490d C404 — Noah-to-Shem transport of the three-point return graph

24 September 2026. Step 1 of 10 in the C404–C413 authorization.

The prior vertical E comparisons do not carry the complete three-point Noah return graph to a sourced Shem return graph. Only the forward J arrows survive.

For the lower branch, the existing comparisons send Noah3031/3033/3035 to SP primary or LXX Cainan-OFF Shem2991/2993/2995, holding Noah3491/3493/3495 respectively. The endpoint displacement is−40, although each vertical comparison has slope25/23.

For an original arrow F:u→v and the two existing vertical maps L_u,L_v, the transported whole affine map is L_v∘F∘L_u⁻¹. All six arrows retain their original slope and require the original pivot minus40. The inverse here is an algebraic calculation, not an added source protocol.

All402 recorded paths through six arrows have the expected transported normal form. Only six have every primitive pivot sourced: three empty paths, the two J arrows and JJ. No nonempty closed path survives this primitive-arrow requirement. The general all-path conclusion follows because any nonempty return must contain an E arrow, whose required pivot is absent.

Both uniformly matched±¼ components were checked for each arrow. They shift each required pivot by the same component offset and preserve the same source obstruction. This is a matched-component check, not an exhaustive search over independently altered phases or a physical-time seasonal dilation.

Source identities and SP/LXX aliases remain explicit in C385–C388 and the frozen register. The new information is the missing E return, not a repetition of the already absent P lift. A formal affine conjugacy alone cannot establish source closure.

Verification and limits

430 main checks and 19 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.

Source absence is confined to the frozen regular register. Uniform matched phases were tested; no arbitrary phase repair or new point was adopted.

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

C405, proposed and unexecuted: Test whether the existing same-Gear500-year Noah-to-Shem relation carries all six C396 E/J coordinate loops and the two complete E/P/J graphs to sourced Shem birth/death records. Check every endpoint and pivot, preserve source labels, and use the fixed source500 rather than a fitted translation.

C404 distinguishes the prior expansion comparison from a complete source transport. The already sourced500/600 biographies supply a different, fixed candidate that can be checked finitely before any wider search.