s1222.py

from research import *
s=begin(1222,'Write the source-change to Rounded-path synthesis','What has the full-row test established beyond endpoint agreement?',{},['C1213–C1221','C1189'])
body="""# How source changes pass into Rounded chronology

The row grammar survives rounding in a precise form. Changes divisible by five—the century, half-century, forty and sixty adjustments—translate whole nearest-five cells. Their Rounded amplitudes remain unchanged.

Two common-row MT–LXX changes lie off that grid. Lamech’s lifespan difference−24 becomes−20, while the two early27 increments become25. Their rounding changes cancel: +4−2−2=0. Thus both exact and Rounded Cumulative head differences equal430, despite different interior comparison boundaries. The hidden field shifts by−4 at Noah, Shem and Arphaxad, then−2 at Shelah.

Retaining the rounding residual explains all cases. If x=y+ρ with y rounded and −2≤ρ≤2, an exact shift d changes y by the rounded value ofρ+d and leaves the remaining residual. This rule matches all105 measurements in the35 ordinary MT–SP and MT–LXX row comparisons. The native Cainan row remains an insertion, and the three inclusive SP cap rows retain their separate count treatment.

The same rule composes coherently through successive changes. Omitting residuals works universally only for shifts divisible by five. Thus a common operation can connect exact and Rounded families without pretending that rounding preserves every detail.

The larger lesson is constructive: keep the source-labelled rows, change their measures using the declared operations, retain the rounding carries, and then accumulate. Agreement at a head is one consequence of the complete field. The next test traces these source operations into the Strategy’s SP equal-gain rectangle.
"""
a=artifact('deliverables/Source_Changes_to_Rounded_Paths.md',body)
finish(s,{'synthesis':a},'The full-row test explains both stable totals and shifted internal boundaries through located residuals. It supplies the mechanism needed to carry source families into Rounded representations.','Bind the source-appointed nodes and wrappers of the SP rectangle before substituting cap reductions.',{'whole_field':'interior' in body,'scope':'inclusive SP' in body,'next_strategy':'equal-gain rectangle' in body})