490d C430 — Source rules and Gear boundary of the Flood-held E family

24 September 2026. Step 7 of10, C424–C433.

The nine Flood-held E coordinate arrows have 20 labelled source realizations:16 from T2 and four from T3. Their overlap is the MT2240 coincidence already resolved in C427.

For T2, fix common Cainan and sojourn flags C,F and an upper Gear g=1 or2. Hold SP/LXX Flood start with Terah+60. The input is MT Noah death with Terah0 at Gear g+1; the output is MT Shem death with Terah+60 at Gear g:

H =2951 +130C +215F +2(g−1)

input =1893 +130C +215F +2(g−1)

output =1801 +130C +215F +2(g−1).

The input gap is1058, the output gap1150, and the input moves92 under E. All eight coordinate cases are sourced. The change from Noah death to Shem death is explicitly coupled to Terah and Gear changes; it is not one unchanged MT biography.

At C=F=1, T3 supplies a second input route: MT Flood close with C0/T0/F0 at Gear g−1. That route exists for g=2 or3. The resulting strip is:

The first route occupies upper G1–G2; the second occupies upper G2–G3. They meet at the middle coordinate through two distinct source records. No single input role covers all three Gears. Extending the Noah-death formula formally to upper G3 would require Noah Gear4, which is absent and not admitted. Of the four formal G3 C/F cases, only C=F=1 has any sourced coordinate input, through the independent Flood-close record2242.

Each successive coordinate triple is+2, and the maps satisfy E_(H+2)(x+2)=E_H(x)+2. This compares changed pivots; it does not supply one fixed-pivot action or identify the two2240 source histories.

This result turns the nine arrows into two qualified source families with an explicit domain boundary. The remaining immediate harmonic question is whether the nine squared-E endpoint-only cases from C429 can acquire a sourced path by using different existing pivots.

Verification and scope

54 calculation checks and 15 source/predecessor authentication checks passed. A separate main replay is byte-identical. Root-agent analysis and replay; no new independent-agent review is claimed. Verification counts are not independent historical witnesses.

These are derived source comparisons. The changing-pivot+2 relation does not create a single physical-time action, a new phase or an identity between MT Noah death and Flood close.

Mirror/529 focus: K=529, E=25/23, P=70/69; J=300/299 remains File02 gap conversion, not a calendar date operator or Residue Protocol. Regular Gears are Noah/Shem/Flood only. SP person companions are local to Noah/Shem; Flood close is an independent event boundary. Both500/100 and502/98 bindings remain valid; SP primary Noah death retains its inclusive/harmonic qualification. LXX native Cainan is ON; OFF is theoretical removal. Global paired Mirror January AD1; local junction January AD2; no civil year zero. No new source point, phase, fitted axis, upstream/cumulative Gear, primer reopening or canonical/graph edit. Capture now; canonize later. Coordinates, source labels, context aliases and derived comparisons remain distinct. Counts are not independent historical witnesses.

Decision after this result

C431, proposed and unexecuted: For all13 sourced squared-E endpoints in C429, solve the complete same-map two-E pivot equation over existing regular coordinates and test intermediate membership. Use the positive E/P/J slope restriction to determine whether any of the nine endpoint-only cases can be repaired without changing its complete map.

The positive Flood-held family is now source-qualified. Completing the remaining endpoint-versus-path test will close the harmonic inventory before the final source/completeness audit.