# 490d Mirror checkpoint after C447

25 September 2026 UTC. **C447 complete; C448 unexecuted.** 22 steps remain in the current authorization. Current decisions override archived next-step text.

## Current result

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.

## 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.

## 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

This excludes 529 spans within the four fixed-reflection reachability relation only. It does not exclude direct 529 pairs elsewhere in the source register or paths using other declared operators.

192 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

C448: Classify all simple cycles and fixed-point loops in the finite reflection graph, compute their full affine word, and separate formula identities from returns valid only at a particular point.

The 529 closure question is settled. The remaining unclassified feature of the graph is its cycle structure, which may explain repeated sourced returns without creating new 529 spans.

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