# 490d Mirror checkpoint after C423

24 September 2026. **C423 complete; C424 unexecuted.** 0 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

C414–C423 complete. The finite source menu has26 coordinate pairs at2K, with46 labelled endpoint pairs. Six coordinate pairs survive a simultaneous−500 translation; none survives two. The six have10 continuous role-defined lifts; nine of19 raw coordinate lifts would switch source identities, and the separate3395→2895 bridge adds none. A complete same-role person profile is found: SP companion G3/CainanON/Terah+60/full430 versus MT G1/CainanOFF/Terah0/short sojourn. Noah births3899/2841, Shem births3399/2341, Noah deaths2949/1891 and Shem deaths2799/1741 all differ1058. Both950 and600 endpoint lifespans and all six pairwise intervals are preserved. Its one context offset is650+130+60+215+4−1=1058; the matches are not independent witnesses. An unfiltered96-context/4560-pair census finds exactly one such labelled profile. SP primary or LXX native at the selected upper settings gives1059. Adding SP Flood close3299 versus MT Flood start2241 yields a common500+100+350+150 five-station partition. Like-named Flood boundaries differ1059; all18 same-boundary Gear controls fail2K. The five new pairs yield no17K join in30 cumulative-source comparisons and no sourced image in20 inherited corner-exchange slots. Across20 fixed-pivot E/E²/P/J gap tests, one E² endpoint is sourced: held SP companion Noah3899 maps MT Noah2841 to MT G3 C1/T1/F1 Flood close2649. Its E intermediate2749 is absent. All sourced pivot choices reduce to3899,3899 for the same whole map; prime valuations extend the exclusion to every finite positive E/P/J word with that map. Twelve current excerpts reconstruct23 relevant records. Matched quarter-offset components pass the translation; fixed held3899 E² fails all four component assignments, while jointly shifting pivot and input gives a distinct comparison. No new source, prescribed combined protocol, global529/Mirror action or canonical edit is established.

Latest completed C423; C424 is unexecuted and outside this completed authorization. Read the C423 synthesis and checkpoint, then the C414–C423 reading index. Use the C423 compact restart kit as the active packet; older archives are selective references. The new2K person profile is SP companion G3 C1/T1/F1 versus MT G1 C0/T0/F0. Keep the four person pairs and the explicit SPclose/MTstart fifth station distinct from a same-boundary Flood-year translation, which fails by one year. C414 is the complete26-pair source census, C415 the record-identity audit, C416 the four-station profile, C417 finite uniqueness, C418 Flood-boundary controls, C419 fixed Mirror failures, C420 the exact3899-held squared-E endpoint, C421 the absent-path proof and C422 direct source/component audit. The profile does not replace original i3/i5 two17K joins. The scalar1058→1250 is prior arithmetic; the new3899/2841/2649 source context is an endpoint comparison with absent2749. Preserve prior C413 source500/Shem-loop results and their limits; no completed research needs rerunning. K529,E25/23,P70/69; J300/299 is File02 gap conversion, not Residue Protocol or general date operator. Global paired Mirror January AD1; local junction January AD2; no civil year zero. Regular Gears Noah/Shem/Flood only. SP person companions remain local; Flood close is independent; SP primary Noah death remains inclusive/harmonic; both500/100 and502/98 modes remain valid. LXX native CainanON is not given a second insertion; OFF is theoretical removal. No new sourcepoint, phase, fitted anchor, global axis, upstream/cumulative Gear, primer reopening or canonical graph edit. Corrected LXX8464 supplement remains awareness only:1564→1700,2484→2700,920→1000; AD3746/2300 superseded. C-series, original unprefixed reports and Engine reports remain distinct. The earlier incomplete September17 local ZIP differs from the later verified intact original. Arithmetic, aliases, repeated paths and alternate implementations are not independent historical witnesses. Proposed C424 is a bounded audit of the16 labelled Flood-start/Noah-death2K pairs already enumerated by C414, checking their exact contexts and any additional station correspondence; it has not been performed.

## Earlier results in this batch

**C414**: The complete373-coordinate census contains26 pairs exactly2K apart and46 original labelled endpoint pairings. Six pairs retain both endpoints after one−500 application; none survives two consecutive applications. The originali3/i5 cross-spans become8493 with cumulative corners fixed.

**C415**: The six paired2K coordinate translations lift to10 continuous role-defined record comparisons. Nine of19 raw coordinate pairings fail label continuity; the separate C411 bridge adds none. The extra birth and mixed-Flood-boundary cases share upperSP-companionG3 C1/T1/F1 versus lowerMTG1 C0/T0/F0 contexts, motivating a whole-person-profile check.

**C416**: One coherent SP-companionG3 C1/T1/F1 versus MTG1 C0/T0/F0 profile has four same-role2K pairs:3899/2841 Noahbirth,3399/2341 Shembirth,2949/1891 Noahdeath,2799/1741 Shemdeath. Translation−1058 preserves all six pairwise intervals, including Noah950 and Shem600. Its single source offset is650+130+60+215+4−1=1058; Flood boundaries and uniqueness remain separate.

