Inverse spine Keys: a connected circuit and its exact limits
Research support for C1433–C1482. Prepared September 29, 2026. This document assigns no cycle numbers and does not amend a source file.
Recommended synthesis: the proposed SP–LXX return closes through the Covenant
The supplied September 28 comparative study already observes that the Prophetic expansion of the LXX regular three-stage head reaches 13306 BC and that this is 1700 years from the SP regular two-stage head 11606 BC. It calls this a possible reciprocal relationship. C1432 supplies another independently named connection that closes the comparison into a two-route circuit.
All coordinates below are BC. Write K_q(x) = q + (25/23)(x−q) and P_q(x) = q + (70/69)(x−q).
| Route | Operation | Result |
|---|---|---|
| Direct | K_1866(13136), with the MT Minimum Covenant held | 14116 |
| Through the SP regular spine, first step | P_1406(13136), with the Conquest held | 13306 |
| Second step | Subtract the original SP regular Flood–Conquest span, 3106−1406 = 1700 | 11606 |
| Third step | Add the common two-stage to three-stage displacement, 2700 | 14306 |
| Fourth step | Change SP regular to cumulative inverse head, 14116−14306 = −190 | 14116 |
Thus the same SP cumulative three-stage head is reached by both routes:
The head displacement is transparently accounted for:
The direct edge is the already established C1432 result; the 1700 return and common 2700 shift are already in the supplied study. The new contribution is their connected synthesis with the SP regular/cumulative change. Every intermediate value is already supplied by a named operation or independently constructed spine. No fitted pivot or newly invented ratio is needed.
The circuit is reversible at its stated nodes: undo the SP mode and stage translations, add 1700, and apply the reciprocal Prophetic factor 69/70 with 1406 held. The reciprocal Priestly factor 23/25 with 1866 held supplies the direct return. These are inverses of named affine operations, not a second decimal reversal. The relations do not establish a universal mapping of all SP and LXX dates.
The two routes use the same underlying source register, so this is not an additional statistically independent witness. The 190 is obtained from the two separately reconstructed SP heads; it is not chosen to repair a missed endpoint.
A diagnostic exact miss clarifies the target states
The supplied LXX study also records 13306−4106 = 9200 and its Priestly expansion to 10000. Completing the held-endpoint calculation gives
This is 10 years later than the accepted SP cumulative head 14116. The SP head's independently recorded 10000-year interval is to actual MT Year-6 4116, while this LXX calculation holds rounded MT Creation 4106. The two 10000-year intervals are a complete-pair translation:
That translation accounts exactly for the difference without pretending the original composite operation reaches 14116. Changing only the held anchor from 4106 to 4116 would instead produce 324418/23, not 14116. The input 13306 also must shift by 10 to transport the whole affine construction. This is a concise example of why endpoint identity, construction identity, and equal duration must be distinguished.
The Covenant map is specific to the three-stage heads
Applying the same Covenant-held Priestly map directly to the LXX two-stage regular head gives
whereas the corresponding SP cumulative two-stage head is 11416. The exact shortfall is
The discrepancy is the ordinary affine translation relation: with the pivot fixed, a 2700-year source shift produces a 2700×25/23 output shift. To carry the complete three-stage Key relation down to the two-stage coordinates, the pivot would also have to move by −2700. That is a different pivot, not the source Covenant at 1866.
Likewise, retaining the Covenant pivot while replacing LXX regular 13136 with cumulative 13636 gives 337168/23. This does not reach MT 14726 (shortfall 1530/23), SP regular 14306 (overshoot 8130/23), or SP cumulative 14116 (overshoot 12500/23). The regular/cumulative interchange is not automatically transported by the successful head-level Key relation.
Two compact structural corollaries
A translated MT upper edge appears within the SP comparison
The MT cumulative two-stage upper edge is
The SP regular two-stage inverse head to the upper rounded SP Creation member has the same length:
Both endpoints move by −420: 12026−11606 = 4836−4416 = 420. This joins a complete MT inverse segment to an SP inverse-to-source comparison. It is a useful corollary of the existing 9890 comparison after removing the common 2700 stage shift, not an independent new reversal result.
The mode changes differ by one shared Key-compatible module
At either stage, the regular-to-cumulative head changes are MT 0, LXX +500 and SP −190. Therefore
This 690 becomes 750 under 25/23 or 700 under 70/69. The modular content is precise: the LXX and SP mode changes are both congruent to 17 modulo 69, hence modulo 23. No named-head landing follows from those two expansions by itself. Keep this as a secondary description of the mode interaction, rather than promote a factorization to another closed circuit.
Sources and scope
- The supplied Reversed Creation–Flood Spines: LXX Comparison and the Accepted SP Solution, especially §§2–3, 6.2, and 7.2–7.7, supplies all six spine constructions, 13306, the 1700 return, and 10000/9890 comparisons.
- C1432 supplies the Covenant-held 13136→14116 relation and expressly limits it to the named heads.
- File60 §§2.6, 3 and 5 supplies the MT Minimum Covenant 1866, the 161→175 Priestly law and the distinct status of the three Keys.
- File22's state register and §7.1 control MT actual Year-6 4116 versus its rounded comparison 4106. File51a §3 and Appendix A.1 explicitly retain their 10-year difference.
- File18 §3.1 expressly retires the 4415→4414 repair in its preferred chain. A tempting additional 299→300 Creation comparison was therefore not opened from that superseded source state.
No general Enochian 300/299 head-to-head conversion was established here. The source report's existing two-stage LXX 10436 BC to AD 30/65 Enochian comparison remains valid in its civil cross-axis state; it does not transfer to the three-stage LXX head automatically.
Suggested reader treatment: add the two-route Covenant/SP circuit as the main contribution; keep the exact 10-year composition miss and mode-transport limitation in the technical companion. The 7190 translation may be one explanatory sentence. The 690 modular relation can remain in this supporting research record.