Complete MT/LXX five-versus-four parameter model

Independent preparation only. The question was frozen in model/whole_genealogy_extension_question.json before this calculation. No root journal or numbered-action file is edited. All 122 exact checks pass.

Main result

The complete19-shared-row MT→LXX comparison is reproduced by five parameters (u,λ,a,e,n)=(100,−24,27,40,60). Its38 local begetting/lifespan outputs have rank5. Imposing the additional source-value relation e+n=u gives a rank4 family with parameters (u,λ,a,n). Both fit the received full field exactly. The four-parameter restriction is genuine extra content of this fitted model; it does not follow from lifespan compatibility or from the five named masks.

The useful consequence is internal: under the restriction, increasing n while decreasing e by the same amount changes the Cumulative boundaries at Peleg, Reu, Serug and Nahor equally, while all Regular boundaries and both whole-span heads stay fixed. The complete Cumulative field retains information that the heads lose.

Exact supported model

Write all differences as LXX minus MT. The shared source order is Adam through Terah, with native Cainan retained separately between Arphaxad and Shelah.

Every unlisted measurement change is zero. The calculated remainder change is Δr=ΔL−Δb. In the root’s R/A normal form the row coefficients are exactly(Δb,ΔL); no new operation basis is needed.

Jared, Methuselah, Noah, Shem and Terah are unchanged as full rows. Thirteen begetting values and eight lifespans change; these support counts are descriptive, not independent evidence. Main LXX Lamech uses182/753 and calculated571. Noah’s equal +2 binding cancels in the comparison.

Ranks and exact local recovery

Adding calculated remainders to the38 outputs leaves ranks5 and4. Since U is invertible, ordered suffix accumulation preserves the ranks of each local projection; no new U proof is needed.

The five observation rows Δb(Adam), ΔL(Lamech), ΔL(Arphaxad), ΔL(Eber), ΔL(Nahor) form an identity matrix on(u,λ,a,e,n). Under the restriction, omit Eber and recover(u,λ,a,n); e=u−n follows. The omitted Eber row is an additional test of the four-parameter restriction. The same four rows leave e wholly free in the unrestricted model. Dropping any row from either stated basis loses one rank.

A life-only basis can use Peleg for u, together with Lamech, Arphaxad, Eber and Nahor. Thus Regular changes see only the century parameter, while the complete Cumulative life field sees every parameter.

Totals, native insertion and complete boundaries

With e+n=u, T_C=4u+λ+2a and n disappears from this total. The two totals together have rank2 in either model: three parameter directions remain invisible in the five-parameter family and two in the four-parameter family. Source substitution gives1250 and430 before the separate Cainan contribution.

Native Cainan contributes the tagged biography130|330|460. Its regular130 and cumulative460 additions act on the shared-node prefix Adam through Arphaxad; the named inserted node remains explicit. The native heads become1380 and890. This fixed insertion changes affine offsets, not parameter rank, while its name, slot, values and source permission remain input costs. The source equality of Cainan and Shelah130/330/460 is not automatically preserved under arbitrary changes to the five formal parameters.

Every native value agrees with the inherited full displacement artifact, including the gap field ΔC−ΔR. Zero terminal differences are retained; no absolute anchor was fitted.

What the four-parameter restriction adds

The restriction is the single output relation ΔL(Eber)+ΔL(Nahor)=Δb(Adam), equivalently Δr(Eber)+ΔL(Nahor)=0. In the four-parameter model, the n direction has life changes−1 at Eber and+1 at Nahor. Accumulation cancels it from Adam through Eber, leaves+1 at Peleg/Reu/Serug/Nahor, and returns to0 at Terah. This gives a finite internal plateau rather than an upstream translation.

Two bounded algebraic controls expose its status. First, e→e+1 with all other parameters held remains in the five-parameter family but violates the four-parameter condition by1. It changes only Eber’s local life/remainder and all cumulative boundaries upstream through Eber. Second, (e,n)→(e−1,n+1) preserves the restriction and both outer totals while moving precisely the four internal boundaries above. Neither control is an admitted new chronology.

Source and model domain

Ranks are over rational parameters on a fixed named support. Integer outputs require even u and integer λ,a,e,n; the received values satisfy this. Nonnegative source components place further inequalities on formal parameters. These mathematical domains do not confer source authorization. The model applies to the ordinary MT/LXX rows and does not absorb SP inclusive counts or replace nominal/counting distinctions.

All remaining years in the packet retain their calculated L−b provenance. Five or four change amplitudes do not erase the38 baseline MT b/L values, the named masks, the insertion packet, or frame choices. Lower rank alone is not an explanation score. No historical priority, statistical independence or whole-system minimum is claimed.

Prior overlap audit

The whole-genealogy block should therefore remain bounded: adopt the complete support comparison, explain the single extra four-parameter relation and its internal plateau, then move to Rounded inverse fibres as planned. Further determinant variations would add little.

Reproduction and bindings

Run python c1132_c1431/prep/whole_genealogy_extension.py in a fresh copy after removing only its own generated .json/.md outputs, or direct those outputs to a fresh path. The script uses only Fraction and standard-library matrix elimination, and imports no root model helper.

• current_source_packet: /workspace/scratch/1b40da62dcbd/c1132_c1431/model/complete_source_row_packet.json; SHA256 1bd5961126532673e6fda1535befc5e64cf21d67d01a3c5e78d1a613bbb8ab59.
• root_frozen_question: /workspace/scratch/1b40da62dcbd/c1132_c1431/model/whole_genealogy_extension_question.json; SHA256 826ee1186994592063674adc6bdb4c228acf9a60b905f281e5bdecfbba031b8e.
• inherited_displacement_target: /workspace/scratch/1b40da62dcbd/c732_c831/model/tradition_displacement_profiles.json; SHA256 a30d1703e4ddaa7670451a1e32597fde8825da57aace1430526d3a8f688fb4f2.
• source_File18: /workspace/scratch/1b40da62dcbd/project_sources/38-File_18.Chronological_Data_Tables-20260919-141048-.md; SHA256 68301ab760bfbe2e874aedc5c8d943ced7a6219d34bc2859332a70713f9630d5.
• script: /workspace/scratch/1b40da62dcbd/c1132_c1431/prep/whole_genealogy_extension.py; SHA256 0f73cd3c5bda902e671bdadc1dec9c6f76529a138b0cb8278448123aff734f63.