from research import *
s=begin(1335,"Draft the Regular kernel bridge","Where do its 1250/650 gaps and 405-wide variant field come from?",{},["C1253–C1264","C1323"])
t=json.loads("\"## The Regular kernel has two generators\\n\\nThe first generator is the **located sequence of row changes**. In the matched Cainan-OFF comparison, the complete MT/LXX Regular difference from Adam through Abraham is\\n\\n\\\\[\\n1250,\\\\ 1150,\\\\ 1050,\\\\ 950,\\\\ 850,\\\\ 750,\\\\ 750,\\\\ 650,\\\\ 650,\\\\ 650,\\\\ 650,\\\\ 650,\\\\ 550,\\\\ 450,\\\\ 350,\\\\ 250,\\\\ 150,\\\\ 50,\\\\ 0,\\\\ 0.\\n\\\\]\\n\\nThe steps record source changes at particular names. Six pre-Flood century changes account for the 600 difference between the Creation level 1250 and Noah level 650. Native Cainan adds 130 from Arphaxad upstream, retaining the native 1380/780 levels separately.\\n\\nThe second generator is the **finite field of source variants**. Let the Terah difference be \\\\(T=60\\\\), Cainan’s Regular interval \\\\(C=130\\\\), and the separately sourced Sojourn choice \\\\(S=215\\\\). Their eight combinations give:\\n\\n| Choice | Offset |\\n|---|---:|\\n| Base | 0 |\\n| T | 60 |\\n| C | 130 |\\n| T+C | 190 |\\n| S | 215 |\\n| T+S | 275 |\\n| C+S | 345 |\\n| T+C+S | 405 |\\n\\nThe consecutive gaps are \\\\(60|70|60|25|60|70|60\\\\). The 70 and 25 are differences between combinations; they are not additional switches.\\n\\nThese structures meet in the Strategy’s fivefold formulas:\\n\\n\\\\[\\n1250=5(C+2T),\\\\qquad650=5C.\\n\\\\]\\n\\nThe row mechanism gives \\\\(12.5u\\\\) and \\\\(6.5u\\\\), where the observed century is \\\\(u=100\\\\). Requiring the fivefold form yields \\\\(C=1.3u\\\\) and \\\\(T=.6u\\\\). Thus the coefficient five expresses a calibration between two source mechanisms. It does not itself generate the patriarchal ages.\\n\\nSP supplies a further located comparison. Its post-Flood birth additions total 650; its pre-Flood shortening is \\\\(100+120+130=350\\\\) in the completed-year comparison, leaving 300. The Lamech contribution retains its nominal 129 plus the one-year boundary completion, counted once. These locations explain more than the identity \\\\(950\\\\pm300=1250,650\\\\): the latter is a useful description of the resulting pair, while the row model explains its construction.\\n\\nSource basis: File07 finite states; File18 source rows; C1253–C1264.\\n\"")
a=artifact("draft/03_regular_kernel.md",t)
finish(s,{'artifact':a,'words':len(t.split())},"The Regular chapter separates the row staircase from the finite variant field and identifies the exact source calibration linking them.","Draft the SP birth-to-lifespan mechanism.",{'nonempty':len(t)>100,'offset_span':60+130+215==405})