# 490d Mirror checkpoint after C396 24 September 2026. **C396 complete; C397 unexecuted.** 7 steps remain in the current authorization. Read this checkpoint and report first; frozen predecessor records retain earlier findings. Current decisions override stale archive instructions. Do not repeat completed research. ## Current result The4096-case unfiltered coherent-family census finds six coordinate E/J loops and12 labelled comparisons. Two MT loops also have sourced P returns at2893/2895 and coincide with the lower-full430 common P/J repairs. SP companion loops require existing Flood close; four SP/LXX coordinate loops remain J-only. ## Retained context C393 is the latest preceding synthesis. The sourced E/J square connects MT Noah two-year repair to SP primary/LXX Cainan-OFF Shem births; E_(N+2) after J_A equals J_(A-40) after E_N with the transported pivot at next-Gear Shem death. Four coordinate squares have eight labelled contexts and form two two-edge strips. The required P pivots are absent; the two original17K reflections lack three cumulative image points each. Primary500/100 passes; companion/502 modes remain valid but fail the vertical E comparison. A4096-case coherent-family census without529 prefilter recovers the same cases. Source500/600 gives460+598=1058=2K; target1100 differs by42. The1492-evaluation held-Noah E census has29 nontrivial edges and25 maximal paths; only the four old double-E ladders have two edges. Two extra source E23→25 edges are3683→3681 about3706 and3685→3683 about3708, with explicit−215+130+60 context displacement. No global529-preserving E/P/J action is established. C383 is an earlier synthesis. The complete frozen Flood-pivot common-P/J census has six cumulative signed-minus-two and four regular signed-plus-two source quadruples. Two regular lower-full430 contexts are minus215 translations; only original full430 i3/i5 joins retain17K. P/J moving-pivot squares commute exactly when pivot separationD=230h. Finite paths have at most three cumulative or two regular edges. In translated frames the maps share the existing source input as center; operator counts determine the word map, and distinct counts retain distinct slopes. Paired iteration raises cross-spans by4, so it does not preserve17K. Fixed-pivot order defect is±20/897. J300/299 is File02 gap conversion, not calendar Residue Protocol. C373 is an earlier synthesis. At source Flood pivots 460 apart, P=70/69 on 138→140 and J=300/299 on 598→600 reach the same existing two-year repair. All four complete cumulative rows and regular primary i3/i5 pass; companion regular rows fail. Twenty C319 controls leave 22:i3/i5 conditionally. Equal integer gains have family69m→70m,299m→300m,pivot230m, source-qualified side529m; actual460 fixesm2. The pairing is not a reviewed source prescription or a global map. Same-offset comparisons pass; fixed-pivot phase transport fails. Native cumulative Noah950 translates by existing19K to reflectedSP950 with birth/death roles exchanged. The full source bridge matrix has primary69/138 and companion70/140 remainders; the companion459 includes an explicit annual-index difference. The cumulative joined500/1100 comparison has no source support in its frozen menu. C373 retains all earlier qualifications. C363 is an earlier synthesis. Joined460/598→500/600 reaches sourced SP Shem birth/death and changes one original17K span by42;550/529 is diagnostic only. The source Shem600+50+600 rectangle gives1250; Shem-held squaredE maps1058→1250 but has no admitted2056/2058 intermediate. Both new constructions leave02/22:i3/i5, with cumulativea unselected. Phase ancestry and source membership remain explicit. C353 adds the primary458+600=1058 paired source realization with original2K/17K outer endpoints unchanged, the598→650 SP/MT Shem image under E, and bounded partial relations.600 output alone leaves nine primary controls; both598 inputs select22 conditionally. Whole-affine gap conversion is not biography or seasonal-component transport. C343 is the earlier source-ladder synthesis. The primary Noah-held source ladder1058→1150→1250 under E=25/23 has refinement460+490+108+92+100. Companion actual MT Shem gives1149 and the valid502/98 mode gives1152; both retain double-E outer endpoints. C341 distinguishes component-preserving comparisons from one physical-time affine dilation or a biography-preserving map. C334 shared Shem±2 origin is explicit, but exact cumulative/regular endpoint coupling is unestablished in reviewed passages. C342 full regular ladder leaves C319 controls02 and22 at i3/i5; separate17K selects22. C287 full SP domaini2…5 remains; C319 is onlyi3…7. C314 reversal requiresi+j=10 with opposite cumulative ancestry phase; C323 conditionali=j5 uses its extra support requirements. SP primary death retains inclusive/harmonic qualification; matched lifespan950 remains. Source500/100 and502/98 bindings are valid alternatives. Scalar/C89 prior art remains distinct from the Noah-held endpoint realization. Corrected LXX8464 supplement is awareness only:1564→1700,2484→2700,920→1000; AD3746/2300 superseded. Earlier incompleteSeptember17 ZIP differs from the later verified intact original. Original unprefixed reports, Engine reports and C-series remain distinct. No independent witness or source-prescribed selector is inferred from repeated coordinates. Mirror/529 focus: K=529, E=25/23, P=70/69. Global paired Mirror January AD1; local junction January AD2; no civil year zero. Regular Gears are Noah/Shem/Flood only. SP minus-one person companions remain local to SP Noah/Shem; Flood close is a separate boundary. No upstream/cumulative Gear, new endpoint or phase, fitted anchor, global axis, primer reopening, canonical or graph edit. Capture now; canonize later. Source identity, context, modal binding, generated coordinates and phase ancestry stay distinct. ## Verification 94 main checks and 15 frozen-input/predecessor authentication checks passed. A second main replay produced byte-identical DATA/RESULTS. These checks and the source interpretation were performed by the root agent; no new independent-agent review is claimed. All frozen originals and standing controls remain unchanged. Verification counts are not independent-witness counts. ## Best next bounded step C397: Determine the affine composition structure of the two fully sourced E/P/J loops. Test whether the closed P–E and J–E circuits commute at each source vertex, classify their multipliers, and separate loop equality from equality of the three individual operators. The complete census reveals two source graphs containing all three operators. Their closed-loop algebra is the strongest new structural question before testing broader transport or Mirror claims. Continue within the authorized batch, reassessing after the next completed result.