# Independent review of C665–C676

28 September 2026. Reviewer: separately assigned SP/source-check agent.

## Disposition and scope

**No numerical correction is required.** The completed journal entries, twelve step scripts, and C671 interim synthesis were inspected. Nineteen independent exact-fraction checks recomputed the current core/flank, ladder, calendar, and phase claims directly from the source values; all passed. No old research was replayed. No journal, script, or canonical source was edited.

Source checks used Supplement A §§1.1–1.5, 2.2–2.3, and 4.1–4.3, plus File12's reconstructed intercalation statement at lines1009–1016. C671's earlier File70 results are inherited from the prior review; this review checks its retained-core summary and does not recertify C652–C664. The checks below establish arithmetic and source-state compatibility, not historical independence.

## C665–C667: retained flanks

With flank f=30 and core c=720−30=690=23f, the native bracket is c+2f=25f=750. The Priestly core also equals E(c)=25f. The equality follows from the source's coefficient relation while preserving the two object classes.

The complete table independently reconstructs as:

| Operator | Core | Gain | One retained flank | Two retained flanks |
|---|---:|---:|---:|---:|
|Identity|690|0|720|750|
|P=70/69|700|10|730|760|
|E=25/23|750|60|780|810|

Whole-bracket conversion differs from core conversion with retained flanks by

\[
k(c+2f)-(kc+2f)=2(k-1)f.
\]

The excesses are exactly20/23 for P and120/23 for E, agreeing with C667. The reports correctly preserve the distinction between the gain assigned to the core and gain assigned to the entire object. No additional ratio or endpoint is required.

## C668–C671: ladder, cells, and calendar units

The source's ten coordinates are generated by4326−720i−e, for i=0,…,4 and e=0,30. Their ordered gaps are30,690,30,690,30,690,30,690,30; their outer width is2910. This reconstructs the admitted source ladder without adding SKL transport permission or changing the node roles.

The six-node inner field has width2c+3f=1470=49f. Both its outer pair3606/2136 and its central rail2886/2856 have midpoint2871. The source comparisons690+780 and720+750 reduce to the same total.

**Partition qualification:** the690+780 expression is a scalar regrouping of the cell's components and its retained-flank comparison. It does not by itself establish a new contiguous cut at3606−690=2916 in the native six-node path. The720+750 split does correspond to its displayed2886 junction. Thus “the source-displayed scalar partitions” is more precise than treating every equal sum as the same ordered subdivision. No completed computation in this range adds that unlisted cut.

The intercalation arithmetic is exact:

\[
4\cdot360+30=1470,\qquad
6(6\cdot360+30)+(4\cdot360+30)=14610=40\cdot365.25.
\]

File12 classifies the cycle as a reconstructed scheme meeting the ideal Julian mean target. C670 correctly distinguishes its1470 **days** from the chronological1470-year cell. In prose, call365.25 the reconstructed **Julian-mean year target**, rather than an unqualified universal civil-year length; the script's `civil_year_days` key should be read with that source meaning. The numerical match does not establish that every chronological30 is a historical leap month.

## C672–C673: full phase table and affine obstruction

The source convention is coord(Xn)=X and coord(Xt)=X−1/2. Taking C=2871, epsilon=0 for Nisan and1/2 for the corresponding Tishri center, the formula

\[
x=C+\epsilon\pm w/2
\]

reconstructs all eight coordinates for w=34,40:

| Width | Suffix | Exact coordinates | Source labels |
|---:|---|---|---|
|34|n|2888 /2854|2888n /2854n|
|34|t|2888.5 /2854.5|2889t /2855t|
|40|n|2891 /2851|2891n /2851n|
|40|t|2891.5 /2851.5|2892t /2852t|

The labels' one-year numeric difference is not the exact phase separation: the latter is one half-year. Corresponding centers remain2871 and2871.5.

For the role-preserving before/after correspondence, an affine map would require slope40/34=20/17 from the width, but slope1 from the preserved half-year gap. These requirements conflict. Fitting the Nisan pair and then applying that map to either Tishri endpoint misses the correct target by3/34. The stated family of maps about each phase's own center is correct; it requires the phase label as an additional input.

## C674–C675: scalar normalization versus coordinate widening

For s=34.5, P(s)=35 and E(s)=37.5. Their gap is2.5, exactly the supplied normalization residual. Hence the defined result40 can be written2E(s)−P(s). This is a valid compression of the source construction.

**Inference qualification:** the2.5 residual is already supplied by the source. Its equality with E(s)−P(s) does not independently derive why that residual was selected, nor does it establish a new general normalization law. C674 appropriately declines to introduce a universal Key.

The source measurement classes reconstruct as:

| State | Inner cross-phase | Same suffix | Outer cross-phase |
|---|---:|---:|---:|
|Before|33.5|34|34.5|
|After|39.5|40|40.5|

Every matched width increases by6 because each endpoint moves outward3. The scalar comparison34.5→40 increases by5.5 because it changes measurement class. C675 states this distinction correctly.

## C676: inward withdrawal and suffix change

Applying the specified inward withdrawal gives:

| Starting pair | Exact resulting coordinates | Resulting labels | Exact center |
|---|---|---|---:|
|2892t /2852t|2891.5−2.5 /2851.5+2.5 =2889 /2854|2889n /2854n|2871.5|
|2891n /2851n|2891−2.5 /2851+2.5 =2888.5 /2853.5|2889t /2854t|2871|

Both resulting widths are35, exactly as printed in Supplement A §4.3. The source gives the recovered labels; their derivation through a suffix change is the current step's correctly identified phase-resolution inference.

Each exact numerical center is preserved. **The suffix changes do not mean the centers exchange their numerical positions:** the recovered Nisan-labelled pair remains centered on the original Tishri coordinate2871.5, and the recovered Tishri-labelled pair remains centered on the original Nisan coordinate2871. This distinction should be carried into the forthcoming center discussion. The recovered35 pairs are not the original34-wide brackets.

## Synthesis recommendation

Carry the arithmetic forward unchanged. Preserve three brief qualifications in the explanatory synthesis: scalar1470 regroupings do not automatically supply new path junctions; the40 identity compresses a supplied residual choice; and the recovered35 suffix swap preserves the starting exact center. All reviewed operations remain within their declared objects and source fields.