**C417**: All96 complete person contexts and4560 unordered pairs were tested without context preselection. Exactly one labelled same-role2K profile survives: SPcompG3 C1/T1/F1 versus MTG1 C0/T0/F0. There are24 zero-offset aliases and416 offset values. Replacing the chosen upper SPcomp by SPprimary or LXXnative gives1059. The four station matches share one context offset; finite uniqueness is not statistical independence.

**C418**: The unique person2K profile gains a fifth station at SPclose3299/MTstart2241, yielding a shared500+100+350+150 partition. Like-named Flood boundaries differ1059 at selectedGears. All18 same-boundary comparisons across availableeventGears fail1058 by parity; three mixed-boundary hits exist but onlycloseG3/startG1 retainsbothselectedGears. Translation maps SPstart3300 to MTG2close2242, so it does not map a whole same-Gear Flood year.

**C419**: Five new2K station pairs × six sourced cumulative2K Shem/Flood pairs give30 joins, none with17K cross-spans. All ten required role-specific cumulative endpoints are absent. The inherited C=−2639/−2635 corner exchanges give zero sourced images in20 slots. The coherent2K person profile remains separate from the original2K/17K joins; no newaxis is fitted.

**C420**: Acrossfivefixed2K stations×E/E²/P/J, onlyoneof20outputs is sourced: holdingSPcompNoah3899, E² mapsMTNoah2841 toMTG3 C1/T1/F1 Floodclose2649. E intermediate2749 is absent; allfiveE outputs andfourotherE²outputs are absent. P/J outputs are nonintegral. This is a newcontext endpoint comparison of the old1058→1250 scalaridentity, not a complete E ladder.

**C421**: The held3899 E² map has no sourced intermediate realization. Acrossall373possiblefirstpivots, onlyp=q3899 solves25p+23q=48×3899 withbothpivots sourced, and its2749 intermediate is absent. Themax3900 bound gives the same result algebraically. Prime7/13/5 valuations forceanyfinitepositiveE/P/J word withthetargetwholemap toE²alone. Different-slope endpoint coincidences and inverse words are outside this result.

**C422**: Twelvecurrentexcerptcards directlyreconstructall23relevantperson/event/controlrecords. Endpoints and qualifiedsourcebindings are explicit; the2Kprofile andnewE²selection remain derivedcomparisons. Thefive-stationtranslation preserves10of20inheritedquarter-offset assignments, exactlythematchedpairs. Fixedheld3899E² preservesnoneof4assignments (matched errors±24/529); jointlyshiftingpivotandinputpreservestwooffsetcomparisons butisnotonefixedaction. Nonewsourcepointorprotocolprescription is established.

## Retained context

C404–C413 complete. The existing Noah-to-Shem E charts retain only the two sourced J arrows; required Shem E pivots3016/3018 and P pivots2853/2855 are absent. The fixed source500 correspondence succeeds: all12 labelled/six coordinate Noah E/J loops translate to Shem births/deaths, including both complete E/P/J graphs. The complete target graph has MT Shem2531,2533,2535, E pivots2556/2558, J death pivots1933/1935 and P death pivots2393/2395. Every path is conjugated byT(t)=t−500 with unchanged slope and circuit multipliers1750/(3K),7500/(13K). A direct2048-case Shem-family census recovers exactly those loops. The valid502/98 binding maps only originalG2–G3 to targetG1–G2; the other six labelled cases would require unavailableGear0. The older translated squared-E endpoints were already established inC361/C363; the new return paths cannot replace their missing2056/2058 intermediate. Three slope-compatible EE paths fail all six whole-map comparisons and48 phase comparisons; the closest discrepancy is−4/529. The existing Mirror corner exchanges admit none of104 reflected loop-record slots or208 inherited components. Translating the original regular2K side−500 preserves1058 but changes both17K cross-spans to8493. The full fixed−500 source-domain census has169 coordinate arrows,392 labelled pairings and141 maximal coordinate chains. A single extra coordinate bridge3395→2895 produces3895→3395→2895→2395→1895. Its formula100+405−4−1=500 forces all three variant differences, SP companionG1 and FloodG3. It has two continuous record lifts, choosing SP or LXX CainanOFF for the Flood/death pair; the sequence is not one biography. All528 regular records reconstruct from twelve current source excerpts. The new graphs and bridge remain derived comparisons; no new source endpoint, protocol prescription, canonical edit or global529/Mirror action is established. 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

75 main checks and 63 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

C424: Audit the16 labelled Flood-start/Noah-death2K pairings already enumerated in C414 as one closed class. Retain their exact source contexts and test whether an additional documented station in the same contexts supports a coherent correspondence, without adding sources, pivots, phases or Gear scope.

The same-role person profile and its immediate extensions are now bounded. The largest remaining mixed-role class in the existing2K census is a concrete next target, with a fixed finite menu and no need for a new anchor. This is proposed only; the C414–C423 authorization ends here.

The current authorization ends here. C424 requires a new instruction.