# Start here: the chronological families

Expanded September 28 edition: the C1431 explanation now includes the supplied MT/LXX/SP spine comparison. The same segmented reversal generates MT convergence and definite LXX/SP head separations; the accepted SP Fall construction connects with MT Creation intervals and LXX comparisons.

- [Main explanation —18-page PDF](490d_Chronological_Families_Explanation_C1431_Print.pdf)
- [Main explanation —Markdown](490d_Chronological_Families_Explanation_C1431.md)
- [Technical companion —9-page PDF](490d_Technical_Companion_C1431_Print.pdf)
- [Complete supplied LXX/SP study](490d_LXX_Reversed_Spines_and_Accepted_SP_Solution_20260928.md)
- [Integration and verification notes](490d_Spine_Integration_Notes_20260928.md)
- [Family map](Chronological_Families_Map.png)
- [C1431 four-part grammar overview](490d_Four_Part_Grammar_Overview_C1431.md)
- [Reading guide](490d_Reading_Guide_C1431.md)

The original C1431 research archive remains the frozen baseline. Its JSON grammar and claim index retain that scope; the new chapter and technical §4A document the extension. The inverse of the inverse remains deferred.