# C39 — The 24-fold and 20-fold intervals share a local centre

22 September 2026 · Step 17 of the authorized 30-step Mirror continuation (C23–C52).

On N01 the outer interval [H,U] has radius 12K and the inner [A,D] has radius 10K, both centred at Z=−2. Their left and right margins are each 2K=1058:

\[
[H,U]=[Z-12K,Z+12K],\qquad [A,D]=[Z-10K,Z+10K].
\]

This is a genuine symmetric nesting of those two intervals. It differs from the off-centre 13-fold nesting inside the 17-fold interval.

The local centre −2 is not the project's canonical Mirror axis. Reflection about −2 exchanges these interval boundaries, but does not preserve every internal source role. It maps the SP Noah coordinate −3705 to +3701, outside the permitted SP Noah field, and alternate MT Flood −2647 to +2643, outside that profile's Flood field.

Therefore boundary symmetry is not a symmetry of the entire typed chronology graph. The canonical paired reflection remains x→−x. The local centre is a property of this constructed interval, not a new historical event or permission to reflect all dates about 2 BC.

**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.** Record the admitted partitions of the 24-fold path without counting them as independent evidence.