490d C388 — Finite E/J strip composition and source boundaries

24 September 2026. Step 5 of 10 in the C384–C393 authorization.

The E/J squares compose into two finite coordinate strips, each spanning the complete recorded G1→G2→G3 path. Their SP and LXX interpretations remain separate context lifts.

For each strip, with its two original Flood pivots A₀,A₁ and transported Shem-death pivots D₀,D₁,

E_(N+4) ∘ J_A₁ ∘ J_A₀ = J_D₁ ∘ J_D₀ ∘ E_N.

The equality holds as a whole affine map. In the translated frame of C382, subtract2t at slice t. The lower J maps become dilations about the first MT Noah input, the upper J maps become dilations about the first Shem input, and the vertical map is the fixed E_N. Since E_N carries the first center to the second, it intertwines the two dilations. This describes existing finite source comparisons; it creates no new date anchor.

Endpoint agreement alone is weaker. Each of the four two-letter bottom P/J words reaches the same final MT Noah source. Following it with the final E therefore reaches the same Shem endpoint in all eight branch/word tests. But only JJ equals the all-J upper route as an affine map. PJ,JP andPP have different slopes. Their unavailable upper P pivots remain unavailable.

Both boundaries were tested. Reapplying E to the first Shem image gives a noninteger coordinate absent from the register. Continuing the MT path would require the unrecorded next MT Noah Gear. The strip therefore has two horizontal source edges and one vertical E comparison; no infinite lattice or unrestricted operator action is established.

Verification and limits

21 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.

Composition is finite and context-labelled. A shared source endpoint is not equality of operators, and no new regular Gear, cumulative Gear, endpoint or phase is 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

C389, proposed and unexecuted: Reflect the source-qualified E/J square through each of the two already recorded17K corner exchanges and test every resulting point against the frozen cumulative menu. Preserve ancestry phases and distinguish algebraic conjugacy from cumulative source availability.

The regular strip is now complete within its finite domain. The Mirror/529 focus makes its compatibility with the original cumulative counterparts the next decisive bounded test.