# 490d C450 — Primitive E Arrows at the Eight Existing Pivots

25 September 2026 UTC. Step 6 of 25, C445–C469.

The eight existing pivots yield37 sourced E arrows in2,984 trials: eight pivot self-arrows and29 distinct nonzero arrows. Another2,854 outputs are fractional and93 are integer coordinates absent from the frozen register.

E_h(x)=(25x−2h)/23 uses the source ratio in File_46 L3, lines117–133. Its pivots are exactly c−432 and c+432 for c=3188,3190,3248,3250. Each pivot is separately present in the register; no generated pivot is admitted.

| Pivot | Sourced arrows | Nonzero | Fractional failures | Integer absent |
|---:|---:|---:|---:|---:|
| 2756 | 7 | 6 | 356 | 10 |
| 2758 | 5 | 4 | 361 | 7 |
| 2816 | 3 | 2 | 356 | 14 |
| 2818 | 4 | 3 | 356 | 13 |
| 3620 | 8 | 7 | 355 | 10 |
| 3622 | 3 | 2 | 352 | 18 |
| 3680 | 4 | 3 | 360 | 9 |
| 3682 | 3 | 2 | 358 | 12 |

The census recovers2148→2020 at3620, then2020→1956 at2756, as well as3206→3170 and3170→3206. It also exposes additional primitive arrows, including2610→2522,2735→2733→2731 and3105→3055→3081. These have sourced endpoints but still require context interpretation.

Fractional outputs are kept as exact numerator/23 records. The absence category applies only to the373-coordinate menu. The next operation is a directed closure: E arrows are not silently reversed. Reflection edges retain both admitted directions.

## Verification and scope

45 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 integer/sourced arrow is an arithmetic comparison. This menu does not authorize applying E to every calendar date or identifying different source contexts.

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

**C451, proposed and unexecuted:** Compute directed reachability for the combined fixed-reflection and eight-pivot E menu, retaining exact shortest operator witnesses and testing every reachable distinct pair for nonzero529 multiples.

Primitive admission is now fixed. A directed finite graph can settle every mixed-word529 comparison without an arbitrary search-depth cutoff or adding inverse E operations.