# 490d C404–C413 reading index and restart guide

**All ten steps are complete. C414 has not been executed.** 24 September 2026.

Read the C413 synthesis and checkpoint first. Use the compact restart kit as the active packet. The continuation archive contains all ten sealed evidence packets and all 30 individual deliverables. Older archives remain selective reference libraries. Current corrections override stale archived next-step instructions.

## Main result

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.

## Read first

- [490d_C413_Source_Shem_Return_Graphs_500_Domain_and_Mirror_Boundaries_Synthesis_20260924.md](sandbox:/workspace/scratch/2cd312e78692/deliverables/490d_C413_Source_Shem_Return_Graphs_500_Domain_and_Mirror_Boundaries_Synthesis_20260924.md)
- [490d_Mirror_Checkpoint_After_C413_20260924.md](sandbox:/workspace/scratch/2cd312e78692/deliverables/490d_Mirror_Checkpoint_After_C413_20260924.md)

## Ten-step locator

| Step | Report | Checkpoint | Evidence |
|---|---|---|---|
|C404 — Noah-to-Shem transport of the three-point return graph|[Report](sandbox:/workspace/scratch/2cd312e78692/deliverables/490d_C404_Noah_to_Shem_Transport_of_Three_Point_Return_Graph_20260924.md)|[Checkpoint](sandbox:/workspace/scratch/2cd312e78692/deliverables/490d_Mirror_Checkpoint_After_C404_20260924.md)|[Evidence ZIP](sandbox:/workspace/scratch/2cd312e78692/deliverables/490d_C404_Evidence_20260924.zip)|
|C405 — Source-qualified 500-year translation of Noah return loops to Shem|[Report](sandbox:/workspace/scratch/2cd312e78692/deliverables/490d_C405_Source_Qualified_500_Translation_of_Noah_Loops_to_Shem_20260924.md)|[Checkpoint](sandbox:/workspace/scratch/2cd312e78692/deliverables/490d_Mirror_Checkpoint_After_C405_20260924.md)|[Evidence ZIP](sandbox:/workspace/scratch/2cd312e78692/deliverables/490d_C405_Evidence_20260924.zip)|
|C406 — Independent coherent-family census of Shem return loops|[Report](sandbox:/workspace/scratch/2cd312e78692/deliverables/490d_C406_Independent_Coherent_Family_Census_of_Shem_Return_Loops_20260924.md)|[Checkpoint](sandbox:/workspace/scratch/2cd312e78692/deliverables/490d_Mirror_Checkpoint_After_C406_20260924.md)|[Evidence ZIP](sandbox:/workspace/scratch/2cd312e78692/deliverables/490d_C406_Evidence_20260924.zip)|
|C407 — 500 and 502 source bindings and the finite Gear boundary|[Report](sandbox:/workspace/scratch/2cd312e78692/deliverables/490d_C407_500_and_502_Source_Bindings_and_Finite_Gear_Boundary_20260924.md)|[Checkpoint](sandbox:/workspace/scratch/2cd312e78692/deliverables/490d_Mirror_Checkpoint_After_C407_20260924.md)|[Evidence ZIP](sandbox:/workspace/scratch/2cd312e78692/deliverables/490d_C407_Evidence_20260924.zip)|
