# 490d C366 — Noah state rectangles: annual and phase bindings

24 September 2026. Step 3 of 10 in the C364–C373 authorization.

**All four complete C287 rows have a source-qualified Noah-rectangle interval match, with an explicit annual-index condition.** Let k=i+2 be the native cumulative index and e=1 on the SP companion. The unique matching OFF index is j=k−e.

| i | SP rail | Native index k | OFF index j | Partition |
|---:|---|---:|---:|---|
|2 | companion |4 |3 |459–491–459 |
|3 | primary |5 |5 |460–490–460 |
|4 | companion |6 |5 |459–491–459 |
|5 | primary |7 |7 |460–490–460 |

Both cumulative Noah biographies and both regular Noah biographies remain950. For primary rows, the460 difference is the pure Cainan-state comparison at the same annual member. The companion459 combines that460 state difference with an existing−1 annual-index change. It is not a shortened Cainan lifespan or a cumulative SP companion operator.

The32 OFF-index controls give exactly these four matches. The coordinate-sum diagnostics are−3591,−3589,−3587,−3585 respectively, so no single center reversal maps all four retained rows. No corresponding axis is adopted.

For each center reversal, the inherited components match only when the cumulative and regular offsets are opposite. Eight of16 phase controls pass; all same-offset choices fail by a half-year. Consequently, the interval match does not become a map of the original same-phase C287 rectangle.

This distinguishes a successful role-labelled interval comparison from a shared coordinate action. The existing19K long cross-span offers a separate test with a fixed translation already present in the retained rectangle.

## Verification and limits

63 main checks and 15 frozen-input/predecessor authentication checks passed. A second main replay produced byte-identical DATA/RESULTS. These checks and the source interpretation were performed by the root agent; no new independent-agent review is claimed. All frozen originals and standing controls remain unchanged. Verification counts are not independent-witness counts.

A finite interval isometry does not adopt a new axis or equate cumulative annual-index motion with SP regular person adjacency.

Mirror/529 focus: K=529, E=25/23, P=70/69. Global paired Mirror January AD1; local junction January AD2; no civil year zero. Regular Gears are Noah/Shem/Flood only. SP minus-one person companions remain local to SP Noah/Shem; Flood close is a separate boundary. No upstream/cumulative Gear, new endpoint or phase, fitted anchor, global axis, primer reopening, canonical or graph edit. Capture now; canonize later. Source identity, context, modal binding, generated coordinates and phase ancestry stay distinct.

## Decision after this result

**C367, proposed and unexecuted:** Test the fixed existing19K translation on native cumulative Noah birth/death and the retained SP Noah death/birth endpoints. Check whether it preserves the original same-phase ancestry and whether the OFF-Noah internal point can also land on the restored-MT Noah birth.

The interval reversal has a phase and placement limitation. The retained19K cross-span supplies a fixed comparison that can be tested without fitting an axis.