Preparation: a complete Covenant–Jacob carrier lift

This is preparation for the root agent, not an executed numbered step. The supplied local files were read, the C831 checkpoint/synthesis inspected, and the C482–C831 journal titles, findings, and relevant results compared. Sources remain unchanged. The packet covenant_inputs.json freezes four source hashes, seven bounded excerpts, nine exact Markdown tables, 103 literal code blocks, named inputs, and explicitly derived diagnostics.

Best new family

Use File63 §§7.7–7.9 as one complete, typed family. The best new test is the whole map from the source endpoint pairs to the six published twelvefold macro heads. The source's twelvefold multiplier is already stated, so it is not fitted to these heads. File63 §7.2–7.3 supplies the paired source endpoints for the cumulative branch.

For source head C, source target R, and admitted multiplier m=12, source-span expansion anchored at R gives

M = R + 12(C−R) = 12C − 11R.

All six source-appointed macro heads follow from this one rule:

The new explanatory result is the complete endpoint-response field

ΔM = 12ΔC − 11ΔR.

It accounts for four different published displacements without another operator:

The 770 is especially useful: the body increases by 12×70=840 while its held target moves forward70, yielding net770=11×70. A rule that multiplies every date by12 would fail both this change and the unchanged3/30 paired shifts. The map is an anchored span transformation with typed endpoints, not a global chronology conversion.

The coefficients sum to1, explaining whole-pair translation covariance. This connects the new family to the existing anchored-operation grammar. It is also an extrapolating affine endpoint functional, whereas the older weighted Creation bridge (4C+R)/5 is an interpolating one. Their shared translation property does not make their roles or coefficients interchangeable.

The full ordered carrier chain

The source declares 11960→12000→12005→12075 with changes40|5|70=115. The corresponding endpoint pairs are (14011,2051), (14006,2006), (14011,2006), (14011,1936). The span changes are consequently:

1. Both endpoints move: −5 − (−45) = +40.
2. Only the head moves: +5 − 0 = +5.
3. Only the target moves: 0 − (−70) = +70.

Thus the ordered scalar chain is generated by endpoint changes with different supports. It is not one continuous historical sequence running through the four values. At twelvefold scale its complete change vector is480|60|840, totaling1380=12×115. The mixed regular/cumulative source hinge2166→2051→1936 gives115|115; it supplies the interpretation of115 but retains the proposed2051 offering-age premise.

The scalar step11960→12000 agrees with J(11960). That old scalar fact is not new. Here it is joined to the full source-pair response, showing why moving the head by−5 and target by−45 can realize the same +40 total while retaining different interior meanings.

New scalar terminal branch, with old calculations identified

File63 §7.8.2 supplies the full branch

• input144900 = 900×161;
• P output147000 = 1000×147;
• E output157500 = 900×175.

The gain vector is2100|12600 and the output gap10500, or1|6|5 in2100 units. The interpreted lifespans are source-supplied; the arithmetic follows from the Keys. The P macro head148936, held at cumulative1936, has ordered terminal decomposition999×147 |147, with the source cumulative Jacob biography2083→1936 as its final unit. The already known regular Jacob2006→536 path uses Jacob's147 as its first of ten units. This is a source-controlled change of component position, not a new claim that those two biographies have identical nodes.

A useful distinction to test: this retained147 subdivision is appointed after the outer macro span is expanded. It is not the image of the same147 interval under a uniform anchored P map. Uniform P about1936 sends the internal2083 boundary to2085+3/23, making its terminal interval149+3/23. Keeping2083 as the source boundary instead gives147. The two readings share the outer147000 body but retain different internal roles. The source's terminal-thousandth construction is coherent as a new outer head with the historical biography retained; it should not be called transport of that complete biography by P. Its corresponding unexpanded preimage length would be144.9.

Do not count these old results anew: C574–575 already evaluated143520 within the full897n lattice, including J144000, P145600 and diagnostic E156000. C576 already gave the12000/12075 scalar carrier ladder. C578 already gave the whole Creation-week translations. C550 already treated the regular Jacob1470 lifespan inclusion. The new work is the whole typed lift, endpoint response, and ordered source network.