|C408 — Return-path obstruction to the missing squared-E factorization|[Report](sandbox:/workspace/scratch/2cd312e78692/deliverables/490d_C408_Return_Path_Obstruction_to_Missing_Squared_E_Factorization_20260924.md)|[Checkpoint](sandbox:/workspace/scratch/2cd312e78692/deliverables/490d_Mirror_Checkpoint_After_C408_20260924.md)|[Evidence ZIP](sandbox:/workspace/scratch/2cd312e78692/deliverables/490d_C408_Evidence_20260924.zip)|
|C409 — Fixed Mirror-corner test of the Shem loop translation|[Report](sandbox:/workspace/scratch/2cd312e78692/deliverables/490d_C409_Fixed_Mirror_Corner_Test_of_Shem_Loop_Translation_20260924.md)|[Checkpoint](sandbox:/workspace/scratch/2cd312e78692/deliverables/490d_Mirror_Checkpoint_After_C409_20260924.md)|[Evidence ZIP](sandbox:/workspace/scratch/2cd312e78692/deliverables/490d_C409_Evidence_20260924.zip)|
|C410 — Complete regular-source domain of the fixed 500-year translation|[Report](sandbox:/workspace/scratch/2cd312e78692/deliverables/490d_C410_Complete_Regular_Source_Domain_of_Fixed_500_Translation_20260924.md)|[Checkpoint](sandbox:/workspace/scratch/2cd312e78692/deliverables/490d_Mirror_Checkpoint_After_C410_20260924.md)|[Evidence ZIP](sandbox:/workspace/scratch/2cd312e78692/deliverables/490d_C410_Evidence_20260924.zip)|
|C411 — Source formula and record-path lift of the four-step 500 chain|[Report](sandbox:/workspace/scratch/2cd312e78692/deliverables/490d_C411_Source_Formula_and_Record_Path_Lift_of_Four_Step_500_Chain_20260924.md)|[Checkpoint](sandbox:/workspace/scratch/2cd312e78692/deliverables/490d_Mirror_Checkpoint_After_C411_20260924.md)|[Evidence ZIP](sandbox:/workspace/scratch/2cd312e78692/deliverables/490d_C411_Evidence_20260924.zip)|
|C412 — Direct reconstruction and source warrant of the 500 comparison domain|[Report](sandbox:/workspace/scratch/2cd312e78692/deliverables/490d_C412_Direct_Register_Reconstruction_and_500_Comparison_Warrant_20260924.md)|[Checkpoint](sandbox:/workspace/scratch/2cd312e78692/deliverables/490d_Mirror_Checkpoint_After_C412_20260924.md)|[Evidence ZIP](sandbox:/workspace/scratch/2cd312e78692/deliverables/490d_C412_Evidence_20260924.zip)|
|C413 — Source Shem return graphs, the finite500 domain and Mirror boundaries|[Report](sandbox:/workspace/scratch/2cd312e78692/deliverables/490d_C413_Source_Shem_Return_Graphs_500_Domain_and_Mirror_Boundaries_Synthesis_20260924.md)|[Checkpoint](sandbox:/workspace/scratch/2cd312e78692/deliverables/490d_Mirror_Checkpoint_After_C413_20260924.md)|[Evidence ZIP](sandbox:/workspace/scratch/2cd312e78692/deliverables/490d_C413_Evidence_20260924.zip)|

