# 490d Mirror checkpoint after C440

25 September 2026 UTC. **C440 complete; C441 unexecuted.** 4 steps remain in the current authorization. Current decisions override archived next-step text.

## Current result

Opposed500 shifts Noah birth→Shem birth (−500) and Shem death→Flood start/close (+500) biject all16 coordinate pairs of the two reflection classes.40 source-label pairs yield40 tradition-preserving targets within48 target labels; the extra8 are LXX Flood-close aliases, not LXX companions. Four bounded context-sum templates classify the source class. One pair atc3250 reverses coordinate order:3705/2795→3205/3295.

## Earlier results in this batch

**C435**: All2238 six-map/input trials yield23 sourced first-leg outputs,10 integer final outputs,8 sourced final outputs and two complete coordinate paths: old2148→2020→1956 and additional3206→3170→3206, both withp3620/q2756. The loop has signed gaps414/−414 and changes36/−36, with SP/LXX-OFF Shem-birth endpoints and SP/LXX-OFF Flood-start intermediate. Its16 Cartesian label assignments are not yet16 same-record returns.

**C436**: The3206→3170→3206 loop has16 Cartesian labels:8 same-record returns and8 SP/LXX alias switches; one all-SP assignment and zero unchanged-context assignments. Source36=100−60−4. Signed gaps414→450 and−414→−450 establish a mixed-direction fixed-point return, not chronological repetition. Both pivot and station pairs share3188, already MT Noah birthG2/C1/T0/F1, with radii432 and18 (ratio24).

**C437**: Six derived c=N−518 profiles yield four sourced MT Noah centers3188,3190,3248,3250;3192/3252 require unavailableGear4. Onlyc3188 has all five points c±432,c±18,c. Source offsets are650−215−1−2=432;650−500−130−2=18;650−600−130+60+2=−18;650−950−130−2=−432. The ratio450/414=25/23 follows from432:18=24:1.

**C438**: All1492 local-reflection trials at3188/3190/3248/3250 yield maximal source domains61/67/19/61,106 coordinate orbits including4 fixed centers,258 unoriented labelled pairs and512 directed label pairings. Original432/18 pairs survive; additional Noah/Shem/Flood role exchanges occur. All four reflections remain partial on the373-coordinate domain; no global Mirror or full group action is inferred.

**C439**: All36864 Noah-birth/death reflection trials reduce exactly to one rule: SP/LXX endpoints, Cainan sum1, sojourn sum1, equal referenceTerah, Gear sum2g and exactly one SP companion. The unique bounded sum equation is6032+344=2×3188 with344=130+215−1. Counts bycenter are8/24/8/24 coordinate pairs and16/48/16/48 labels, totaling64/128. MT endpoints are excluded by maximum sum6200<6376.

## Baseline and standing scope

C434 is the authenticated baseline. Its checkpoint is frozen in sources/C434_CHECKPOINT.md. It derives25(215−130+1)+23×950=48×500, and the six source-pivot comparisons p=N−86, q=N−950, H=N−500. Only G1/T0 has its complete2K path2148→2020→1956. The SKL appendix and corrected LXX8464 observations remain supplemental; no redirection follows. C432’s E excerpt locator was corrected in C434 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

Opposed endpoint shifts preserve a pair sum but are not a shared chronology translation. The eight extra Flood-close aliases do not license LXX person companions or independent witness counts.

86 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

C441: Close the C438 reflection inventory by deriving the remaining Flood-start/close, MT Noah/Gear and Noah-birth/Flood-close alias classes, then verify that the resulting source grammar accounts for every labelled and coordinate pair without double-counting aliases.

The Noah950 complement class and the paired500 classes account for216 of258 labelled pairings. Explaining the remaining42 will determine whether the entire finite reflection inventory has a compact source grammar.

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