# C97 — The first 529+23 triangle is now source qualified

22 September 2026 · Step 5 of the authorized ten-step Mirror continuation (C93–C102).

The new apparent-Creation→Joseph-closing interval supplies the missing source qualification for C05's first-stage arithmetic:

\[
6348\xrightarrow{+529}6877\xrightarrow{+23}6900,
\qquad 552=529+23.
\]

The five intervals needed for this and C05's retained second triangle are:

| Interval | Signed source endpoints | Width |
| --- | --- | --- |
| U | [-4444, 1904] | 6348 |
| A | [-4421, 2456] | 6877 |
| C | [-4444, 2456] | 6900 |
| B | [-4419, 3056] | 7475 |
| D | [-4444, 3056] | 7500 |

```mermaid
flowchart LR
 U["6348"] -->|"13/12"| A["6877"]
 A -->|"300/299"| C["6900"]
 U -->|"25/23"| C
 C -->|"13/12"| B["7475"]
 B -->|"300/299"| D["7500"]
 C -->|"25/23"| D
```

The 13/12 arrows are derived comparisons between the specified intervals. The 300/299 arrows hold the right endpoint and extend the left. Their product is 25/23, whose direct action uses the fixed apparent anchor−4444.

From U to A, the left endpoint advances 23 while Joseph 1904 advances 552 to MT Flood 2456, so the width increases 529. Extending A leftward by 23 then restores the apparent anchor and produces C. The retained second triangle similarly gives 6900→7475→7500, with gains 575+25=600.

The apparent 25/23 map sends the entire first triangle U/A/C to the second C/B/D, including both seasonal components. This is now a comparison of named source intervals throughout. The new contribution is the first triangle's original-Joseph base; the second triangle and its apparent field were established in C05.

The labels 13/12 and 300/299 do not introduce new canonical chronology operators. The next step makes the anchors behind the two 13/12 comparisons explicit, so the ratio labels do not conceal different affine maps.

**Validation.** 11 exact arithmetic/structural checks passed. The 20 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 6/6A (regular fields and cumulative collateral source); File_61 §§3.3–3.4, 11.1–11.4 and 14.3 (fixed Jacob events, original Joseph portion and its 500-year Conquest comparison); File_62 collateral-scope guards; C01/C05 retained endpoint and apparent-field results; frozen C15/C43/C65/C67/C68/C74–C76/C86/C89/C92 dependencies (source, phase and family controls). The declared phase model does not infer an unstated birthday or event month from an annual source row.

**Best next bounded step — High sufficient.** Derive the affine anchors of the two 13/12 comparisons and test their conjugacy under the retained 25/23 map.