# 490d C356 — Five source pivots and three460→500 realizations

24 September 2026. Step 3 of 10 in the C354–C363 authorization.

**A second translated realization survives at SP Shem death.** The five source-determined pivot offsets are0,−500,−600,−950,−1100 from SP Noah birth. Forty checks cover the four original forward E relations at those five pivots in both primary fields.

| SP fixed endpoint | MT input | Output | Gap conversion |
|---|---|---|---|
| Noah birth3706 | Restored Noah birth3246 | SP Shem birth3206 |460→500 |
| Flood start3106 | Restored Flood start2646 | SP Shem death2606 |460→500 |
| Shem death2606 | Restored Shem death2146 | Base MT Noah death2106 |460→500 |

The second field adds2 to every displayed coordinate. All endpoints belong to the frozen register under the same named contexts as the preceding reports. The new final row is `2606+(25/23)(2146−2606)=2106`.

The first two columns follow the same roles: Noah birth→Flood start→Shem death, spaced600 then500. The output column follows SP Shem birth→SP Shem death→MT Noah death, also600 then500, but the final move crosses traditions. Keeping that change explicit is essential.

Ten nontrivial triples survive across both placements: the six original triples and four translated ones. Offsets−500 and−950 yield no complete nontrivial relation. At−600 and−1100 only the translated460→500 arrow survives. The longer1058→1150→1250 chain remains confined to its original Noah-held placement in this census.

These repeated460→500 triples are connected by source-determined translations. They therefore share arithmetic ancestry and must not be counted as independent confirmations. Their value is a smaller description of the admitted endpoint structure.

## Verification and limits

56 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.

Translation covariance explains related triples; repetition is not an independent witness count. No whole-field translation action or broader Gear domain is inferred.

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

**C357, proposed and unexecuted:** Derive the three-row construction from the source offset and lifespan constants, then exhaust the held context/Gear/SP-rail menu to determine which settings support all three rows together.

The finite pivot census found a repeated structure. Its evidential value now depends on isolating the independent source constants and testing whether the same pattern survives the declared alternatives.