# 490d C437 — Finite Source Census of the 432 and 18 Midpoint Profile

25 September 2026 UTC. Step 3 of 10, C435–C444.

The five-point profile has **one complete source realization**, centered at3188 BC. Four of its six derived centers are existing MT Noah-birth records; the lower inner station is sourced only in the original G1/Terah-base case.

| Base Gear/Terah | Derived center | Center sourced? | Upper/lower inner stations | Full profile? |
|---|---:|---|---|---|
|G1/T0|3188|MT Noah G2/C1/T0/F1|3206 /3170|Yes|
|G2/T0|3190|MT Noah G3/C1/T0/F1|3208 /3172 absent|No|
|G3/T0|3192|Absent; formal G4|3210 /3174 absent|No|
|G1/T1|3248|MT Noah G2/C1/T1/F1|3266 /3230 absent|No|
|G2/T1|3250|MT Noah G3/C1/T1/F1|3268 /3232 absent|No|
|G3/T1|3252|Absent; formal G4|3270 /3234 absent|No|

Both outer pivots are sourced in every row. They lie at c±432; the inner stations lie at c±18. The central record has a direct formula: SP reference Noah N minus650 for MT, plus130 for Cainan, plus2 for the next Gear gives **c=N−518**. The midpoint is therefore identified by source differences as well as by averaging.

Relative to that MT Noah center, the four source-role equations are:

| Position | Source/context difference | Value |
|---|---|---:|
|Upper pivot, SP companion Noah birth|650−215−1−2|432|
|Upper station, SP-primary/LXX-OFF Shem birth|650−500−130−2|18|
|Lower station, SP/LXX-OFF Flood start|650−600−130+60+2|−18|
|Lower pivot, SP-primary/LXX-OFF Noah death|650−950−130−2|−432|

The lower station requires base Gear+2 and Terah+1, recovering the same G1/T0 boundary as C436. The center requires base Gear+1, so four centers survive even though only one full profile does.

The E ratio is determined by the two radii: `(432+18)/(432−18)=450/414=25/23`. Thus the local24:1 geometry and the existing E expansion describe the same exact comparison. This does not add an independent witness to the ratio.

All checks use the frozen528-label Noah/Shem/Flood register. The source equations retain the SP-local companion, the distinct Flood boundary, qualified SP Noah death and theoretical LXX-OFF aliases. No absent center or lower station is admitted.

## Verification and scope

28 calculation checks and 18 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.

No new source or global axis is selected. Only four derived centers are admitted as source records; all negative statements concern the frozen finite domain.

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

**C438, proposed and unexecuted:** For the four already sourced centers3188,3190,3248,3250, census the local reflection R_c(x)=2c−x over the373 fixed regular coordinates. Identify the exact source domain and any role/context pairs, keeping these local comparisons distinct from the global Mirror.

The five-point profile supplies source-derived local reflection candidates. A complete fixed-domain census can determine whether they exchange only the known pairs or a wider source pattern.