s1334.py

from research import *
s=begin(1334,"Explain whole-field accumulation","How do local changes account for interior nodes as well as heads?",{},["C1182–C1189","C1323"])
t=json.loads("\"Once the row measure and terminal are fixed, ordered addition generates the entire field. If \\\\(w_j\\\\) are the selected intervals downstream of a boundary and \\\\(a\\\\) is the terminal,\\n\\n\\\\[\\nX_i=a+\\\\sum_{j\\\\ge i}w_j.\\n\\\\]\\n\\nThe difference between adjacent boundaries recovers the intervening interval. Consequently, a complete field records where changes occur; its head total records only their sum.\\n\\nThe current model reconstructs the changes in all nineteen shared MT/LXX genealogical rows. Five amplitudes summarize their located changes: the repeated century \\\\(u=100\\\\), Lamech’s lifespan change \\\\(-24\\\\), the Arphaxad/Shelah lifespan addition \\\\(27\\\\), Eber’s lifespan addition \\\\(40\\\\), and Nahor’s lifespan addition \\\\(60\\\\). The relation \\\\(40+60=100\\\\) reduces this description to four amplitudes if retained as a further source condition. The named rows on which each change acts remain necessary.\\n\\nOn the matched Cainan-OFF comparison, the Regular head difference is 1250 and the lifespan difference is 430. Native LXX Cainan contributes another 130 and 460, making 1380 and 890. The two measurements therefore change differently even though they share the same inserted person.\\n\\nThe century is a useful summary of paired source rows, not an extra independent input after those rows are given. This model explains the changes across a complete selected family. It does not derive every source age from the amplitudes or prove that the particular changes occurred in this historical order.\\n\\nSource basis: C1182–C1189; complete source-row packet and five-amplitude model.\\n\"")
a=artifact("draft/02b_whole_fields.md",t)
finish(s,{'artifact':a,'words':len(t.split())},"Whole-field accumulation connects local source changes to every interior boundary and distinguishes matched from native comparisons.","Explain the two generators of the Regular kernel.",{'nonempty':len(t)>100,'native_totals':1250+130==1380 and 430+460==890})