490d C364 — Cumulative joined-comparison source boundary
24 September 2026. Step 1 of 10 in the C364–C373 authorization.
The joined460/598→500/600 comparison has no source-qualified cumulative counterpart in the declared32-member LXX Shem/Flood register. All six existing598 arrangements fail both the internal and terminal membership test; the four complete C287 rows are included.
For the first primary row, the cumulative chain is native-ON Shem−6345 → OFF Shem−5885 → OFF Flood−5287. The joined map would require−5845 and−5245, giving500+600=1100. These are generated coordinates only. They move the internal point by+40 and the terminal point by+42, outside the source windows. The other five rows repeat the same offsets.
The negative result also has a finite interval proof: no pair of the32 existing annual centers is500 or1100 apart. Neither inherited quarter component supplies a missing source member. This is a statement about the frozen LXX Cainan ON/OFF Shem/Flood menu, not an absence claim about all chronology.
C351’s source-qualified458+600 repair remains intact at i2…5. It changes the internal OFF-Shem annual member by−2 while holding the1058 outer span. It does not enlarge the460 Cainan lifespan. The regular500/600 realization and the cumulative458/600 repair therefore retain distinct source meanings.
The source corpus also documents cumulative Noah fields and the950 lifespan. The adjacent same-state Noah→Shem seam, combined with the460 Cainan difference, may supply a source partition closer to the regular Noah950 configuration. That is a different, finite question from forcing the failed500 cumulative leg.
Verification and limits
30 main checks and 17 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 failure is bounded to the declared register and joined mapping. It does not exclude other source-labelled correspondences or invalidate the regular construction.
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
C365, proposed and unexecuted: Use the previously derived cumulative Noah field and the native-ON source dependencies to test a950-year Cainan-state rectangle with460/490 partitions. Compare only with the already retained regular SP/restored-MT Noah biographies; do not adopt a fitted axis.
The failed500 cumulative leg directs attention to the sourced950 lifespan. C300 already retains cumulative Noah ancestry, allowing a role-qualified comparison without changing lifespan or annual-member controls.