# Restart checkpoint after C831

Cycle: C732–C831, continuing the sealed C731 foundation. This checkpoint is prepared at C830 and bound by the C831 closing record. Final VERIFY.json is authoritative for the completed100-step count. Next unused step: **C832**.

## Research objective and current answer

The Strategy asks how chronological families fit together. The current constructive answer is an ordered, state-labelled source path with measures, endpoint roles, anchors and admitted subdivisions. Regular/cumulative select different measurements; finite variants act on declared supports; rounding propagates row residuals; weighted contraction and coarsening explain BJ; retained-component transforms, calendar measures and File52c’s admitted one-pass reversal join the wider families.

Source values and selected anchors remain premises. Reconstructing their consequences does not independently establish their historical cause, providential interpretation, or statistical rarity.

## New results to retain

- C733–748: Complete MT20/LXX21/SP20 native-Cainan mode-gap fields in a common full430 regular frame. Local recurrence G_i−G_(i+1)=L_i−b_eff_i; terminal lower-envelope gap267. Adam gaps9890/9400/8982. NativeSP215 instead gives9197. Ordered profiles recover local differences; totals alone do not.
- C743–744,C778,C787–788: Restored-SP/native-LXX twelve-node Noah→Abraham birth suffix agrees in all four matched Sojourn/Terah placements. Official SP Terah145 retained. Lifespan difference vector0,0,27,0,27,100,100,100,100,60,60,0 accumulates574,574,574,547,547,520,420,320,220,120,60,0. Derived rounded field begins570 after27→25 twice.
- C749–770: Q(n)=5 floor((n+2)/5); K=Q(b)+Q(r)−Q(L) lies in−5,0,+5. MT Methuselah AND Reu have−5; source uniqueness sentence qualified. Complete26-row MT cumulative residual field reproduced. LXX residual support relativeMT: Lamech+4, Arphaxad−2, Shelah−2. SP: Methuselah−1,Lamech+4. These generate the entire corresponding boundary differences.
- Rounding is row/path dependent. Direct date-grid projection fails at11/26 MT nodes; Enoch→Terah5852 gives5860 by row rounding versus5850 by once-rounding the total. Actual=Rounded−D; delta mode-gap=D_C−D_R.
- C763–764: Conditional SP cumulative13406 provenance13396+2+3+5. The final+5 is roundedAaron125−Moses120, not exactActualphase3.5. Strategy4206 regular side belongs to the−215/native frame. Separate13401 constructions remain distinct.
- C772–786: finite support masks give8/4/2 placements. Terah triangle SP(70,75), MT/LXX(70,135), alternative(130,75) projects to(0,60)+(60,0)=(60,60). OfficialSP cumulative145 unchanged. Secondary cumulative+60 display is a different operation from raw lifespan-preserving Terah repartition. Q5 equivariance holds on admitted multiples-of-five moves and corresponding existing boundaries.
- C792–810: BJ index22/23, secondary57 deletion, and role-sensitive2450→2400 relation50=57−7 reconstructed. Reflection is the mixed original-node comparison, not the expunged chronology. Biological/surface full575 paths differ11,−1,−5,−5 with total0; terminal17 retained. Six timestamps follow49-year ordinal encoding. Six-node290 refinement yields100|60|130 and115|60|115. Bookend460|1490|460|40 is equivalent to retained1950+E460=2450. NT2450 uses5326 and envelope2876, not birthhead2806.
- C813–815,C820: integration checks retain latestFile52c12026/14726 one-pass component backbone,12600 shared completion with different inner junctions, exact calendar day-volume8400/23, File70 ordered shape and weightedCreation12026.

## Source tensions and domain controls

LatestFile52c SHA256: a5ea84562101158b60d0cf296765d6eff38e7a2abda4e74ad1b353dfd13b9530. Sources are local supplied files; do not retrieve attachments through Library. Do not edit canonical sources.

Second decimal inversion remains deferred. Moses and1876 primers remain quarantined;1486 unopened. Gear remains Noah/Shem/Flood only. No new statistical tally or remoteSKL extension.

LXX main182/753, calculated571;777 appendix,188 nonoperative; nativeCainanON. SP Lamech53rd counted versus52 completed; Jared847/Methuselah720/Lamech653 inclusive ledger values. Person−1 companion stays local.

BJ source-prose Isaac–Jacob70 conflicts with literal59. Surface Jacob lifespan142 conflicts with147. Primary BJ Shem2650/2050 remains distinct from comparison2649/2049. The290 refinement is the project’s reconstructed biological/sacrifice path, not wholly transmitted surface dates. InheritedSP7+1300 remains the controlling BJ derivation.

## Deliverables and evidence

Root folder: /workspace/scratch/1b40da62dcbd/c732_c831

Final reading files are in deliverables/:
- 490d_Chronological_Families_Integrated_Synthesis_C831.md
- 490d_Chronological_Families_Reading_Guide_C831.md
- 490d_Chronological_Families_Map_C831.svg and .png

Exact models are in model/. The journal stores each question, inputs, result, finding and reassessment. evidence/s732.py through s831.py are reproducible steps. Five substantive independent review notes and the final preflight are in evidence/. Forty-one frozen source snapshots and bindings remain there. Final evidence ZIP and research report are created after C831 verification.

Do not repeat prior endpoint totals as new discoveries. The next useful research should freeze one complete admitted source family not used to choose its proposed rule, test the whole ordered object, and distinguish reconstructed consequences from unexplained source selections. Reassess that choice from the source packet before executing C832.