Independent review of C1202–C1222

PASS. All 22 recorded exact checks pass. No substantive arithmetic error or universal-theorem scope defect was found. One reader clarification is recommended; it does not change any calculation.

The review checked the completed journal records, every bound model and the two associated reader texts against the frozen round_joint_fibres preparation and the complete source-row packet. A second reviewer independently checked the universal fibre, cap, visibility, translation and carry proofs and found no outstanding issue. Exact checks and reviewed-file hashes are in review1202_1222.json.

Reader clarification

In Source_Changes_to_Rounded_Paths.md, label the preserved 430 explicitly as the matched 19-row cumulative head difference. Restoring native LXX Cainan adds460, giving890, as C1187 already states. C1216 correctly retains the matched-row domain and the calculations use it throughout. The current paragraph begins with the common-row comparison and later separates the insertion, so this is a useful scope clarification rather than a numerical correction.

Cap and rounding: C1202–C1212

The global composite fibre is correct for nonnegative integer counts. At the rounded capacity, its lower endpoint is max(0,Q(c)−2) and its upper end is unbounded. Thus the source lower bounds843,718,653 and their uncapped/tie/clipped subdivisions are exact. Rounded saturation does not necessarily identify clipping.

All nine branch records and their reconstructions match the frozen source ledger. The clipped rows need their located excesses because capacity fixes the capped value and its residual. The unclipped rows have zero excess and need only the finite residual. Ties are separately qualified. The retained branch labels, capacities and loss values remain explicit source costs.

The same-total diagnostic (116,248,124) preserves488 and all cap outputs while changing the baseline. Its formal status is explicit. The total has rank1; adding the two named excess measurements gives determinant1 and recovers (115,249,124). Necessity is properly limited to unrestricted rational positive-branch recovery with the stated located measurements. Holding the already calculated488 is a conditional information assumption, not an independent explanation of its source values.

The complete loss identity and signs agree: exact losses115/249/124 become rounded losses115/250/120, so488 becomes485. The baseline and capped rounding-error totals are−5 and−2. Monotone rounding preserves minimum when both arguments are rounded consistently. Its proof is valid for every nondecreasing scalar rule on a total order.

The old C1209 witness is explicitly repaired. Inputs12/11 give equal outputs and therefore do not distinguish the constructions. C1210 says this directly and supplies14/11, giving10 for the consistently rounded cap and11 when capacity remains exact. Its separate721/720 example correctly hides one unit of strict clipping. Visible rounded clipping begins exactly at Q(c)+3, giving848,723,658 for the three capacities.

The cap reader explanation retains inclusive-count qualifications and does not treat rounded date labels as replacement inputs for resolved lifespan counts.

Source changes and carries: C1213–C1222

C1213 supplies the signed algebraic extension needed by C1199. Q_Z(x)=5 floor((x+2)/5) is used for signed residuals and translations while chronological durations remain nonnegative. Multiples of5 commute with rounding exactly.

All 19 common MT–LXX source rows reproduce the stored exact and rounded change field. Only lifespan changes at Lamech, Arphaxad and Shelah alter amplitude:−24→−20 and27→25 twice. All common begetting changes survive unchanged. Their located difference errors are+4,−2,−2 and cancel in the matched-row total430.

The entire cumulative error field is also correct. It is−4 at Noah, Shem and Arphaxad;−2 at Shelah; zero at the other matched boundaries and the common terminal. Adjacent differences recover the local error vector. This is stronger than the zero head error alone, and C1216 preserves the matched19-row qualification.

All 19 carry changes agree with ΔQ(L)=ΔQ(b)+ΔQ(r)+Δcarry. Lamech alone changes the carry by+5. The rounded lifespan shift−20 and rounded remainder shift−25 therefore describe distinct, compatible observables.

The residual lift reproduces all105 measurements in the complete35 ordinary existing comparisons:19 MT→LXX and16 MT→SP. The three SP inclusive rows remain excluded from ordinary biography matching, and the native LXX Cainan row remains an unpaired insertion. No source value or new chronology route is inferred from the formal comparison.

The lift composition proof is exact: retain the bijective representation x↔(Q_Z(x),ρ(x)), perform integer translation, and re-encode. The declared25 diagnostics agree with that proof. A shift descends to all nearest-five cells precisely when it is divisible by5; the four nonzero residue witnesses split a whole cell. Restricted finite source exceptions and authorization of intermediate chronology states remain separate.

Both the model and reader synthesis correctly describe residual retention as information preservation, not compression of the source inputs.

No root journal, model, reader text or frozen preparation file was edited. Only these new review artifacts were created. No second decimal inversion, endpoint search or target tally was performed.