Separates the full event budget from its viable-lane and residual idle-response contributions. Theorem — Viable-Lane Index Plus Idle-Response Index v0.1 Status: EXACT DERIVED / CIRCULARITY FIREWALL Physical promotion: 0 For two ordered admissible source/response states, write q±=ω±+h± q^\pm=\omega^\pm+h^\pm using the idle-mask decomposition. Because θ=1−q, \theta=1-q, the Hamming event budget is μΘ=wH(θ+)−wH(θ−)=wH(q−)−wH(q+). \mu_\Theta = w_H(\theta^+)-w_H(\theta^-) = w_H(q^-)-w_H(q^+). The exact viable-lane continuation index is μω=|ω−|−|ω+|=indFω. \mu_\omega = |\omega^-|-|\omega^+| = \operatorname{ind}F_\omega. Therefore μΘ=μω+|h−|−|h+|. \boxed{ \mu_\Theta = \mu_\omega + |h^-|-|h^+|. } Define the residual idle-response index νh=|h−|−|h+|. \boxed{ \nu_h=|h^-|-|h^+|. } Then μΘ=indFω+νh. \boxed{ \mu_\Theta=\operatorname{ind}F_\omega+\nu_h. } This identity was exhaustively checked over all 1252=15,625=56 125^2=15{,}625=5^6 admissible ordered source/response pairs. Saturated-prior corollary If the previous completed event satisfies the POC-1 saturation condition, h−=0, h^-=0, then μΘ=indFω−|h+|. \boxed{ \mu_\Theta = \operatorname{ind}F_\omega-|h^+|. } Consequently, on this domain, μΘ=indFω \mu_\Theta=\operatorname{ind}F_\omega holds iff h+=0. h^+=0. Thus identifying the viable-lane index with the full Θ\Theta Hamming budget already selects the no-idle-open response on the new state. It cannot be used as an independent proof of POC-1. This is an append-only circularity firewall: the exact viable-lane index remains valid, but its promotion to the full constitutive event budget requires a separately sourced idle-response law or receipt.