# 490d Mirror checkpoint after C433

24 September 2026. **C433 complete; C434 unexecuted.** 0 steps remain in the current authorization. Current decisions override old archived instructions. Do not rerun completed research.

## Current result

C424–C433 complete. The46 labelled regular2K pairs at26 coordinate pairs reduce to four context offsets:458,708,1057,1059, with separate role and local companion terms. The Flood-start/Noah-death class is1058=350+650+60−2 and has16 labels/eight coordinates; it adds no second2K station within its fixed contexts. The sole coordinate-template overlap3298/2240 comes from distinct MT Noah-death and Flood-close contexts;349=130+215+4 also produces2300, whose required2K upper3358 is absent. All156 fixed17K join trials recover only existing C287 i2–i5, all in the458 template; companion rectangles do not remove narrower primary operator qualifications. The104 fixed-upper E/E²/P/J tests have13 sourced E and13 sourced E² outputs, no P/J outputs and four complete fixed-pivot Noah ladders. Nine Flood-held E coordinate arrows have20 labelled realizations: two two-Gear input families meet at2240, while the three-Gear strip uses Noah death2238, Noah death/Flood close2240, and Flood close2242, with Shem-death outputs2146/2148/2150. No Gear4 is admitted. The all-pivot squared-E search gives39 sourced pivot-pair solutions and five sourced coordinate paths. One is new:2148→2020→1956, using pivots3620 then2756, exactly the held3206 squared-E map. Its64×23→64×25 and32×23→32×25 legs give128+64=192. Pivot3620 is SP companion Noah birth G1/C1/T0/F0;2756 is SP-primary or LXX-OFF Noah death G1/C0/T0/F1. The stations are different MT Shem-death states G2→G3→G1. Their own Noah biographies remain950; pivot separation864 crosses contexts. The fixed3206 intermediate2056 remains absent. The+2 target still lacks2022; eight other endpoint-only squared-E maps remain unrepaired. Nine current source cards reconstruct18 relevant records; fixed quarter components do not follow the two fixed pivots, although jointly shifted comparisons remain exact. No combined source prescription, new phase, global529/Mirror action or canonical edit is established.

## Earlier results in this batch

**C424**: The16 labelled Flood-start/Noah-death2K pairs occupy eight coordinates, with SP/LXX aliases. All768 fixed-context station comparisons yield no additional2K station. Corresponding primary/native person and Flood roles differ708; SP companion person roles differ707. The mixed-role2K matches are separate from the C416 same-role profile.

**C425**: All6912 Flood-start/Noah-death record pairs were tested; exactly16 hits recover C424. Their single source equation is1058=350+650+60−2. Cainan and sojourn settings match, Terah differs+60, upper Gear is one below lower, and lower Noah death is MT. The16 labels are eight coordinate repetitions of one708-context/350-role relation.

**C426**: All46 labelled2K pairs reduce to four context offsets:458 (20 labels/12 coordinates),708 (16/8),1057 (4/2),1059 (6/5). Role and local companion terms complete1058. Their coordinate union has26 rather than27 pairs because3298/2240 belongs to both708 and1057 templates through two distinct MT lower records: Noah deathG3/C1/T0/F1 and Flood closeG1/C0/T0/F0.

**C427**: The576 MT Noah-death/Flood-close comparisons yield only2240 and2300, both from349=130+215+4 with matched Terah. Only2240 has an existing2K upper coordinate3298;3358 is absent. At2240, Noah3190→2240/Flood2590→2589 and Noah2841→1891/Flood2241→2240 remain separate contexts. The template overlap is a coordinate alias, not one historical identity.

**C428**: All26 regular2K pairs × six cumulative2K Shem/Flood pairs give156 fixed17K trials. Four coordinate joins survive, with six labelled regular realizations: precisely C287 i2–i5, all T1. Companion i2/i4 remain valid source rectangles; later primary i3/i5 operator qualifications remain separate. T2/T3/T4 add no Mirror branch.

**C429**: All26 source2K pairs under E/E²/P/J give104 trials:13 sourced E outputs,13 sourced E² outputs, no P/J outputs, and four complete two-E ladders. T2/T3 supply nine distinct Flood-held E arrows to MT Shem death, sharing3298/2240. Nine E² cases remain endpoint-only. Existing source aliases at outputs remain explicit.

**C430**: Nine Flood-held E coordinate arrows have20 labelled realizations. T2 uses next-Gear MT Noah death/Terah0 to same-Gear MT Shem death/Terah60 at fixed SP/LXX Flood/Terah60, with common C/F. T3 supplies a Flood-close route at C=F=1. The strip3296/3298/3300 has inputs2238 NoahG2,2240 NoahG3 or FloodcloseG1,2242 FloodcloseG2, and outputs2146/2148/2150. Two two-Gear input families meet; no Gear4 Noah or single three-Gear input role is admitted.

**C431**: The13 sourced E² targets ×373 first pivots yield39 sourced pivot-pair solutions and five complete coordinate paths. Four are known fixed-pivot Noah ladders. One new distinct-pivot path repairs the held3206 map:2148→2020→1956 about3620 then2756, with effective pivot3206. Parameter t18 gives gap expansions64×23→64×25 and32×23→32×25, gains128+64=192. Eight endpoint-only maps remain unrepaired; fixed intermediate2056 remains absent.

**C432**: Nine current excerpts reconstruct18 records and two labelled paths for2148→2020→1956. Pivot3620 is SP companion Noah birth G1/C1/T0/F0;2756 is SP-primary or LXX-OFF Noah death G1/C0/T0/F1. The three stations are MT Shem-death states G2→G3→G1. The map equals(625t−307776)/529, effective pivot3206. Actual Noah biographies stay950; pivot gap864 crosses contexts. The+2 counterpart lacks2022 (analogous Gear4); no fixed quarter-component assignment passes. The composition is derived, not a reviewed combined source prescription.

## Inherited C423 context — historical next-step wording superseded

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.

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.

## Verification

75 calculation checks and 63 source/predecessor authentication checks passed. A separate main replay is byte-identical. Root-agent analysis and replay; no new independent-agent review is claimed. Verification counts are not independent historical witnesses.

## Best next bounded step

C434: Test whether one source formula built from Noah950, the Noah–Shem500 relation, and the existing sojourn/Cainan/SP-companion context shift explains the new128+64 factorization. Then census its finite Gear/Terah family while requiring every pivot and intermediate to remain sourced, without fitting another anchor.

The positive factorization is now authenticated and its immediate limits are known. Explaining why these specific source roles and variant shifts produce its effective pivot is the next useful reduction; that source formula and family census have not been executed. The current authorization ends at C433.

The authorization ends here. C434 needs a new instruction.