490d C471 — Source Bindings and Ancestry Gates of the Three 1250 Outputs
25 September 2026 UTC. Step 2 of 10, C470–C479.
All three admitted expansions end in the same qualified source form: MT Shem death to SP-primary or LXX-OFF Shem birth at matching Gear, Cainan, Terah and full430 settings. Its span is600+650=1250. The three output contexts are G3/C0/T1/F0, G1/C0/T0/F1 and G3/C0/T1/F1.
| Input pair | Endpoint changes | Source explanation |
|---|---|---|
| 1955,3105 | −150,−50 | MT Noah death→Shem death; Flood close→Shem birth with role+101, Gear+4, Terah+60, full430−215 |
| 2020,3170 | −64,+36 | Common Terah−60 and Gear−4; upper Flood start→Shem birth adds100 |
| 2148,3298 | −128,−28 | Common Cainan−130 and Gear+2; upper Flood start→Shem birth adds100 |
The last two inputs already have the coherent1150=500+650 Shem-death/Flood-start binding. The first input instead uses MT Noah death and SP/LXX-OFF Flood close across different contexts:350+650+215−60−4−1=1150. Flood close remains an event boundary, not a person companion.
For an inverse E candidate x=(23m+2p)/25, integrality requires p≡m modulo25. The1955/3105 row matches pivot3680 and gives2093/3151, both absent. The2020/3170 row matches3620 and gives the sourced2148/3206 pair. The2148/3298 row has residue23, absent from the eight fixed pivots, so every predecessor is fractional.
The respective complete source assignments, including every distinct endpoint and the pivot, number4,8 and4. They retain all labels and are not independent historical witnesses. The shared output binding suggests a finite1250-family census before extending the operator menu.
Verification and scope
52 calculation checks and 21 source/predecessor authentication checks passed. Main result files replay byte for byte. These are root-agent checks, not an independent-agent review or independent historical witnesses.
The650 offset is between normalized MT and SP/LXX-OFF states. LXX native Cainan-ON input alternatives at3298 do not make its C0 output a native-ON record. No missing predecessor is generated or admitted.
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.
Best next bounded step
C472, proposed and unexecuted: Census all1250-year source pairs and their labelled role/context families, locate the three admitted E outputs, and distinguish the matched Shem600+650 family from other1250 comparisons and aliases.
The three outputs share a clear source structure. The complete1250 inventory will show whether that structure accounts for all such spans or only one identifiable family.