Calendar Keys preserve a declared measure
The Keys explain how another kind of agreement crosses families. Write
Their corresponding schematic year lengths give
Consequently different year counts can carry the same modeled day-volume. The completed 14720 duration gives 16000 under E, 44800/3 under P, and 192000/13 under J. Multiplying those counts by 336, 360 and 364 respectively gives 5376000 in every case. File52c appoints the E completion here; the P/J values illustrate the inherited calibration conditionally. Equal modeled volume does not itself appoint a new chronological route or a historical calendar. [Strategy §3.3; C1062]
Placement is specified by a held anchor: . This acts on a distance from the anchor, not a naked BC date. Source units, moving components and anchor together define the chronological comparison.
For the appointed E route, holding 6 BC converts 14720 to 16000 and locates the expanded endpoint at 16006 BC. The intermediate positions need not become integers. Every proper prefix of the four transformed paths has a nonzero residue modulo 23. For example, the shared first 4100-year prefix becomes 102500/23; the whole 14720 becomes 16000. Uniform multiplication remains additive over exact rational durations, so componentwise conversion and whole-span conversion agree at the endpoint. What fails is the further requirement that every retained internal position lie on an integer-year grid. The rational path is a conditional display of the same uniform conversion, not a universal map between all original chronological date labels. [File52c §3.6; C1059–C1062]
This distinction gives 23 and 529 their structural roles. The first controls integral Priestly conversion. Its square 529 permits the duration ladder
For the 12026 backbone and Exodus 1446, the supplied interval is 10580=20×529, yielding 10580→11500→12500 under two successive Priestly expansions. The coefficient 20 is obtained from that span; the later values follow from the same factor. Endpoint placement additionally requires the declared anchor and counting convention. [File52c §§6.1–6.2]