Supplement A §§8–11 and13: bounded source-family preparation

Prepared for the C632–C731 cycle. No numbered research step or new SKL extension has been executed. Exact source tables, named roles, formulas, locators and exclusions are in suppA_macro_inputs.json.

Source: /workspace/scratch/1b40da62dcbd/project_sources/14-file_70-supplement-a-key-of-23-fine-resolution-720-30-rail-2-.md. The inherited body is the August28 Final. Section13 is a September6 verification-complete, centrally registered working amendment; it was not separately author-Finalized or full-file pressure tested. This preparation does not change that status.

Scope decision for the existing SKL protection

The prior research checkpoint and integrated draft preserve the existing SKL treatment and prohibit new Gear transport, source promotion, primer work and deferred decimal-inversion work. A read-only reconstruction of a fixed, already supplied family can preserve those limits: it copies the source inputs, reconstructs its declared outputs, and leaves its prior status unchanged. It must not become a new SKL variant, a new source-chain execution, or an expansion of the project's permitted Gear domain.

The Supplement itself explicitly supports that bounded method. At §0.8, line339, its frozen-parent guard says:

The Supplement may cite and recompute admitted data but may not alter a parent equation, source state, anchor, node class, operator, guard, claim ceiling, or dependency boundary.

Its File21 scope guard at line351 likewise permits coordination of the existing Short/Long states while barring new variants and source-node promotion. These source-file statements govern interpretation of its own data; they do not override the current session's scope. In particular, the Supplement's local “Primary theorem” classification for §8 must not promote the project's protected SKL appendix into a new principal historical proof.

The safest later selection is the already printed two-by-two Key matrix, or the two MT common-parent routes, with source labels retained. For §13, a fixed twelve-node permutation test can read the twelve literal phase nodes as input, rather than using its local Gear notation to authorize transports elsewhere. The36-node macro extension, remote SKL Creation/Flood propagation,360:1 amplification and missing Long-member repairs remain summary-only in this preparation. No permission override is inferred. No additional user confirmation is demanded by this memo; root should keep any chosen test inside the existing authorized reconstruction scope.

A. Directional paired-Key family

Controller: §§8.1–8.6, lines1251–1488. Let E=25/23=75/69 and P=70/69. The source input span is u=690, giving Eu=750 and Pu=700. The difference50 is exactly the declared variant offset; the gains60 and10 sum to70 and differ by50.

Each row uses the same positive-BC anchored expression D(k,a,x)=a+k(x−a). The two convergences are conditional on both the50 source offsets and the directional assignment of E/P. Arbitrarily swapping a ratio breaks the family. This supplies a concrete whole-family test with four rows, not selected successes from an unrestricted search.

The inputs are not all raw SKL anchors. Short2936/2906 and Long2886/2856 are source anchors;3626/2216 are generated Short-ladder endpoints, with2216 separately co-registered as a File68 schematic label;3576 is a declared comparison node;2166 is Abraham's supplied birth. The direct Key outputs are2876 and2916. The former also carries Enoch's source-controlled schematic close, while the latter is a generated pure720 landing.

The complete source rows are:

Their source totals differ6530=6480+50 and their anchors compensate by50, leaving Flood separation6480. The corresponding source-only pure720 calculations use25 and34 copies of720, yielding2916 on the+30 Flood rails and2886 on the physical rails. These are comparisons of already supplied source states; neither total corrects the other.

The source's complete ordered anchor field is

with gaps10|20|10|20|10|20. Its first six nodes span the70-year Enoch generation;2856 extends the field to90. Three nested pairs around2911 have half-widths35,25,5. The principal quartet2946|2916|2906|2876 has gaps30|10|30. The direct paired-Key outputs are 2916 and 2876. The quartet also retains the Short physical source anchor 2906 and the generated 2946 companion; the declared 30 rail relates the pairs 2946/2916 and 2906/2876.

Subtracting1470 from that complete quartet gives1476|1446|1436|1406, retaining Joshua birth, Exodus, generated comparison rail and Conquest as different roles. This translation preserves topology and gaps; it does not identify the SKL/Enochic source nodes with biblical events.

Optional source summaries in the JSON retain §8.7's paired32400 Projective-Pillar durations, §8.8's670+50=720 and672+50=722 comparisons, and §8.9's generated24500 companion. Remote amplifications remain unexecuted. Source24510 is not replaced by24500; Pillars remain Projective Boundaries.

B. One common operator-parent, two source states and anchors

Controller: §§9.1–9.7, lines1631–1894; dual-route ownership remains with File22.

The source-state gap190=60+130 equals the difference between Key gains232−42. The completed radii differ40, matching the40-year difference between anchors. Exact anchored contractions23/25 and69/70 recover the two source states. This is ordinary rational-map reversibility; it is unrelated to the deferred second decimal inversion. The common operator-parent label does not establish a transmitted Creation date or an earlier historical textual layer.

The full carrier ladder4346BC→2876BC→1406BC→AD65 has three1470 arms. Its first arm refines as 4346→2946→2876=1400+70 and contains the complete 70-year quartet from 2946 to 2876; the separate 2856 anchor lies beyond that arm. A uniform five-year forward civil translation gives4341BC→2871BC→1401BC→AD70, preserving all three arms. The roles remain different:2871 is a Long-source-pair center;2876 is an Enoch close;AD65 is the carrier terminus;AD70 is the five-year Temple companion.

