Selective expansion and successive Keys
A Key can act on a selected part while the rest remains fixed. This produces a different operation from applying a Key to the whole span. The distinction links two source families. In the 483 carrier, the final 80.5 is one sixth of the total: expanding that part by E produces 402.5+87.5=490, the same total as applying P to all 483. In the 12558 path, the final 483 is one twenty-sixth: expanding that part by E produces 12075+525=12600, the same total as applying J to the whole.
The general rule is simple. If fraction f receives factor k, the effective total factor is 1+f(k−1). This explains the selected fractions 1/6 and 1/26 without treating their source boundaries as interchangeable. The computed intermediate fraction 3/13 connects P to J, but calculation alone does not appoint a corresponding chronological cut.
Nested selection multiplies selection fractions: one sixth followed by three thirteenths selects one twenty-sixth. Successive whole-span conversion instead multiplies the Keys themselves; P followed by J gives 7000/6877, not J.
Together with calendar calibration, the two inherited completion relations form four equations with three independent constraints. Solving them backward recovers the Keys, but supplies an equivalent description of established relationships, not independent evidence for their historical origin.
Sources: File63 Scale-Neutral 480/483/490 Carrier §1.3; §§7.3–7.4; §9.7; 490d_Unification_Research_Strategy_v0_2_20260906.md §3.3; §5E.
Research record: C984, C985, C986, C987, C989, C990, C991, C992.