# C59 — N01 aligns all four cumulative members with the 2+2+3 boundaries

22 September 2026 · Step 7 of the authorized ten-step Mirror continuation (C53–C62).

The four source-field requirements are separate:

| Required source member | Admitted j range |
| --- | --- |
| Fminus | 0…7 |
| Fplus | -1…6 |
| Sminus | -2…5 |
| Splus | -5…2 |

Their common domain is j=0,1,2. In each row the mixed rectangle retains widths 20K,22K,22K,24K and has 20/24 centres at −j. The source-member positions and their shared cut support are:

| j | F₊: MT ON | F₋: LXX OFF | S₊: ON Shem | S₋: ON Shem | All-four boundary template | Noah join |
| --- | --- | --- | --- | --- | --- | --- |
| 0 | 5290 | 5290 | 6348 | 6348 | none | no |
| 1 | 5291 | 5289 | 6349 | 6347 | none | no |
| 2 | 5292 | 5288 | 6350 | 6346 | 2+2+3 | yes |

N01 (j=2) is the only one of these rows with the regular Noah join. It is also the only row whose four Moses-relative offsets all occur in one of the three numeric cut templates: **+1,+3,+5,+1**, within the **+5,+3,+1,−2** boundaries of 2+2+3.

The other two rows remain valid cumulative rectangles. Their lack of all-four named-boundary support does not invalidate their envelope members. This is an additional description of the retained N01 construction, not a new count of independent witnesses or an assignment of cumulative template 2+2+3 to regular Gear 2.

At j=0 the mixed rectangle has the same coordinate geometry as C56's single-tradition rectangle, but the left Flood role is MT ON here and LXX OFF there. Coordinate coincidence does not identify those roles. At j=1/2 the left Flood values 5291/5292 are outside the LXX OFF field, making the distinction unavoidable.

The upper ON Shem boundary limits this four-field box to j≤2; the full Creation expansions at j=3/5 therefore cannot add this head. Their previously proved 13/19/right22 paths remain admitted.

**Validation.** 11 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.** Test which conclusions actually require the source gap to equal six rather than a nearby formal value.