The JSON also records two bounded subsidiary source families:

• §9.8's raw4304→2648→1406 partition1656+1242 becomes4346→2666→1406 with1680+1260 under P. The2648/2666 nodes are generated seams and cannot inherit other BJ/genealogical identities sharing those labels.
• §9.9's matched LXX/MT endpoint and Year6 pairs preserve1380. Its outer registers repeat30|1410|30. The E route from actual LXX5494 about Exodus1446 generates5846; the proposed5846→5816 leveling remains an appendix-led hypothesis. Neither label is a transmitted LXX Creation date; no upstream Gear operation is needed or opened.

C. Two69-coefficient arms at the4346 hinge

Controller: §§10.1–10.5, lines2062–2234; File53 owns the inherited cumulative family.

The native arms are

Thus the complete civil span43470 partitions2|7 in4830 units. Two uses of the same69 coefficient have different units, endpoint roles and held points.

For the cumulative-facing side, hold4346 and the lower4346→1406 segment2940 fixed:

This is a particularly useful retained-partition test after the calendar-half work: one component changes and the lower component stays fixed. The resulting12740 path14146→1406 is separate from the inherited14036→1296 execution with the same total. The generated heads retain their source-declared provisional/appendix-led status.

Cainan supplies one additional explicitly sourced row:14466−4346=10120; E sends10120 to11000 and produces15346. The input radius difference460 becomes output difference500, so this is the existing affine pair-difference law instantiated at the source's cumulative insertion boundary. It does not replace regular Cainan130 with460.

D. Whole and refined Danielic paths

Controller: §§11.1–11.6, lines2235–2382.

The coarse whole path is4836BC→4346BC→6BC→AD30→AD65 with spans490|4340|35|35, totaling4900. The refined path inserts2946,2876 and1406 into the middle body:

or7|20|1|21|20|1/2|1/2 in70-unit counts. Its common4346 seam joins the two regular-MT routes, Enochic carrier ladder and cumulative/Pillar coefficient field. The partitions are dependent resolutions of one labelled path, not extra independent witnesses.

At one-tenth scale this instantiates the declared49+434+3.5+3.5 pattern-template. It does not establish a literal434-year historical lock. Retain source Christological roles:AD25/35 comparison nodes,AD30 exact schematic midpoint/possible Passion state, parent-preferredAD33n Passion,AD65 carrier close andAD70 Temple companion.

E. Fixed Sothic phase set and affine involution

Controller: §13, lines2420–2727. This is a different phase chart from the rounded mirror used by File52c. Set x=0 at January1 AD1, and use

The exact source input is six pairs, twelve nodes:

The source compresses this fixed set as X={−2921+15r+2g+p/4}, with r,p=±1 and g=−1,0,1. For a later test, the literal twelve inputs above are sufficient; the g notation records source-supplied local positions and grants no new Gear transport. The exact center is the January instant x=−2921, distinct from its bracketing2922t/2921n pair, and the width is34.5.

The source-declared whole-set relation is

It exchanges all twelve nodes by six transpositions. This is an affine reflection of a fixed phase field, not decimal inversion. Complete source pair mappings and the corresponding-phase3×3 sum matrix are in the JSON.

The general source identity M(T_L(X))=X+(5842−L) reduces the overlap question to translations2,0,−2,−4 of the same fixed set. Conditional uniqueness follows by comparing centers: c+5842=−c gives c=−2921 once the template is fixed. The period alone does not specify the shape or the historical placement.

Section13.7 supplies a compact anchored placement packet rather than an unrestricted fit: e=1446, Q=4×365=1460, F=4×360=1440, rail30. Then

The30|20|30 gaps, two1380 Moses/Joshua comparisons and50 rectangle are dependent consequences of this packet. The Short center is1460+(1476+1446)/2=2921. Calendar-body counts360/365 remain distinct, and this selection does not independently establish Exodus/Joshua historicity.

Two constraints should accompany any later Sothic test:

1. Section13.6's36-node nested macro field and opposed±720 identity are existing source summaries only here. They neither license same-direction shifts nor extend unchanged four-cycle closure to remote SKL Creation/Flood or360:1 chains.
2. Section13.9's Long six-source/two-target matrix genuinely lacks4383=3×1461. Keep that missing value. The Long twelve-node center is−2871 and its own self-Mirror translation5742, so it cannot silently substitute for the Short5842 field. No extra adjacent date or phase is opened to repair the failure.

Suggested future selection, after primary calendar-half work

First choose the four-row directional Key matrix and its fixed source-role quartet; then the dual4346 MT routes and their retained-path ladder. The cumulative matrix gives a strong next test of partial expansion versus equal total spans. The fixed twelve-node Sothic family can then test affine reflection, source-induced overlap counts and conditional uniqueness, while remaining a bounded source reconstruction. The remote/macroscale material and conjectural LXX leveling can remain summarized without execution.

This selection would test entire supplied objects and connect their mechanisms to the existing grammar without reopening the protected source corpus or claiming that local arithmetic permission overrides session constraints.