C43 — The extended typed graph has eleven selected family labels
22 September 2026 · Step 21 of the authorized 30-step Mirror continuation (C23–C52).
The bounded joined extension adds four reflected native-ON Shem nodes, four reflection relations and 37 duration records. The complete registered graph now has 81 typed nodes, 161 duration records and 19 reflection relations.
| Family | New duration records |
|---|---|
| 2 | 4 |
| 12 | 4 |
| 15 | 8 |
| 17 | 8 |
| 19 | 8 |
| 22 | 4 |
| 24 | 1 |
The selected family labels are 2,10,11,12,13,15,17,19,20,22,24. The 3/5/7 partition legs remain in the duration graph; this family list is a selected research register, not a census of every integer multiple obtainable between any two source points.
All 37 new records have distinct directed endpoint pairs and no duplicate old directed interval. They include the canonical reflections of the newly explicit 15/17/19 paths, the right-hand 12/22/2 extensions, and N01's 24-fold span. Every new endpoint derives from an already admitted source member.
The 37 records are not 37 independent constraints. Four reflected nodes are determined by four applications of the same canonical reflection. Their widths then follow by subtracting existing coordinates and composing paths. C41's raw source-only 24-fold pairs are kept separate; they have not been inserted into the joined graph as if they possessed missing Noah bindings.
This certificate preserves the entire old graph unchanged and appends the extension explicitly, allowing later work to distinguish inherited data from the present additions.
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. Test the failure caused by confusing the two different ON Shem members.