# C76 — The 6875 construction completes a same-Gear 600-by-650 Noah square

22 September 2026 · Step 4 of the authorized ten-step Mirror continuation (C73–C82).

Three of the six 11-fold chains continue through MT and SP primary Noah births, all in the **same regular Gear**:

| j / Gear | Creation BC centre magnitude | MT Flood | MT Noah | SP Noah |
| --- | --- | --- | --- | --- |
| 3 / G1 | 4419 | 2456 | 3056 | 3706 |
| 5 / G2 | 4417 | 2458 | 3058 | 3708 |
| 7 / G3 | 4415 | 2460 | 3060 | 3710 |

The corresponding four source roles form this interval rectangle:

| Reflected target | MT: Creation span | SP: Creation span |
| --- | --- | --- |
| Same-Gear Flood start | 6875 | 7525 |
| Same-Gear primary Noah birth | 7475 | 8125 |

Each birth-to-Flood comparison is 600; each MT-to-SP comparison is 650. Both routes add 1250 and reach the same SP Noah pair. The 7475 and 8125 endpoints already belong to the 13-fold expansion on N02/N04, but here they are reached from the lower 6875 Flood comparison.

The j=7 row adds a source-qualified **G3 completion** at fixed Creation member 4415 BC, with reflected MT Flood 2460, MT Noah 3060 and SP Noah 3710. It does not create a third 6877 chain: that width from the same origin would require MT Flood 2462, outside the retained field. Creation 4415 is selected inside the fixed source week; no Adam-to-Creation repair or upstream Gear movement is applied.

The three close-ending rows cannot acquire this specific birth completion: their required MT Noah coordinates 3055/3057/3059 are absent from the ordinary MT birth field. Their 11-fold prefixes remain valid. The new result is therefore a three-row same-Gear construction, with a different source domain from the two complete adjacent-Gear 6877 chains.

**Validation.** 14 exact arithmetic/structural checks passed. The 15 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 §11 and File_62 collateral-scope guards (original Joseph portion only); frozen C15/C16/C22/C43/C65/C72 certificates and C01/C05/C09 reports (retained source, phase and family dependencies). The declared phase model does not infer an unstated birthday or event month from an annual source row.

**Best next bounded step — High sufficient.** Test whether the 600 interval has a named 300+300 midpoint and compare it with the existing 299+299 companion midpoint.