NT source-family preparation for C832–C931

Preparation only. No numbered action has been executed. The exact frozen packet is nt_inputs.json; prepare_nt_inputs.py extracts it reproducibly from four supplied local sources. The packet contains 41 literal tables, the complete 78-row File43 display ledger, source-line locators, exact raw text and SHA256 identities. The underlying sources have not been changed.

Recommended strongest transfer

Treat File43’s complete ordered display ledger as an explicitly schematic source object. Its constant edge weight70 is another measurement of an ordered genealogical path. Compare the whole Adam→Jacob part against the supplied MT Rounded path, keeping Cainan’s different topology and each node’s role. This extends File54’s two highlighted Creation/Jared bridges to a complete22-boundary field; it does not promote the schematic NT dates to historical dates.

File43 §3.4 explicitly says the ledger is display-only, not a source for overriding locked spans or a textual chronology. Therefore the result should be described as exact reconstruction and transfer to another declared source object, not independent corroboration of the original locks. Prior C587–607 already reconstructed the separate File68/69 indexed Enoch families; C808–809 already used5326−2876=2450 and5326−2806=2520. These should not be presented as fresh discoveries.

1. One civil generator reproduces the complete display

Use civil chronological coordinate x=1−BC on the BC side and x=AD on the AD side. Let r denote the number of70-year slots backwards from the6BC hinge. Then

x(r) = -5 - 70r.

The ledger’s opening boundaries have r=76,…,−1 and its final closing boundary has r=−2. Each row spans70 civil years. The primary77-row object runs from5326BC toAD65; the78th row, AD65–135, is a further display extension. Thus it is necessary to separate:

The figurative God bookend is not a divine-origin chronology. Matthew’s visible Abraham→Jesus sequence occupies41 names,40 inter-name intervals and41 carrier slots throughAD65. The2876 envelope is not Abraham’s2806 birth-hinge coordinate. The extended Matthew column before Abraham is a supplied display and is not a claim about Matthew’s textual genealogy.

2. Complete Luke-to-MT Rounded difference field

Convenience data: derived_candidate_diagnostics.complete_Luke_to_MT_rounded_bridge.

Sources: File43 §3.4, lines673–696, and File51a §3.1, lines384–416. The latter is explicitly the strict regular table without Shem’s+2, anchored at Jacob2006. Do not substitute File18’s standard regular Creation4114 for this table’s strictActual4112.

For the22 common nodes Adam, Seth, Enosh, Kenan, Mahalalel, Jared, Enoch, Methuselah, Lamech, Noah, Shem, Arphaxad, Shelah, Eber, Peleg, Reu, Serug, Nahor, Terah, Abraham, Isaac, Jacob, Luke-display minus MT-Rounded is:

1150,1210,1245,1265,1265,1260,1350,1345,1460,1570,2000,2030,1925,1885,1850,1810,1770,1730,1690,1690,1720,1710.

These are one field G, not22 independent agreements. Its local generator is

G_i - G_(i+1) = NT_edge_i - MT_rounded_begetting_i.

Most NT edges are70. On the shared-node path Arphaxad→Shelah the NT edge is140 because its source has Cainan while native MT does not. Thus2030−1925=105=140−35. At Noah,1570−2000=−430=70−500. The terminal difference at Jacob is1710. That terminal plus the complete ordered edge differences reconstructs every member, including the source-highlighted1150 and1260.

A follow-on can restore MT’s admitted Cainan130 row and preserve the NT70 Cainan row explicitly: the shared name graph then has two different weights at that edge, rather than a collapsed140 comparison. Restoring a name does not require equating the two source measurements. This would use the current admitted insertion operation; it is not a new Cainan choice.

Actual-strict versus Rounded changes the field by the negative MT residual. This is a direct new-object application of the existing residual theorem. It is not a new theorem. Joseph after Jacob in File51a is a collateral Joseph branch, while Luke proceeds throughJudah. Stop this shared source path atJacob; do not confuse Luke’s several later Joseph entries with Genesis Joseph.

