| N03 | 4 | -5286 | 3707 | -4 |
| N04 | 5 | -5285 | 3708 | -5 |
| P6 | 6 | -5284 | 3709 | -6 |
All five rows have B=17K, A→D=20K and A→Z=10K. Measuring those lengths alone cannot distinguish a primary Noah row from a companion row, cannot select 3 BC rather than 5 BC as a comparison landing, and cannot authorize the missing MT Noah on N01/N03.
The agreement of four reconstructions is a consistency check on retained assignments, not four independent determinations. A formal increment of j moves c and s forward by one and their reflected coordinates backward by one. Source admission must then be checked separately: arbitrary real or integer j is not an admitted chronology.
This distinction will matter for any longer Mirror path. Adding a multiple of 529 may preserve its length for every j while its required endpoint occurs in the source field only on a restricted set of rows.
Validation. 11 exact arithmetic/structural checks passed. The ten 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 §3.1 (paired Mirror); File_18 §§2.1.3, 3.1–3.2, 6B and 6D (qualified regular and cumulative fields); frozen C15 typed graph, C16 domain certificate, and C22 reduced scale/constraint certificates.
Best next bounded step — High sufficient. Verify the signed formulas against paired civil counting before using longer reflected paths.