Independent review: C732–C742

Disposition: PASS. No numerical correction or source-state change is required for this completed prefix. The family reconstruction is useful as an ordered explanation of previously known aggregate differences; the 61 generated node comparisons are not 61 independent witnesses.

Verification performed

• Safe read-only replay through C742 passed: 11 sequential records, 34 declared checks, 41 frozen source hashes, 41 current source copies, and the C731 predecessor/checkpoint/synthesis bindings. The report is VERIFY_C742.json.
• Independently compared all 58 regular input rows with the exact current File18 Markdown lines, including birth, death, selected lifespan ledger, and begetting ledger. All matched.
• Compared all 26 supplied literal MT cumulative rows with their source lines, including their envelope text.
• Reconstructed all 61 native node comparisons by descending from the independently printed cumulative Adam centers (MT14006, LXX14896, SP13398). This uses the opposite direction from the step scripts' ascent from Abraham2435. All nodes agree, and all three chains end at the common Abraham center2435.
• Derived all 58 effective-edge corrections from the source regular coordinate differences. They are precisely Noah+2 in each tradition and SP Lamech−1; all other selected corrections are zero.
• Checked all twenty MT lower-envelope members against their printed source envelopes. The selected lower member is center−2 throughout this upper genealogy.
• Independently checked all three SP capped-life ledgers: Jared847, Methuselah720, and Lamech653 equal birth−selected death+1.

The independent comparison results are saved in INDEPENDENT_C732_C742.json. No old research suite was replayed, and neither canonical sources nor the completed journal was edited.

Mathematical finding

For the declared source state,

This follows directly by subtracting the two adjacent-edge equations. Its explanatory value is the full ordered support: one terminal displacement and the source row contributions reconstruct every intermediate labelled boundary. The recurrence is not a newly inferred universal conversion between absolute chronology modes.

The complete inter-tradition fields and their finite differences are correct. In particular:

• The LXX shared Arphaxad→Shelah edge combines two native rows: regular230=100+130, cumulative487=27+460, and bridge257=−73+330. The inserted Cainan row is retained in the native LXX field, rather than replaced by a fictitious zero-life row in MT/SP.
• The SP Lamech regular difference is −130=−129−1. Its cumulative difference is −124 from the selected653 versus777 ledger values. These belong to different counting roles.
• The eight LXX/SP birth positions from Shelah through Abraham agree in the common full430 frame. Their cumulative differences547,520,420,320,220,120,60,0 are generated by the selected local lifespan differences27,100,100,100,100,60,60.

Source-role qualifications to carry into synthesis

1. Ledger lifespan is not always completed elapsed lifetime. C737 explicitly protects SP Lamech653; the same distinction also applies to Jared847 and Methuselah720. File18 §3.1 puts their selected deaths at Flood start and treats birth−Flood close as equivalent capacity arithmetic, not another physical-death assignment. The recurrence is valid for the cumulative ledger inputs without claiming that every L−b_eff is a literal remaining physical lifetime.
2. Noah's correction is a binding correction. The selected G2 Noah birth is compared with the Arphaxad-bound Shem position, producing an effective502-year edge against the ledger500. This does not propagate a new Gear through Adam→Lamech or the later genealogy.
3. Center and lower-envelope comparisons are distinct. C734's mixed-role MT head9892 uses cumulative AdamYear6 center14006 against regular completion4114. C735's completion-profile head9890 uses the source lower14004. The uniform−2 profile preserves adjacent differences; it is not a node-by-node fitted adjustment.
4. Printed and generated cumulative coordinates remain distinct. MT has the full printed trunk. LXX/SP intermediate cumulative positions are reconstructed from the selected lifespan chain and checked against their separately printed source checkpoints. “Native” here describes the admitted project table state, not a fresh claim of manuscript attestation for every generated coordinate.
5. LXX source hierarchy remains intact. Lamech182/753 is the component-wise project reconstruction; no joint manuscript attestation is claimed. The corrected LXX Peleg/Reu/Serug lifespans339/339/330 and Nahor208 are used. The777 appendix and non-operative188 are absent from execution.

The completed C736 record uses the normalized name Cainan2, which maps to File18's literal “2nd Cainan” row. The final record occurs once in the contiguous journal and replays successfully. This review certifies the completed record and current fixed packet, not an uncompleted preparatory attempt.

The next productive extension is to test whether matched insertion states or controlled row perturbations preserve the whole ordered field. Merely repeating the head totals would add little to the Strategy's larger explanation.