# Independent review: C749–C770

**Disposition: PASS, with the source-status and frame qualifications below.** No numerical repair is needed. Canonical files, immutable packets, model artifacts, and completed records were left unchanged. No package or upload was made.

## Checks performed

Safe prefix replay through C770 passed: 39 current-cycle records, 102 declared checks, 41 frozen source snapshots, and 41 current source copies. The C731 predecessor bindings remain valid. Replay made no journal changes.

Independently cross-checked the 58 native upper-genealogy rows against the earlier source-bound File18 packet, including LXX753 and the corrected339/339/330 suffix. Checked all ten literal source excerpts in the rounding packet against the current source files. The shared lower lifespans match File18's MT cumulative trunk; Jacob91 remains explicitly a Joseph collateral input, and the final four begetting values remain unavailable.

Using a nearest-multiple-by-distance implementation rather than the step scripts' floor expression, reconstructed all 79 cumulative Actual/Rounded node comparisons in the three native row sets. Every saved node, row residual, boundary residual, and terminal agrees. Independently checked the complete ordinary nonzero defect lists and the SP frame and conditional-branch arithmetic.

## Mathematical findings

- The complete25-class defect table is correct for integer inputs under nearest-five rounding. `K(b,r)=Q(b)+Q(r)−Q(b+r)` takes only−5,0,+5. MT Methuselah and Reu both have−5; native LXX additionally has Lamech−5; the ordinary SP list has Reu−5. This does require qualification of File51a's unrestricted “unique case” prose, while retaining the literal tables.
- The boundary residual is the suffix sum of row residuals at a held terminal. Thus a zero head residual does not imply that the internal coordinates are unchanged. The reconstructed MT field ranges from−4 to+5.
- The LXX-versus-MT residual support is exactly Lamech+4, Arphaxad−2, and Shelah−2. The SP-versus-MT support is exactly Methuselah−1 and Lamech+4. Their reported plateaus and head consequences follow.
- Equal residuals characterize every preserved interval within a mode. Equal comparison residuals characterize preserved differences between traditions. These are consequences of the fields, rather than additional independent observations.
- Cainan's130/330/460 measures have zero rounding residual. Under the explicitly compared inserted/absent chains, insertion preserves corresponding common-node residuals and the new boundary inherits the local Shelah residual. It need not have zero boundary displacement.
- The source subpath Enoch→Terah is5852 Actual,5860 after rounding its retained rows, and5850 after rounding the total once. The10 difference is correct, as is its8-year change from Actual. This gives a concrete subdivision-dependent comparison.
- The strict MT bridge identity and all21 adjacent-row tests are correct. The affine obstruction is also valid within that selected cumulative state:1406 and1526 are fixed, whereas1663 moves to1661. No single affine function of the date coordinate alone can realize these three pairs.

## State qualifications that must remain visible

**Three input operations.** Rounding a begetting edge, independently rounding a local biography's two components, and rounding the whole cumulative lifespan are distinct operations. The SP capped lives retain their inclusive ledger type. Jacob's91 cannot extend the direct trunk from Jacob to Levi. C765 correctly presents accumulation of split biographies as an operator diagnostic, not a replacement cumulative chronology.

**MT source table versus LXX/SP transfer.** File51a explicitly supplies the full MT rounded cumulative table. The immutable packet correctly says that the LXX/SP `Q(L)` fields are derived transfers of that rule, pending comparison with a controlling rounded table. Keep “derived transfer” visible in the synthesis; terms such as “native LXX rows” identify the selected input source state, not independent source attestation for every generated rounded coordinate. The generated Cainan residual comparison has the same status and must not silently overwrite separately printed source node labels.

**Full430 versus native SP frame.** C751 correctly distinguishes

\[
13396-4414=8982,\qquad13396-4199=9197.
\]

The former is the equalized full430 regular comparison; the latter uses the native SP215 regular coordinate. The distinction changes absolute bridge placement by215 while retaining the appropriate adjacent-field structure. C764's Strategy rectangle is the source's SP−215 execution: its regular4206 belongs to that branch. It is not the regular4414 comparison from the first profile.

**Conditional SP4411/4406 mechanism.** C762 deliberately omits the additional Noah binding and holds Jacob2006 in a strict begetting diagnostic. Its raw4413/4412 and rounded4411/4406 results are correct. The agreement with File51a's transmitted and secondary blocks is a possible mechanism, not a proof that the source blocks were historically or authorially generated by this exact procedure. It cannot replace the current primary SP path or move the SP companion rail upstream.

**Conditional SP+10 route.** C763–764 properly retain the decomposition

\[
13396\xrightarrow{+2}13398\xrightarrow{+3}13401\xrightarrow{+5}13406.
\]

Here+2 selects the cumulative center from the lower member,+3 is the derived SP row-rounding residual, and+5 applies the rounded Aaron125-versus-Moses120 branch. File51a's explicit Aaron branch explanation is in its MT cumulative section; the SP use remains a conditional cross-tradition application. This+5 is not the exact Actual Tishri+3.5 phase. The Strategy already supplies13406: the new route explains one compatible provenance, without proving that this provenance was intended. Regular4206 and the original rectangle's application status remain independent source-controlled inputs.

The rectangle arithmetic is exact:2760 under70/69 becomes2800,11960 under300/299 becomes12000, both gain40, and the9200 difference is preserved. It is an inherited rectangle receiving a conditional explanation, not a new independent witness.

## Small wording clarifications for synthesis

- In C760, read “insertion retains topology” as retaining the order and correspondence of existing nodes while keeping the inserted node explicit. Inserting a node does change the full graph's membership.
- Render C768's compressed “nearest1/6 date-grid” as “nearest date label ending in1 or6 on the1406-anchored grid”; it does not mean rounding to one-sixth of a year.
- Rounded plus the recorded residual field recovers Actual. Rounded alone is lossy; this is a reconstruction with retained data, not unique recovery of Actual from rounded values alone.

These qualifications support the principal advance: the connection between Actual and Rounded is carried by source rows, path order, counting type, terminal choice, and a local residual field. It is more informative than a single endpoint offset and remains bounded by the admitted source states.