490d C355 — Shem-lifespan translation of E relations

24 September 2026. Step 2 of 10 in the C354–C363 authorization.

One nontrivial E relation survives a600-year source translation at both retained primary placements. Its fixed endpoint moves from SP Noah birth to the same-Gear SP Flood start. The input moves from restored-MT Noah birth to restored-MT Flood start; the output moves from SP Shem birth to SP Shem death.

Thus 3106+(25/23)(2646−3106)=2606, with every node already present and typed in the frozen register. The MT input retains Cainan ON, Terah+60 and full430; the SP endpoints retain native Cainan OFF, base Terah and full430. In particular,2646 is the same-Gear Flood, not the adjacent2648 endpoint of the first529 rectangle.

The identity is translation covariance: shifting an affine map and its fixed point together by600 preserves its slope. Here the translation is dictated by existing600-year source paths. It introduces neither a fitted fixed point nor a new global translation operator.

All four forward E_N relations in each eleven-node field were checked. Besides the translated fixed point, only M→S retains a full source triple. Translating R→H gives2048→1956 and2050→1958: the Shem deaths are sourced, but2048/2050 are absent from this register. Translating H→F gives1956→1856 and1958→1858, again incomplete. This does not deny endpoints in other corpora; the domain is the frozen regular Noah/Shem/Flood register.

Consequently, the650-year Shem birth separation also exists between matched deaths, but the original598→650 affine construction does not carry along with both sourced inputs. The proven transfer is the460→500 arrow only.

Verification and limits

14 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.

The source translation is a partial comparison; it does not preserve every member of the eleven-node field or establish a total group action.

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

C356, proposed and unexecuted: Test the same three retained E_N arrows at the five same-Gear SP source-event pivots: Noah birth, Shem birth, Flood start, Noah death and Shem death. Use only translations determined by those existing source events.

The600 translation supplies a fully sourced reuse. The remaining existing lifecycle pivots provide a finite test of whether this is isolated or part of a smaller repeated source grammar.