# 490d C357 — Three-row E normal form and context census

24 September 2026. Step 4 of 10 in the C354–C363 authorization.

**The three-row pattern reduces to a small set of existing source constants.** Its460 input gap is the SP–MT offset650 minus regular Cainan130 and Terah60. The first two500 outputs come from the SP Noah/Shem/Flood chronology. The final500 output is650 minus the150-year separation between the matched MT Noah and Shem deaths:

`650−130−60=460`; `500+600−950=150`; `650−150=500`; `460×25/23=500`.

Thus all three rows are dependent realizations of the same source constants. The third row adds a source-role connection, not an independent determination of E.

The census holds same-Gear roles and exhausts384 controls: three Gears, two SP person rails, eight SP contexts and eight MT-input contexts. The final MT-output context matches the SP Cainan/Terah/sojourn settings. Let D be the unqualified same-role SP–MT offset and e=1 on the SP companion:

`D=650+130(cSP−cMT)+60(tSP−tMT)+215(fSP−fMT)`.

The three input gaps are `[D−e,D,D−e]`; the output gaps are `[500,500+e,500−e]`. Flood start has no person companion. Hence a companion’s middle output is501 and final output499, even though its matched Shem lifespan remains600.

Exactly six controls satisfy all three E equations. They use SP Cainan OFF/base Terah, MT input Cainan ON/Terah+60, the primary SP rail, and a shared sojourn frame. The six comprise all three Gears in each of the two sojourn frames. In each column the two steps are600 then500.

The full430 G1/G2 placements participate in the retained529 comparison. The additional G3 and minimum-frame realizations verify the local source grammar; they do not supply missing cumulative members or extend C287’s complete rectangle domain. The finite context result likewise does not choose the cumulative annual index or the adjacent regular Flood endpoint.

## Verification and limits

405 main checks and 14 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.

The context and Gear repetitions share source constants. Six admitted instances do not establish independent witnesses, a prescribed paired selector, or new complete529 rectangles.

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

**C358, proposed and unexecuted:** Apply the three-row criterion to all20 existing C319 controls. Distinguish having the local structure from requiring its same-Gear MT Flood input to equal the rectangle’s selected R, then compare the surviving controls with2K and17K.

The context census fixes a local grammar but does not yet address the rectangle’s endpoint selector. The pre-existing control menu tests exactly that remaining implication without adding states.