Candidate whole-family source-mode extension after C731

Prepared from the supplied local File18, File09 and File22. This is a source/preparation memo, not a numbered research report. No canonical file changed.

Main recommendation

Reconstruct the entire labelled bridge profile $G_i=C_i-R_i$, then recover its local changes. C485–C491 already explained the aggregate MT/LXX/SP Creation differences and the two projections of a source row; repeating those totals would add little. The new explanation asks why the same row changes produce different displacements at every intermediate patriarch.

For a fixed source state, write

Thus one terminal bridge and the ordered effective remainder sequence generate the whole profile. Adjacent differences recover the local effective remainders. A Creation total cannot retain that information. The proposed discriminating comparison is to preserve a total while permuting two unequal row changes: the head can remain fixed while intermediate labelled boundaries fail. This compares explanatory content, not historical probabilities.

Packet contents and exact state

source_modes_packet.json contains literal File18 regular rows for all nineteen shared Adam→Terah patriarchs, plus native LXX Cainan. Every row retains its source line, raw Markdown, birth, death, lifespan cell and begetting cell. r_calculated is explicitly derived from the two selected ledger values, never described as an independently quoted remainder. It also contains all twenty-six literal MT cumulative trunk rows through Moses, which supply the common Abraham2435 terminal for the upper comparison.

The preparatory prepared_native_coordinate_arrays keep generated fields separate from literal source rows. The regular full430 coordinates add215 to File18's literal Minimum-Regular births; the cumulative coordinates sum the selected official lifespans backward from common Abraham2435. All three chains use the same no-+60 Terah state. Native Cainan is OFF for MT/SP and ON for LXX.

Use cumulative lower-envelope boundaries (Moses center−2) if the top comparison is to retain the established completion pair14004/4114 and bridge9890. The common lower-envelope Abraham boundary2433 against regular2166 then supplies terminal267. A Moses-center profile instead has terminal269 and head9892; this remains a different chart pairing. In particular cumulative14006 is AdamYear6, while regular4114 is the Creation completion. Do not silently call9892 the inherited9890 bridge or declare unlike Adam roles identical. A uniform choice of cumulative envelope member preserves all adjacent recurrences.

The three selected Noah births are paired with each tradition's Arphaxad-bound Shem. Their actual birth differences are502, despite the begetting ledger's500; all three require $\kappa=+2$. SP primary Lamech→Noah uses52 completed years, against the displayed53rd-year ledger, so $\kappa=-1$. These are the only nonzero corrections in the selected native Adam→Abraham arrays. They do not authorize Gear transport.

SP Jared847, Methuselah720 and Lamech653 remain inclusive ledger lifespans in the cumulative source. Their regular birth−death differences are one smaller. The formula concerns the selected ledger and declared endpoint conventions; it must not turn those three numbers into unqualified completed elapsed lifetimes. SP Terah uses official145, not the architectural205. LXX Lamech uses restored182, attested753 and calculated571; joint manuscript attestation is not asserted,188 is non-operative and777 remains appendix-only.

Candidate numerical profiles to verify sequentially

These are preparation outputs, not new source rows or already-numbered conclusions. Every profile can be generated directly from the JSON inputs.

Native LXX Cainan has its own intervening bridge2177. Omission from this shared-node comparison table does not remove it from the LXX source chain.

The profile yields natural local blocks rather than a global scalar conversion. For example, LXX and SP regular births match exactly from Shelah through Terah. Their begetting ages and held regular suffix match there, yet their cumulative boundaries and regular deaths differ through selected lifespans. The LXX−SP cumulative displacement in that block is547,520,420,320,220,120,60, followed by0 at Abraham. Its adjacent differences recover27,100,100,100,100,60,60. Those are precisely the selected local lifespan changes. That is a compact whole-block demonstration of two projections having different information.

Additional high-value extensions

1. Maximal translation blocks. With Cainan status matched, LXX−MT cumulative displacement430 is constant from Adam through Lamech; below Lamech it becomes454 through Arphaxad, then427 at Shelah and continues changing. The famous430 head alignment is the upper plateau of a row-generated profile, not a translation of the entire chain. This follows File18 §6D's stated430-alignment rationale but extends it to the full ordered family.
2. Inserted-row alignment. When Cainan is absent, retain absence as a state. On a shared-node graph, the LXX Arphaxad→Shelah edge contains Arphaxad+Cainan. Alternatively enlarge the graph with a labelled insertion slot, without portraying an absent row as a historical zero-lifespan person. This prevents spurious local finite differences.
3. Pointwise composition. Check LXX−SP=(LXX−MT)−(SP−MT) across all shared labels and in both modes, with all states held. This tests one coherent representation rather than three disconnected total comparisons.
4. Source support versus phase. Uniform phase or common frame shifts alter placement but leave adjacent differences unchanged. A local row perturbation produces a step in the upstream boundary field. This makes phase shifts and textual row changes mathematically distinguishable.
5. Matched Cainan insertion. A single admitted insertion changes the upstream bridge by330, but leaves the downstream bridge profile fixed. Native LXX already includes that row. The known single endpoint result becomes a local support statement on the whole family.

Do not convert these candidate results into historical transmission claims. Arithmetic identifies which row choices generate the family; independent textual evidence would be required to identify why or when those choices arose.

Source locations

• File18 §§2.1–2.2, lines1228–1252: literal MT regular rows.
• File18 §3.1, lines1447–1456 and1474–1475: SP primary regular rows and52/53 distinction; lines1532–1534: inclusive lifespan arithmetic.
• File18 §3.2, lines1600–1608: SP Arphaxad-bound suffix and official145 Terah.
• File18 §§4.1–4.2, lines1697–1725: LXX native rows; lines1709,1727–1733 retain Lamech source hierarchy, Terah states and corrected339/339/330.
• File18 §6A, lines1935–1962: literal MT cumulative trunk; §6B, lines1971–2000: Cainan insertion and fixed Shelah suffix.
• File18 §§6C–6D, lines2025–2031 and2061–2077: SP/LXX cumulative checkpoints, official source lifespans,430 plateau rationale and distinct Flood marker conventions.
• File09 file-function and§4: cumulative trunk/variant discipline; File22 §§5,5A,7.1–7.4: existing9890 andCainan-matched bridges. These frame the comparison but do not independently attest newly generated intermediate coordinates.

The JSON binds all three source hashes and keeps every regular row's exact literal location. It does not modify or replace any source.