# C56 — 20, 22 and 24 form a canonical-axis cumulative Mirror rectangle

22 September 2026 · Step 4 of the authorized ten-step Mirror continuation (C53–C62).

Use two source-qualified BC members: OFF cumulative Flood opening F=5290=10K and whole-year Aaron-side ON Shem S=6348=12K. Reflect each pair about the existing January AD 1 axis. The cross-axis widths are:

| BC source → reflected source | Width | Multiple |
| --- | --- | --- |
| F → F | 10580 | 20 |
| F → S | 11638 | 22 |
| S → F | 11638 | 22 |
| S → S | 12696 | 24 |

The 20-fold and 24-fold self-Mirrors are concentric at the canonical axis. Their BC-side and AD-side margins are each S−F=1058. Each crossed interval is 22K=11638, giving the width progression 20K,22K,24K in steps of 2K.

This is a width identity from shared endpoints: 20K+24K=22K+22K. It is not a general date-averaging operator or four independent confirmations. The two crossed intervals are canonical reflections of one another. The determinant identity (2F)(2S)−(F+S)²=−(S−F)² records the same shared-endpoint dependence.

For the 24-fold pair, 6349t/6348n BC → AD 6348t/6349n gives 12696 in both seasonal civil components. This use of the whole-year member will receive an exact phase audit in C61.

At j=0 the MT cumulative ON Flood field also contains coordinate 5290, but that is a different typed role from the LXX OFF opening. The rectangle here uses the LXX role. Neither coincidence supplies the missing SP Noah 3703 or the out-of-field Creation candidate 4422. This is a cumulative-only construction, not an additional full 6877 join.

**Validation.** 10 exact arithmetic/structural checks passed. The 13 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 §0.4 rules 21–22 and the Creation Cell / Aaron Phase guard (week anatomy), §3 (paired Mirror); File_18 §§4.2 and 6A–6D (lifespans and cumulative fields); frozen C15/C16/C22 and C43/C46/C48/C50/C52 certificates (retained graph, unit, and domains).

**Best next bounded step — High sufficient.** Derive the six-year MT-ON/LXX-OFF Flood displacement from the named source lifespans.