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.