# 490d Mirror checkpoint after C441

25 September 2026 UTC. **C441 complete; C442 unexecuted.** 3 steps remain in the current authorization. Current decisions override archived next-step text.

## Current result

Six source classes partition all258 labelled reflection pairs:Noah complement128;Noah/Shem40;Shem/Flood48;Flood boundaries32;Noah/Flood alias4;MT Noah Gears6. Their112 coordinate memberships reduce to106 orbits through six explicit role-alias overlaps. Residual Flood rule usesC1/T1, complementaryF and boundedGear sums; two600-year Noah-companion/Flood-close pairs overlap Noah-death labels via349=130+215+4; MT centerG2 exchangesG1/G3, whileG3 only fixes itself.

## 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.

**C440**: 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.

## 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

Six classes describe a finite source comparison inventory. Their coordinate overlaps do not merge event identities, and partial reflection domains do not establish a global group action.

18 calculation checks and 20 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

C442: Test the reflection conjugacy R_c E_p R_c=E_q at the four sourced centers, census the reversed two-E order on the fixed373-coordinate domain, and determine whether the nonzero2K path and zero-net loop have fully sourced reflected counterparts.

The source grammar is complete. Returning to the E/529 paths will test whether the new local reflection domains support their operators, rather than inferring that from endpoint symmetries.

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