C25 — A compact endpoint form for the retained Mirror branches
22 September 2026 · Step 3 of the authorized 30-step Mirror continuation (C23–C52).
Let K=529, ℓ=598, κ=460=2K−ℓ, p=190 and let j identify the cumulative OFF member 5290−j. In the signed paired coordinate convention, the following formulas reproduce every registered point on N01–N04 and the available P6 base points.
| Point and role | Signed coordinate |
|---|---|
| c: cumulative OFF Flood | −10K+j |
| u: native ON cumulative Shem member | −12K+j |
| cm: derived OFF Shem member | −10K−ℓ+j |
| b: fixed-field SP Creation | −8K−p+j |
| q: reflected Conquest | 3K−p+j |
| f: reflected ordinary MT Flood | 5K−p+j |
| v: reflected alternate MT Flood | 5K+j |
| s: reflected SP Noah | 7K+j |
| r: reflected SP Flood | 7K−ℓ+j |
| mtN: reflected MT Noah | 5K+ℓ−p+j |
| spDeath: reflected SP companion death | 5K+ℓ/2−p+j |
| A, X, Y, Z, D | −10K−j, −7K−j, −5K−j, −j, 10K−j |
| H: the optional left Shem head | −12K−j |
The admitted indices are N01=2, N02=3, N03=4, N04=5 and P6=6. A formula is not an admission: H exists as the retained head only on N01, while mtN and spDeath complete the full expansion only on N02/N04. The evidence compares only points actually present in the completed typed graph.
The formulas expose two opposite field-index signs. Direct branch points carry +j; their reflections and the BC partition points carry −j. They also separate the profile offset p from the common 529 unit. The Creation formula selects among fixed source members; it does not move Creation through the regular Gears.
This is an exact compression of the existing geometry, not a replacement for the role, Gear, boundary and companion tags preserved in the frozen graph.
Validation. 5 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. Determine which data identify the field index and which widths leave it free.