# 490d C428 — Complete fixed 17K joins of the regular 2K census

24 September 2026. Step 5 of10, C424–C433.

The complete fixed17K join census has **four coordinate rectangles, all already in C287**. No newly classified template adds a Mirror branch.

All26 regular2K coordinate pairs were combined with all six sourced cumulative Shem/Flood2K pairs:156 trials. The fixed equations require both cross-spans to be8993=17K.

| C287 index | Cumulative Shem / Flood | Regular upper / lower | Regular labels |
|---:|---|---|---|
|2|−6346 /−5288|3705 /2647|SP companion Noah / MT Flood close|
|3|−6345 /−5287|3706 /2648|SP primary or LXX Noah / MT Flood start|
|4|−6344 /−5286|3707 /2649|SP companion Noah / MT Flood close|
|5|−6343 /−5285|3708 /2650|SP primary or LXX Noah / MT Flood start|

These are six labelled regular realizations at four coordinate rectangles. All belong to T1, the458 context template with the600-year role contribution or its companion/boundary equivalent. T2, T3 and T4 contribute none.

The two companion rectangles are retained source geometries; they were already inside the C287 domain. This does not reverse the later source/operator tests that selected primary i3/i5 for specific P/J or other constructions. A valid2K/17K rectangle and a valid subsequent operator path remain separate claims.

No cumulative Gear, new cumulative point or fitted exchange constant was introduced. This step establishes completeness of the fixed join test over the existing regular census, rather than rediscovering its four surviving rectangles.

## Verification and scope

160 calculation checks and 16 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.

Completeness is restricted to the frozen cumulative and regular registers and the fixed17K equations. Existing companion rectangles are not newly admitted operator paths.

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

**C429, proposed and unexecuted:** Complete the fixed-upper gap-scaling inventory for all26 source2K pairs under E, E², P and J. Record every sourced output and distinguish squared-E endpoints from two sourced E steps, retaining the four context-template labels.

The full Mirror question is closed within the frozen menu. The same complete inventory can now show which2K role families actually support sourced harmonic outputs, without choosing another pivot.