# 490d C472 — Complete 1250 Source-Pair Inventory and Role Families

25 September 2026 UTC. Step 3 of 10, C470–C479.

The frozen register contains **74 distinct1250-year pairs and130 labelled assignments**. The complete partition is:

| Class | Source binding | Coordinate pairs | Label pairs |
|---|---|---:|---:|
|A|MT Shem death ↔ SP-primary/LXX Shem birth, matched context|24|48|
|B|MT Flood close ↔ SP companion Noah birth, matched context|24|24|
|C|MT Flood start ↔ SP-primary/LXX Noah birth, matched context|24|48|
|D|MT Noah-death alias in classB coordinates|2|2|
|E|MT Noah death ↔ SP companion Shem birth, differing contexts|2|2|
|F|SP companion Shem-death alias in classC coordinates|1|2|
|G|SP-primary/LXX Shem-death alias in classB coordinates|2|4|

ClassesA–C are disjoint at the coordinate level: each spans all24 Gear/Cainan/Terah/full430 settings. ClassE adds the pairs1955/3205 and2085/3335. ClassesD,F,G add labels at existing pairs, so the coordinate total is72+2=74, not the sum of all seven coordinate counts.

The matched equations are A andC:600+650=1250; B:601+650−1=1250. The601 comes from Noah birth to Flood close, and the separate−1 is the SP Noah-person companion. They are different node mechanisms.

The remaining equations are D:950+650−130−215−4−1; E:450+650+215−60−4−1; F:1100−130+60+215+4+1; G:1100+215−60−4−1. Every sum is1250, and the corresponding context-difference vectors are checked against every label pair.

The three E outputs found in C470 are in classA. Their common1250 span therefore has a clear role binding, but that binding is not the sole source of1250 intervals. The three large families appear related by ordinary source-role differences and an explicitly qualified adjacent boundary/person comparison.

## Verification and scope

149 calculation checks and 22 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.

A coordinate alias is retained as a distinct record. The B-family −1 does not create an MT or LXX companion operator; its lower endpoint is an independently sourced Flood closing boundary.

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

**C473, proposed and unexecuted:** Construct the typed common-context translations between the three24-pair1250 families, checking the +500 role correspondence and independent −1 Flood-boundary/SP-companion correspondence, then test whether the admitted E arrows translate with their required anchors.

The complete1250 grammar isolates three coherent families. Their source correspondences can now be tested without adding new dates or treating all1250 labels as the same event relation.