File63's linked30-year squares can test the coordinate chart: source pairs14041/14011 and2081/2051 differ30; macro heads145601/145571 differ30; external1BC→AD30 is30 civil years. The two completed145600 arms are therefore consequences of equal143520 bodies and equal2080 terminal spans. The first cross-axis calculation must use BC+AD−1, never the Rounded BC+AD−2 convention. These macro endpoints remain source-declared providential comparisons.

Ranked bounded questions for root reassessment

1. Can the six published macro heads be reconstructed from the frozen typed pair table by M=12C−11R, with the multiplier supplied before evaluating them?
2. Does its complete difference field recover60,770,−3,−30 from the four distinct endpoint-support changes?
3. Which distinctions are lost if only the expanded span is retained? In particular, identical144900 bodies have different1936/1933 placements, and identical143520 bodies have different2081/2051 placements.
4. Can the complete40|5|70 source chain and480|60|840 lift be reconstructed through the endpoint incidence map rather than fitted scalar jumps?
5. Does the source115|115 hinge explain the total carrier115 while preserving its two mixed modes and proposed offering role?
6. How does the144900 branch's newly retained147 terminal biography differ from uniform P transport of the original internal147 interval? The outer147000 agreement is inherited; the internal-boundary distinction supplies the useful new test.
7. Do the two30-year civil squares close with the same source roles and spans? This transfers the existing chart-sensitive reflection/translation grammar to an unused full source object.
8. What is still unexplained after reconstruction? The selected12 multiplier, source endpoint roles, Covenant/offering dates, and theological reading remain premises. Their consequences are not independent evidence of their historical origin.

Secondary complete families, if the primary stalls

File61 §10, six-node exact Amram field. Source nodes1670,1666.5,1663,1656,1652.5,1649 have the complete interval vector3.5|3.5|7|3.5|3.5. Reflection x↦3319−x permutes the six nodes in three pairs about1659.5. This is a whole unused symmetric source object; C552's generic root family did not execute this mixed regular Plenty/Famine and cumulative Amram comparison. The form is1|1|2|1|1 in half-week units. Its reflection pairs roles; it does not claim that those roles are historically interchangeable. No Gear transport or1486 node is needed.

File60 §7, complete phase-resolved Mirror triad. Lower Nisan source labels1567,1728,1866 give three radii3013,3174,3312 against the specified reflected phase pair and Exodus. Both t/n component checks reproduce each radius. Ordered gaps161|138 and total299 are retained. The congruence condition is substantive: each source x≡3 (mod23), while1446≡20, so1446+x is divisible by23. Reflection alone does not cause that divisibility. This was prepared in the old File60 memo but does not appear as an executed C532–831 step. Do not re-open the separate ambiguous cumulative-Abraham Mirror phase branch in Appendix C.

File61 §16, complete four tenfold lifespan rails. The packet has1936→606=10×133;1909→539=10×137;1906→536=10×137;2006→536=10×147. The two1370 rows are a paired3-year translation. The span differences1470−1370=100 and1370−1330=40 are tenfold lifespan differences; the606→536=70 terminal difference is independently supplied. The1936/1909/1906 are whole-year display states. A global historical-date scale factor10 is not established by these four separate anchored span comparisons. This is lower priority because C550 and C659 cover nearby1470/1400 objects.

Status and premise guards

• No canonical edit, second digit inversion, statistical tally, remote SKL extension, primer calculation,1486 calculation, or new Gear scope was performed.
• Source File63 assigns twelvefold unfolding to Israel/tribes; only144000 is the stated Revelation total.144060 and144900 are derived companions, not textual variants.
• Covenant2081 and offering2051 at Isaac age15 are author-designated/proposed. Genesis22 does not state that age.
• The six macro heads are generated coordinates. They must not be promoted to primary chronological anchors.
• Cumulative1936 is the whole-year upper display, distinct from exact1936.5. The companion1933 remains lower Moses/Nisan.
• File59's579600 census derivation and File57's Issachar ledger are imported claims here, not re-audited independent witnesses.
• The source1BC/AD30 comparison does not replace6BC nativity or the preferredAD33 Passion.
• Equal arithmetic consequences do not by themselves establish scribal causation, providential meaning, or statistical rarity.