C41 — Raw 24-fold pairs and the joined path have different domains
22 September 2026 · Step 19 of the authorized 30-step Mirror continuation (C23–C52).
Both native-ON Shem endpoints must lie in 6343–6350 BC. For H's magnitude 12K+j this gives −5≤j≤2; for u's magnitude 12K−j it gives −2≤j≤5. Their intersection is −2≤j≤2.
| j | BC Shem numeral | Reflected Shem numeral | OFF member also admitted | Full joined base |
|---|---|---|---|---|
| -2 | 6346 | 6350 | no | no |
| -1 | 6347 | 6349 | no | no |
| 0 | 6348 | 6348 | yes | no |
| 1 | 6349 | 6347 | yes | no |
| 2 | 6350 | 6346 | yes | yes |
These five ordered pairs all have width 12696. Reflection swaps j and −j, giving two opposite-orientation pairs and one self-Mirror case at j=0 (6348 BC reflected to its own paired AD image). Thus there are three interval classes up to canonical reflection within this specifically defined source-only family, not five independent witnesses.
Requiring the original OFF Flood field restricts j to 0…7 and leaves 0,1,2. Requiring the retained SP Noah/MT cumulative base further restricts j to 2…6, leaving j=2 only, the complete N01 chain.
The negative j rows are admitted only as raw ON-Shem endpoint pairs. Their putative OFF member lies outside its field, so they do not enlarge the joined chronology. This is a closed-inequality derivation on a named field, not a broad search across historical reports or arbitrary event pairs.
Validation. 11 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. Check exactly where the new families coexist with the full 6877 expansion.