490d C449 — Source Domain of the Four-Center Identity
25 September 2026 UTC. Step 5 of 25, C445–C469.
All 8,952 four-distinct-center trials produce exactly eight complete words, all returns: the two directions and four starts of one cycle. Each of the eight identity orders has only one sourced input. The cycle has eight source-label assignments and none keeps one unchanged source context.
| Cycle coordinate | Source identity |
|---|---|
| 2610 | SP primary or LXX OFF Shem death, G3/C0/T0/F1 |
| 3766 | SP primary or LXX OFF Noah birth, G1/C0/T1/F1 |
| 2730 | SP companion Noah death, G1/C1/T1/F0 |
| 3770 | SP primary or LXX OFF Noah birth, G3/C0/T1/F1 |
The two Noah-birth records differ by the permitted G1→G3 shift of four years. The other vertices require changes of role, Terah state, Cainan state, full430 state or SP rail. The all-SP assignment is available, but still crosses those contexts. LXX OFF aliases are the theoretical-removal state; none is an LXX companion.
The eight Cartesian assignments label the same coordinate cycle. They are not eight independent attestations and do not constitute one biography. This resolves the only ordinary cycle of the four-reflection graph. The purely reflective menu is now exhausted for 529 connectivity.
The next comparison can use the E operator already responsible for the2K path. Its eight pivots are already fixed by the existing c±432 profiles, so this extension adds neither an anchor nor a fitted center.
Verification and scope
8952 calculation checks and 19 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.
An affine identity remains admitted on a restricted source domain. Context changes are retained explicitly and do not invalidate the arithmetic; they limit historical interpretation.
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
C450, proposed and unexecuted: Census E_h(x)=(25x−2h)/23 for the eight already sourced pivots h=c±432 at the four fixed centers, retaining every sourced arrow and exact failure category across all373 inputs.
The completed reflection closure cannot yield529. The existing E pivots offer the nearest source-grounded extension, and their primitive arrows must be censused before any mixed-word search.