File70 primary-family preparation

Prepared for C632–C731 from File70 §§1–5, §9.1A, Appendix A.13.1–5, and E.5A. This is source preparation, not a numbered research result or a canonical amendment.

Source: project_sources/24-File_70.Genesis_Toledot_Atonement_Weave-10-1-.md, SHA256 0fa80217c94b395139cfc891c3fd915ea0b5471c49d3f611082c541306566065.

Companion file70_primary_inputs.json contains 13 structured source families and 149 literal manifest rows from twelve source tables, with raw source lines, row IDs, section locators, and the source hash. extract_file70_primary.py reproduces that extraction. Those are preparation coverage counts, not independent evidence counts or completed C-cycle tests.

Most useful new compression: the five-node scale map

The source's outer 14|140|14 theme can be tested more strongly than by comparing outer widths. The complete five-boundary Creation refinement and five-node Terah refinement have identical normalized offsets:

For all three, the candidate expression is

The consecutive gaps are u×(6,1,6,1). Thus the source Terah (60+10)|(60+10) refinement is exactly the tenfold Creation (6+1)|(6+1) refinement. The explicit role-position map is y=2226+10(x−4114), or the corresponding normalized map with restored center4244. This adds internal-incidence information to the already visible outer70+70 versus7+7 comparison.

Source: File70 §§2.3,3.2,4.2; A.2 FML001–010 and A.3 C_STD01–08/C_CAN01–08/C_TRANS01–05. This formula is a proposed derived compression, not quoted source notation. The role positions are structural positions, not an identification of Creation events with Terah's biography. The five Terah nodes deliberately mix Terah +60 birth, base Terah birth, firstborn threshold, Abram birth, and Sarah birth.

The coarse source family has five triples B(c,h)=(c+h,c,c−h): standard Creation (4114,7), restored comparison (4244,7), Terah (2226,70), Jacob bridal (1922,7), Joseph economy (1878,7). Do not force the Jacob and Joseph refinements to match the five-point Creation/Terah refinement: their source segment inventories differ.

The literary count premise remains separate: Terah is sixth of eleven formula occurrences, hence5+1+5. In the ten-major-section register Terah remains sixth but is not an exact five-and-five count center. Neither register dates a heading.

Jacob: a whole reflection family, with source weights retained

File70 §5.3 supplies the chronological path

2006 → 1936 → 1929 → 1859, with gaps70,7,70.

The death-centered field is

1936 → 1929 → 1859 → 1789 → 1782, with gaps7,70,70,7.

The natural candidate is the local reflection R_D(x)=2D−x, D=1859: it pairs1936 with1782 and1929 with1789, preserving the center. This is a full finite family whose two outward arms both have the ordered70+7. The later inner node1789 is traditional Judah comparison data, classified secondary by A.5 JB008–009. The later outer node1782 is the separately controlled Levi death. Therefore the theorem's dependency basis includes a primary endpoint relation and a weaker inner-role identification; it is not five equally weighted event matches.

The source's textual comparison consists of70 Egyptian mourning days and7 Atad mourning days. The journey between them is unnumbered. Preserve them as two numbered ritual stations, not77 uninterrupted elapsed days. The year/day correspondence is the source's structural proposal, not a physical unit identity.

This family intersects already established work at1936 (regular Jacob age70 versus cumulative whole-year Jacob-death/Levi-birth) and at the483/490 Exodus carrier. Reconstruct the new reflection and source-role map; do not count the old483→490 arithmetic as a fresh discovery.

Source: §5.3; A.5 JB001–JB016; §§0.2,0.5 for node roles. The source labels the full77 arms primary and Judah's internal articulation secondary.

Secondary thirty/forty family: optional bounded diagnostic

File70 §5.4 supplies 1959→1929→1899→1859→1819, gaps30,30,40,40. With Haran H1929, Jacob death D1859, and schematic month a30/embalming b40, the common seam requires

The outer interval is automatically 2(a+b)=140; this supplies an exact family-level explanation for the secondary doubling. The30 is a declared schematic month and, on the death side, the residual70−40. A29-day substitution yields1900 instead of1899 and discloses the selection cost. This is useful as a negative-control transfer, not as a new primer or a promoted historical1899 event. Sarah's2029 death adds70 before1959, making210. The170 versus17 Machpelah/Egypt comparison is source-secondary and is not needed for the main reconstruction.

The mixed-resolution bridal form 7 years | 7 days || 7 days | 7 years also has unequal source weights: the first bridal week is explicit, while the second corresponding week is structural inference (§5.2). Keep this distinct from the chronological7+7 year-service triple.

Joseph13+7+7 and local Noah ingress

Freeze birth1915 and ages17,30,37,44. They generate the complete source coordinate sequence 1898,1885,1878,1871, not isolated targets. Entry1876 lies two completed famine years after1878. The source decomposition is:

Creation's (13,1) and Joseph's (13,14) preserve the first component and replace the terminal component. Their outer widths14 and27 do not have a uniform whole-path scale relationship. This is a potentially useful comparison with the earlier partial-expansion principle, provided the replacement14 remains an explicit source input rather than a new universal Key.

