# 490d Mirror checkpoint after C410

24 September 2026. **C410 complete; C411 unexecuted.** 3 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

The373-coordinate−500 census has169 coordinate arrows,392 labelled endpoint pairings and141 maximal coordinate chains:115 of length1,25 of length2 and one of length4. The identified role relations cover168 arrows; the sole extra coordinate bridge3395→2895 creates3895→3395→2895→2395→1895. Source identities remain separate at coincident coordinates.



## Retained context

C394–C403 complete. The two primitive source E23→25 Noah comparisons have exact J return arrows at existing Flood pivots, but not P returns. A4096-trial coherent-family census, without529 or prior-PJ preselection, finds12 labelled E/J loops at six coordinate configurations. Two MT configurations also admit P returns and coincide with the lower-full430 common P/J repairs. Their shared G2 Noah source joins the two graphs into three vertices3031,3033,3035 and six operator arrows. Every admitted path fromu tov has affine formF(t)=v+E^e P^p J^j(t−u), with(v−u)/2=p+j−e. The402 paths through six arrows yield78 classes with endpoints retained as part of the classification; an algebraic proof gives the normal form for every finite admitted path. At each source vertex, complete P–E and J–E circuits commute with independent multipliers1750/(3K) and7500/(13K), K529. Individual E/P/J operators do not commute. The original17K branch obtained by+215 translation lacks required E pivots3271/3273. All ten common P/J source edges were checked: exactly the two lower regular edges admit an E return; no cumulative edge does. Across2238 circuit-generator/input trials in373 regular coordinates, only the fixed source point survives each circuit. Reduced denominators prove this for every nonempty positive circuit, excluding a global529-preserving chronology action. Source-table and variant reconstruction confirms all52 labelled record slots across12 loops. Endpoints, variants and scalar ratios are sourced; the new affine path grammar is a derived comparison, not an established prescription in the reviewed source passages. Whole950 biographies and a single physical seasonal action are not preserved. No new source endpoint, pivot, Gear scope or canonical graph edit was introduced. C393 is an earlier 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

3 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

C411: Audit the unique3395→2895 bridge from the source context formula and test continuous record-labelled path lifts of the500 graph. Separate the existing role-defined arrows from the new cross-context comparison, verify its phase conditions, and determine whether the four-step coordinate chain survives without switching identities at shared coordinates.

The census found one concrete extension and also exposed the risk of joining different source identities by equal coordinates. Its source formula and actual path lift should be settled before interpreting the2000-year chain.

Continue within the authorized batch, reassessing after the next completed result.