3. Complete finite Key-return family

The complete positive Luke index domain is r=0,…,76. The admitted File54 §6 source fork isEnoch r69→Jared r70 underP and→Adam r75 underE. An exact finite classification explains this fork within the whole lattice:

• E=25/23 sends r to25r/23; it returns to an integral70-year slot exactly when23 dividesr. Within the domain, r=0,23,46,69; all image slots0,25,50,75 remain inside it.
• P=70/69 sends r to70r/69; it returns to an integral70-year slot exactly when69 dividesr. Within the domain, r=0,69; image slots0,70 remain inside it.

The6BC hinge is fixed in both lists. The labels are copied from the source display; no theological meaning is claimed for Melki/Cosam orSalmon/Hezron. The first two E results are dependent multiples of the same23-slot condition, not independent numerical hits. This is a bounded domain-classification with no tuning and no new probability tally.

The complete fork is translation-compatible with the source36BC rail: change the hinge from6 to36 while translating the full display by+30BC and preserve every relative radius. Source Enoch4866→Jared4936/Adam5286 follows. File54’s locally applied MT apparent-age+30 remains a distinct source operation and is not automatically a propagated MT chronology.

4. A complete77-edge Luke/BJ measurement interface

File54 §§8.6 and13.2 already supplies the four boundaries5326BC,3856BC,1406BC,AD65 and the source partition1470|2450|1470. Instead of repeating its endpoint calculation, recover the whole common coarsening of the70-year and49-year grids over their5390-year common span.

From the same origin,70k=49j iff k=7m and j=10m. There are12 shared boundaries m=0,…,11, separated by490, as recorded in derived_candidate_diagnostics.common_49_70_coarsening. The full lists of coordinates and display labels are available there. The source’s21|35|21 slots become3|5|3 common blocks;30|50|30 jubilees become the same3|5|3 blocks.

This explains how a single ordered object admits the two integer measurements. It does not assert110 distinct BJ historical jubilees as a newly adopted timeline. BJ’s middle50-jubilee trunk is supplied; the extended49-grid is a derived comparison construction.

The primary78 boundary positions admit reflection k→77−k, or x→−5260−x. Its center is civilx=−2630, i.e.2631BC, lying between source boundaries because77 is odd. It exchanges the outer endpoints and exchanges the BJ Creation andConquest boundaries k21 andk56. Reflection closure of the homogeneous grid is automatic; selecting these two externally named BJ boundaries is the source placement fact. This is different from the prior BJ2599 comparison object.

Material source qualifications

1. File54 §4.3–4.4 explicitly opens JaredGear3/Year6 nodes3656/3716. The current research scope forbids extending Gears upstream. These secondary comparisons are excluded from the proposed transfer. Its controlling Rounded Jared3646 remains available.
2. File54’s metadata/navigation still calls File52c “The Inverse of the Inverse.” The user’s latest52c and instruction excluding second inversion govern; nothing in this preparation executes an inverse or adopts that outdated pointer.
3. File54’s cumulativeFlood4836 comparison is a named rounded horizon. It does not overwrite ActualFlood ranges or identify LukeEnoch with a cumulative event.
4. The complete File43 genealogy table is schematic and display-only. Its exactly homogeneous row widths establish reconstruction of the display, not literal begetting ages or new dates for NT figures.
5. Civil6BC→AD65=70 usesBC+AD−1. Importing the Rounded crossing ruleBC+AD−2 would change the measured object.
6. No direct Luke dependence onJubilees or historical compositional cause is established here. The supplied sources themselves separate arithmetic, structural inference and shared-tradition interpretation.

Suggested bounded sequence

Freeze the complete ledger and source restrictions; reconstruct all78 rows; separate named counts from intervals; extract the complete Adam→Jacob comparison; recover its local difference support including the Cainan contraction; add the strictActual residual response; classify all positiveE returns; classify all positiveP returns; transfer the complete result to the admitted+30 rail; reconstruct the full12-boundary49/70 coarsening; test the complete reflection; integrate the new object into the same ordered-path grammar. Reassess after each action, dropping later items if they cease to add explanatory value.