# C55 — The full 6877 branches occur at qualified cumulative boundaries

22 September 2026 · Step 3 of the authorized ten-step Mirror continuation (C53–C62).

File_09 treats the seven-year week as the primary object and distinguishes three admissible ordered anatomies. Relative to the Moses line their cut sets are:

| Template | Boundary offsets |
| --- | --- |
| A: 2+3+2 | 5, 3, 0, -2 |
| B: 2+2+3 | 5, 3, 1, -2 |
| C: 3+2+2 | 5, 2, 0, -2 |

Their union is +5,+3,+2,+1,0,−2, giving the stated refinement 2+1+1+1+2. It is a set of possible boundaries, not all eight integer members of the envelope and not several simultaneous operators.

For the six 1058 pairs, requiring both member offsets to appear in one of these same numeric templates gives:

| j | Offset pair (Flood, Shem) | Templates supporting both boundaries |
| --- | --- | --- |
| 0 | (5, 3) | A: 2+3+2; B: 2+2+3 |
| 1 | (4, 2) | none: envelope members only |
| 2 | (3, 1) | B: 2+2+3 |
| 3 | (2, 0) | C: 3+2+2 |
| 4 | (1, -1) | none: envelope members only |
| 5 | (0, -2) | A: 2+3+2; C: 3+2+2 |

N02 (j=3) uses offsets +2 and 0, present in the distinct 3+2+2 template. N04 (j=5) uses 0 and −2, present in the default and 3+2+2 templates. Thus both full Creation branches have this boundary support. N01 uses +3 and +1 in the 2+2+3 template. N03 remains a valid envelope-member construction, although its +1/−1 pair is not a two-boundary pair in these three templates.

This distinction does not revoke N03, map the template letters to regular G1/G2/G3, or transfer Creation Day-4 identity to Shem. The source explicitly distinguishes the Aaron whole-year node from the Day-4 node. The result is a bounded numerical classification of member positions within the retained week states.

**Validation.** 7 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.** Construct the canonical-axis 20/22/24 Mirror rectangle at the named j=0 members.