## Restart checkpoint

Latest completed C413; C414 is unexecuted and outside this completed authorization. Use the C413 compact restart kit as the active packet; read synthesis/checkpoint then locator. C404 separates failed E-chart closure from C405 positive−500 role correspondence. C406 gives the independent target-family census; C407 the500/502 Gear boundary; C408 the all-positive-word obstruction to substituting a new return path for C361 squared-E map; C409 the fixed Mirror source obstruction; C410 the complete−500 coordinate domain; C411 the bridge formula and record-path lifts; C412 the direct528-record source reconstruction and warrant matrix. The complete Shem graphs are2531↔2533↔2535, with E return pivots2556/2558, J forward death pivots1933/1935 and P forward death pivots2393/2395. Their source correspondence with the C400 Noah graph isT_-500, not the earlier E charts toSP/LXX Shem2991/2993/2995. Preserve source labels even when affine maps agree. The four-step500 chain3895→3395→2895→2395→1895 begins with SP companionG1 CainanON/Terah60/full430 Noah and Shem births, crosses toSP or LXX OFF G3/base-Terah/half430 Flood start and Shem death, then ends atMT Noah death. Its opening own deaths remain2945 and2795, giving950/600. The bridge alone is a derived cross-context comparison; no2000-year biography is adopted. C361/C363 already recorded the−500 squared-E endpoints; newC408 is the replacement-path obstruction, not a new discovery of that translation. Retain C403/C393/C383 finite source normal forms, conditional529 equivalences and missing Mirror/pivot members. No global2K/17K-preserving action is established. K529,E25/23,P70/69; File02 J300/299 is gap conversion, not Residue Protocol or permission to transform dates globally. Global paired MirrorJanuaryAD1; local junctionJanuaryAD2; no civil yearzero; signed cumulative coordinates are not civil dates. Regular Gears Noah/Shem/Flood only. SP person companions remain local, Flood close independent, primary Noah death inclusive/harmonic; both500/100 and502/98 valid. LXX nativeCainanON is not given a second insertion; OFF is theoretical removal. No new source endpoint, phase, fitted anchor, global axis, upstream/cumulative Gear, primer reopening or canonical graph edit. Corrected LXX8464 supplement awareness only:1564→1700,2484→2700,920→1000; AD3746/2300 superseded. C-series, original unprefixed reports and Engine reports remain distinct. The earlier incompleteSeptember17 ZIP differs from the later verified intact original. Counts, aliases, repeated paths and second implementations are not independent historical witnesses. Proposed C414 tests existing2K regular source pairs under one and two applications of the fixed−500 comparison; no such new pair census has been executed.

## Proposed next step — unexecuted

Within the fixed C410 regular source menu, enumerate existing endpoint pairs exactly2K=1058 apart and test whether both ends remain sourced after one and two applications of the fixed−500 comparison. Preserve source roles and contexts; compare surviving pairs with the established529 rectangle while keeping its cumulative corners fixed. Search no new intervals, shifts, phases or axes.

The current authorization ends at C413. A new instruction is required before C414.

## Verification and access

All 30 individual deliverables were saved incrementally. All ten sealed ZIPs passed CRC, payload hash/size and certificate checks. Fresh isolated replay reproduced 20/20 main DATA/RESULTS outputs and the C413 alternate-method output. 1855 main checks, 225 frozen-input/predecessor authentication checks and 1041 alternate-method integer affine, forced-pivot, residue-class, backward-path and source-reconstruction checks passed. These are verification counts, not independent witnesses; no new independent-agent review is claimed.

The compact kit contains complete C405, C406, C410, C411, C412 and C413 packets: the complete500 loop correspondence, direct Shem census, full500 coordinate domain, continuous record-path audit, direct source reconstruction and final synthesis. It also contains the prior C403 checkpoint/report, C265 reference checkpoint/certificate, and existing C361, C393 and C403 evidence ZIPs as selective references for the prior Shem-held squared-E comparison, Noah-to-Shem E/J strips and Noah return-loop grammar. C413 freezes DATA, certificates, results and next-step decisions for all nine predecessor steps. File_18 and File_09 are frozen in each packet; File_02, File_46 and File_11 are included in C413. All historical next-step instructions are superseded by the current checkpoint.

Portable main replay: run `python3 C413/evidence/check.py --out replay` from the extracted compact kit; compare DATA.json and RESULTS.json with C413/evidence/. The additional check is `python3 C413/evidence/ROOT_SECOND_METHOD.py --sources C413/sources --out secondary_replay`. The other packets have the same main replay convention and their own README. Python3 standard library only.

The continuation archive contains all evidence ZIPs under `published/`, extracted packets under `steps/`, and completion and sealed-packet integrity records. PACKAGE_MANIFEST.json records every included payload hash and size. The separate completion/integrity JSON records the recovery ZIP checksums.

Actual File_18 and File_09 bytes match their retained hashes; File_02 and File_46 match their C403 frozen source manifest, and File_11 matches its C412 frozen source manifest. The C265 checkpoint is readable and its certificate hash matches the retained control. C-series, original unprefixed reports and Engine reports remain distinct. The earlier incomplete September17 local ZIP was not the later verified intact original. Immediate dependencies remain frozen and accessible.