C40 — One 24-fold path has five qualified two-part decompositions
22 September 2026 · Step 18 of the authorized 30-step Mirror continuation (C23–C52).
The N01 chain is fully endpointed:
| Point | Signed coordinate | Role |
|---|---|---|
| H | -6350 | native ON cumulative Shem head |
| A | -5292 | MT cumulative ON Flood |
| X | -3705 | SP G1 companion Noah |
| Y | -2647 | alternate MT G2 Flood close |
| Z | -2 | comparison landing |
| D | 5288 | reflected LXX cumulative OFF Flood |
| U | 6346 | reflected native ON cumulative Shem |
Its consecutive lengths are 2K, 3K, 2K, 5K, 10K and 2K. The retained cuts yield:
| Cut | Decomposition |
|---|---|
| X | 5 + 19 = 24 |
| Y | 7 + 17 = 24 |
| Z | 12 + 12 = 24 |
| D | 22 + 2 = 24 |
| A | 2 + 22 = 24 |
The right-hand 19-fold interval X→U is the canonical reflection of u→s. The right-hand 17-fold interval Y→U reflects u→v. Thus 5+19 and 7+17 preserve explicit source roles rather than being arbitrary numerical partitions. The alternative 2+22, 12+12 and 22+2 cuts use the already qualified cumulative and landing endpoints.
These decompositions are incidence identities of one path. They provide a useful integrated display but do not constitute five extra confirmations of 529. Nor does the N01 chain acquire a valid MT Noah birth for the full Creation expansion merely because its longer outer interval closes.
Validation. 7 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. Solve the exact source-field bounds for raw and joined 24-fold intervals.