# 490d Mirror checkpoint after C450

25 September 2026 UTC. **C450 complete; C451 unexecuted.** 19 steps remain in the current authorization. Current decisions override archived next-step text.

## Current result

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.

## Earlier results in this batch

**C445**: All 5,968 ordered two-reflection trials give 330 complete paths: 208 zero-shift returns and 122 nonzero paths. Sourced shifts are ±4 (48 each), ±120 (5 each) and ±124 (8 each); both ±116 have zero complete paths.

**C446**: The four-reflection graph has 373 vertices, 106 edges including four loops, and 272 components. Its 152 active coordinates form 49 nontrivial components plus two loop-only singletons; 221 coordinates have no admitted reflection. The largest components have six coordinates and the maximum shortest-path distance is four.

**C447**: No nonzero multiple of 529 occurs among all 191 reflection-reachable coordinate pairs. The nonzero E-path coordinates 2148, 2020 and 1956 are reflection-isolated. The source pivots 3620/2756 share a four-point component; 3206/3170 share a different four-point component; midpoint3188 is a loop-only singleton.

**C448**: The reflection graph has one ordinary simple cycle, 2610→3766→2730→3770→2610, through centers3188,3248,3250,3190. Its four-reflection affine word is the identity because3188+3250=3248+3190. The other four cycles are single-center fixed-point loops, not identity maps.

**C449**: 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.

## Baseline and standing scope

C444 is the authenticated baseline. Its checkpoint is frozen in sources/C444_CHECKPOINT.md. The fixed local reflection centers are 3188, 3190, 3248 and 3250, each an existing MT Noah birth record. The 528 labelled Noah/Shem/Flood records occupy 373 integer BC coordinates. These local source comparisons do not replace the January-AD1 global Mirror. The only complete forward 2K E path remains 2148→2020→1956. The SKL appendix and corrected LXX8464 observations remain supplemental; no redirection follows. C432’s E excerpt locator was corrected in C444 to File_46 L3, lines117–133; prior arithmetic already used25/23.

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.

## Limits and verification

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

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.

## Best next bounded step

C451: 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.

Continue within the authorized batch and reassess after the next result.