s733.py

from research import *
s=begin(733,'Derive the full mode-bridge recurrence','What row quantity generates the change in cumulative-minus-regular displacement between adjacent named boundaries?',{'definition':'G_i=C_i−R_i','regular_edge':'R_i−R_(i+1)=b_eff_i','cumulative_edge':'C_i−C_(i+1)=L_i','local_MT_example':{'regular':[2166,2066,2006],'cumulative':[2435,2260,2080],'lifespans':[175,180],'effective_begetting':[100,60]}},['File18 MT regular/cumulative rows; File61 root vector; Research Strategy §5B'])
R=[2166,2066,2006]; C=[2435,2260,2080]; G=[c-r for c,r in zip(C,R)]; differences=[G[i]-G[i+1] for i in range(2)]
finish(s,{'mode_bridge':G,'bridge_increments':differences,'row_remainders':[175-100,180-60],'general_rule':'G_i−G_(i+1)=L_i−b_eff_i'},'The mode bridge has a local generator: lifespan minus the effective regular edge. Telescoping these row contributions reconstructs the whole bridge once the terminal displacement is supplied. Declared binding corrections belong in b_eff rather than being hidden in a global conversion.','Apply this recurrence to every shared MT boundary, retaining source roles and terminal frame.',{'local_increments':differences==[75,120],'projection':[175-100,180-60]==differences,'telescoping':G[0]-G[-1]==sum(differences)})