Source: §§5.5–5.6; A.6 P001–011. Creation Year/Day13/14 interpretations remain typological assignments (§3.4); Joseph's13 follows the source textual age difference. Equal component values do not give equal historical evidential status.

The permitted Noah-side extension is local: G1 Noah death variants [2296,2236,2166,2106], G2 [2298,2238,2168,2108], each with gaps60,70,60. Appending Joseph1898 to G2 adds210, producing the complete400 path60+70+60+210. The G1 Shem death companion [2146,2086,2016,1956] preserves the same three internal gaps. These are source-defined variant rows, not successive deaths. No Gear motion is applied to Terah, Creation, or later patriarchs. The400 Noah–Joseph structure and400 Affliction are different event pairs (§§4.3–4.5; A.7).

Cumulative macro: the new information beyond3430

The prior cycle already established the Shem/Flood→Jacob/Conquest600×3430 square. Use it as an inherited edge, not a new test. File70 adds three whole-family structures around it.

The4900 body and its three cuts

Freeze Shem head5436 and restoration536. Then the candidate index rule

has source cuts k49 at regular Jacob2006, k50 at cumulative whole-year Jacob/Levi1936, k69 at captivity606, and terminal k70 at restoration536. The source partitions are49|21,50|20,69|1. They are alternate cuts of one4900 body, not three independent bodies.

The two Jacob cuts differ by70 and create the source1400 square:

Horizontal gaps1400 and vertical gaps70 follow together. The lower1400 leg has Exodus cut1446, yielding490+910 or7|13 in70-units. The1400 can also be read8×175,14×100,35×40, but these are refactorizations of one duration.

Source: §9.1A; A.13.3 CM019–027; A.13.4 CM028–030; E.5A.

One77-unit macro spine

The four-node source path is 14011→5436→1936→536, with gaps8575,3500,1400. In175 units these are49|20|8, total77. Consequently13475=77×175=275×49. Matched upper/lower Creation–Shem pairs (14011,5436) and (14004,5429) preserve8575 by shared−7 translation.

This is a source-conditioned indexed path whose unit175 connects to the prior Abraham/Covenant family. Its explicit source coefficients49,20,8 and fixed restoration536 remain premises. Do not silently make the phase-exact Jacob1936.5 a whole-year1936: replacing just that junction changes3500/1400 to3499.5/1400.5 while preserving the outer total. That is a useful diagnostic of role/phase sensitivity.

Source: §§1.4,5.8,9.1A; A.13.1 CM001–010; E.5A.

First-to-last vector and corporate Jacob boundary

The complete source triples (14011,14004,13997) and (1936,1929,1922) differ component-wise by12075. This gives a new full vector context for the already tested scalar12075=25×483=69×175 and P output12250=70×175. The upper Creation input13997 is a source lower companion, not a newly inferred event.

The source cumulative Jacob2083→1936→1446 has147+490=637, or3|10=13 Jubilees. Its whole-year1936 belongs to cumulative Jacob-death/Levi-birth, described corporately as Jacob's household boundary. This does not identify Levi with Joseph or date all sons' births to1936. The secondary21 and35 links to Joseph1915/1898 only compare coordinates and do not prove the corporate interpretation.

Source: §5.8; A.13.5 CM035–049; A.5 JB012–015. Keep phase/display inputs explicit for the483/486.5/490 ladder; no fixed-endpoint repair is needed or authorized.

Natural next bounded families

After the already assigned §6 calendar-half work, the strongest non-redundant candidates are:

1. Reconstruct all three five-node Creation/Terah refinements under R(c,u), then all five coarse bilateral triples, preserving source roles and comparing the extra internal constraints.
2. Reconstruct Jacob's entire death-centered reflection field, explicitly separating Levi's controlled endpoint from Judah's traditional inner role and the textual day/year interpretation.
3. Reconstruct Joseph's complete age/chronology path and the (13,1)→(13,14) component replacement; test why uniform whole-span scaling fails.
4. Add the complete permitted Noah G1/G2/Shem variant rows and appended400 path as local source-conditioned transport, without upstream Gear extension.
5. Reconstruct the4900 three-cut family and1400 square from the same index rule; derive dependency count rather than treating each partition as a new witness.
6. Attach the four-node49|20|8 Abrahamic-unit spine and the first-to-last three-vector to the existing source-object network, testing whole-year versus exact-phase junctions and retaining imported source placements.
7. Only if useful for explanation, test the secondary30/40 seam with its explicit29-day failure. It should remain lower priority than the primary families.

All are proposed preparation routes. Existing3430/989/clutch results, old arithmetic manifests, and source historical pressure tests need not be rerun. No canonical file has changed. Primers,1486, second decimal inversion, and upstream Gear transport remain deferred; SKL and Terah cumulative-center appendices have not been promoted.