# C65 — The 25/23 expansion acts on centres while preserving seasonal phase

22 September 2026 · Step 3 of the authorized ten-step Mirror continuation (C63–C72).

The retained 6877→7475→8125 expansion has a precise phase-preserving realization. Let b be its fixed Creation centre, r=25/23, and εₜ=−¼, εₙ=+¼. The centre map is

\[
D_{b,r}(x)=b+r(x-b).
\]

To preserve the declared pair, its component action must be

\[
\widetilde D_{b,r}(x+\varepsilon_s)
=(b+\varepsilon_s)+r\bigl[(x+\varepsilon_s)-(b+\varepsilon_s)\bigr]
=D_{b,r}(x)+\varepsilon_s.
\]

Each seasonal span is measured from the corresponding Creation component. This fixes both Creation components and preserves half-year spacing. Applied to N02 and N04, it maps the reflected MT Flood pair to the MT Noah pair and then to the SP primary Noah pair, with exact gains 598 and 650 on each rail.

| Branch | Fixed Creation centre | Flood pair | First image | Second image |
| --- | --- | --- | --- | --- |
| N02 | -4419 | AD 2458t/2459n | AD 3056t/3057n | AD 3706t/3707n |
| N04 | -4417 | AD 2460t/2461n | AD 3058t/3059n | AD 3708t/3709n |

A single dilation of physical component times about the numerical centre b is a different map: it multiplies the phase offsets as well. After one step it makes the pair 25/46 year wide, rather than 1/2; its two points miss the retained target pair by −1/46 and +1/46 year. After two steps the width is 625/1058 and the errors are −24/529 and +24/529.

These fractions are diagnostics in File_09's proof-year coordinate model. They are not calendar corrections to apply to the chronology and are not converted into solar-day claims. C05 already specifies centre action with the half-year display retained; this report supplies its explicit component formula. The source-qualified expansion is preserved without treating a numerical reconciliation ratio as a literal dilation of every historical calendar instant.

**Validation.** 12 exact arithmetic/structural checks passed. The 14 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 and Appendix A (paired Mirror and exact phase); File_18 §§2.1.3, 2.4, 3.1 and 3.2 (regular source bindings and seasonal limits); frozen C15/C16/C22/C43/C50/C61/C62 certificates (retained graph and phase); C01/C04/C05 reports (completed expansions and their source limits). The declared phase model does not infer an unstated birthday or event month from an annual source row.

**Best next bounded step — High sufficient.** Follow the named 299 midpoint through this phase-preserving expansion and determine whether its image retains a source identity.