# 490d C362 — Shem source-domain and seasonal-component controls

24 September 2026. Step 9 of 10 in the C354–C363 authorization.

**The Shem-held squared-E comparison has the same four source-admitted controls as the joined mapping:02/22 at i3/i5.** It leaves a unresolved. The source controls also establish a sharper rail boundary.

Translating an MT Flood start by−500 lands on the corresponding MT Shem death. Translating a Flood close by−500 lands one year below that death. MT has no SP-style person companion, so the companion route has neither its required restored-MT input death nor its base-MT output death. No extra MT death station is inferred. Primary edge controls with a missing next Gear likewise remain unadmitted.

The inherited C319 component offsets are exactly−1/4 and+1/4. For the direct squared-E relation,16 pivot/input/output phase controls give four exact matches: both shared offsets in each primary placement. For the joined two-segment construction,64 assignments across its five distinct endpoint roles likewise give four matches, with every offset shared. These are component-preserving source comparisons, not new phase choices.

A single physical-time map behaves differently. Squared E displaces the source endpoint components by±24/529 relative to their retained positions. At the joined map’s interior break, the lower component uses300/299 and the upper component25/23; their separation becomes625/1196, exceeding the inherited half-year by27/1196. These are exact diagnostics of the map and have no adopted calendrical or residue interpretation.

The tests therefore preserve the same distinction as C341/C348: source centers and their matched inherited components can be compared, but those comparisons do not establish one physical-time dilation of the biographies. Both new constructions keep their stated finite source domain.

## Verification and limits

152 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.

Source center matches, component-preserving comparisons and physical-time maps remain distinct. No MT/LXX person companion or new phase is licensed by a translated event boundary.

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

**C363, proposed and unexecuted:** Synthesize C354–C362, independently reimplement the central arithmetic and source joins within the root process, replay the sealed packets, and publish C363 plus complete recovery files. Choose a subsequent question only after this synthesis; do not execute it.

Nine completed bounded results now connect the Shem source lifespan with the529/E structure and delimit the selector and phase claims. Consolidation and an alternate calculation are the necessary final step of this ten-step authorization.