# Research checkpoint for the C532–C631 cycle

28 September2026 UTC. This checkpoint preserves the substantive research and decisions through C628. Final closure is recorded in C631 and the accompanying VERIFY.json. The cycle contains100 sequential bounded research, synthesis, review and verification actions; these are not100 independent discoveries.

## Goal and current conclusion

Continue the Research Strategy’s search for a compact state-aware generative grammar explaining how the chronological families fit together. The main explanatory object is a labelled source expression: rows or segments, their order, roles, measured units, chosen state and anchors. Different realizations preserve different features. Bare dates alone discard information needed for subsequent operations.

The new integrated draft foregrounds the Actual-to-Rounded cumulative bridge, then connects the calibrated Keys, Covenant and clutch families, retained rounded paths, indexed Enochic carriers, and the existing529 width families. The source register, typed relation inventory and normalized module graph accompany it. The eight-module graph is weakly connected through15 typed relations; this is organizational connectivity, not universal event transport or a global group theorem.

## Main additions

- **C532–C551, Covenant family.** The source299+161=460 partition, common1566 endpoint, equal137-life rectangles and23-year death gap reconstruct from the local packet. The complete principal11-node network uses explicit Ishmael and Levi137-year lifespan premises. Mixed J/E475 is a diagnostic total, not a source-appointed terminal.
- **C552–C567, cumulative family.** C0=(2435,2260,2080,1933,1796,1663,1526); C(p,d)=C0+p−d with p=0 or3.5 and d=0,7,14 generates42 coordinates. Two collateral constructors generate12 Joseph intervals; nine comparisons additionally use p=3 whole-year display. Fixed regular Joseph is1915–1805. The component cycle is a rotation of duration triples, not people. Joshua430/460 uses its declared mixed states; exact Aaron requires460.5.
- **C568–C575, allocation and endpoint bridge.** E=25/23, P=70/69, J=300/299; J is Enochian. P−1=(E−1)/6 and J−1=(E−1)/26. Source483=402.5+80.5 supports partial E versus whole P. Source14004→1929→1446 supplies12075+483, supporting partial E versus whole J. Both end at1404, while the junctions1929 and24552/13 differ. Translate the resulting endpoint pair+2 to Rounded14006/1406. This is separate from the weighted12026 conservation of Actual and Rounded Creation pairs.
- **C576–C586, carrier links.** The40→40.25 replacement generates480→483; P then gives490. The3|2|2 Creation cell translates by25/26/27 copies of483. Flood core4834/4831 minus6×483 reaches whole-year1936/1933. The Shem/Flood to Jacob/Conquest rectangle has sides600 and3430. Source phases remain distinct.
- **C587–C605, Enochic families.** x=(N−7)u−64 with N=77,63,50; g=70,72; u=g or g+110; role cell=(x+110,x,x+110−g,x−g). All48 printed coordinates reconstruct. The full grid a(j)=65−(49−j)g+r, j=0…49,r=−110 or0, reconstructs196 interval cells. Enochic ordinary cell equals the corresponding grid row. The18-row attribution overlay changes occupants at fixed coordinates. Ordinary and crossed generation centers require different endpoint roles; wrong-role transport misses by55.
- **C606–C612, new integration.** Enochic50×180/182 gives9000/9100=J/P(8970), a derived duration connection. Generation carrier transport is affine separately by role, with constants46,−64,156,46; these are algebraic offsets, not historical anchors. Frame translation is covariance of anchored dilation. Actual3430 anatomy is2401+1029=7×343+3×343. The989 Abraham–Exodus interval supplies2 and8 units of the Actual12026 bridge, becoming2150/8600 under E. These do not create new inverse breakpoints.

## What remains distinct

The primary weekly Enoch table uses D=600, with distances10D,8D,6D+70 before subtracting64 for BC labels. File69 supplies bounded companion transports, not a complete strict614 table. Resolution embeds110 once per field, week or generation; extending49 to50 adds a complete g+110 cell. Whole-span equality does not imply equality of intermediate paths. Decimal inverse endpoint sums depend on partition; order also determines interior roles.

The prior MT/LXX/SP source-row reconstructions,12026/14726 rounded backbones and529→575→625 width grammar remain established from C531. Their full evidence need not be rerun. The shared operators do not force identical cross-tradition anchors. The candidate grammar is compact, but no global minimum, historical construction sequence or new statistical tally is claimed.

## Frozen controls

Latest supplied File52c remains primary, SHA256 a5ea84562101158b60d0cf296765d6eff38e7a2abda4e74ad1b353dfd13b9530. Second decimal inversion remains deferred. Moses and1876 primers remain quarantined;1486 was not reopened. Gear scope remains Noah/Shem/Flood only. Main LXX Lamech182/753;777 appendix;188 nonoperative; native Cainan ON. Regular Cainan130 and cumulative460 remain separate. SP653 inclusive and53rd-year52-completed convention remain primary; minus1 companion stays local. Actual/rounded, phase/display, source/generated and regular/cumulative node roles remain explicit. Civil crossing uses BC+AD−1; rounded crossing BC+AD−2; no year zero. Canonical sources were not edited.

## Evidence and continuation

The archive includes journal.json, evidence/s532.py…s631.py, the read-only verifier,28 frozen source snapshots, preparation tables, independent reviews, review reconciliation, model registers and deliverables. The completed-prefix portability test replayed94 steps from an extracted archive without current originals. Current-source audit matched29 available copies. Final100-step results belong in VERIFY.json; historical review clarification records are retained rather than rewriting prior journal entries.

**C632 is proposed, not executed:** freeze the complete File70 §6 calendar-half source packet, then test its Prophetic/Priestly/Enochian bridges and minimum/corresponding/maximum roles under the existing grammar. Its2340/2352/2366 headings are candidate source inputs, not new results. This follows the supplied68–70 progression and tests a whole family without fitting new anchors or reopening deferred branches.